id	sid	tid	token	lemma	pos
ap-1829	1	1	acta	acta	PROPN
ap-1829	1	2	polytechnica	polytechnica	PROPN
ap-1829	1	3	acta	acta	PROPN
ap-1829	1	4	polytechnica	polytechnica	PROPN
ap-1829	1	5	53(4):347–358	53(4):347–358	PROPN
ap-1829	1	6	,	,	PUNCT
ap-1829	1	7	2013	2013	NUM
ap-1829	1	8	©	©	PROPN
ap-1829	1	9	czech	czech	PROPN
ap-1829	1	10	technical	technical	PROPN
ap-1829	1	11	university	university	PROPN
ap-1829	1	12	in	in	ADP
ap-1829	1	13	prague	prague	PROPN
ap-1829	1	14	,	,	PUNCT
ap-1829	1	15	2013	2013	NUM
ap-1829	1	16	available	available	ADJ
ap-1829	1	17	online	online	ADV
ap-1829	1	18	at	at	ADP
ap-1829	1	19	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	ADJ
ap-1829	1	20	algorithms	algorithm	NOUN
ap-1829	1	21	for	for	ADP
ap-1829	1	22	solving	solve	VERB
ap-1829	1	23	darcian	darcian	NOUN
ap-1829	1	24	flow	flow	NOUN
ap-1829	1	25	in	in	ADP
ap-1829	1	26	structured	structured	ADJ
ap-1829	1	27	porous	porous	ADJ
ap-1829	1	28	media	medium	NOUN
ap-1829	1	29	michal	michal	PROPN
ap-1829	1	30	kuráža,∗	kuráža,∗	PROPN
ap-1829	1	31	,	,	PUNCT
ap-1829	1	32	petr	petr	PROPN
ap-1829	1	33	mayerb	mayerb	VERB
ap-1829	1	34	a	a	DET
ap-1829	1	35	czech	czech	PROPN
ap-1829	1	36	university	university	NOUN
ap-1829	1	37	of	of	ADP
ap-1829	1	38	life	life	PROPN
ap-1829	1	39	sciences	sciences	PROPN
ap-1829	1	40	prague	prague	PROPN
ap-1829	1	41	,	,	PUNCT
ap-1829	1	42	faculty	faculty	NOUN
ap-1829	1	43	of	of	ADP
ap-1829	1	44	environmental	environmental	ADJ
ap-1829	1	45	sciences	sciences	PROPN
ap-1829	1	46	,	,	PUNCT
ap-1829	1	47	department	department	NOUN
ap-1829	1	48	of	of	ADP
ap-1829	1	49	water	water	NOUN
ap-1829	1	50	resources	resource	NOUN
ap-1829	1	51	and	and	CCONJ
ap-1829	1	52	environmental	environmental	ADJ
ap-1829	1	53	modeling	modeling	NOUN
ap-1829	1	54	b	b	PROPN
ap-1829	1	55	czech	czech	PROPN
ap-1829	1	56	technical	technical	PROPN
ap-1829	1	57	university	university	PROPN
ap-1829	1	58	in	in	ADP
ap-1829	1	59	prague	prague	PROPN
ap-1829	1	60	,	,	PUNCT
ap-1829	1	61	faculty	faculty	NOUN
ap-1829	1	62	of	of	ADP
ap-1829	1	63	civil	civil	ADJ
ap-1829	1	64	engineering	engineering	NOUN
ap-1829	1	65	,	,	PUNCT
ap-1829	1	66	department	department	NOUN
ap-1829	1	67	of	of	ADP
ap-1829	1	68	mathematics	mathematics	PROPN
ap-1829	1	69	∗	∗	NOUN
ap-1829	1	70	corresponding	correspond	VERB
ap-1829	1	71	author	author	NOUN
ap-1829	1	72	:	:	PUNCT
ap-1829	1	73	kuraz@fzp.czu.cz	kuraz@fzp.czu.cz	NOUN
ap-1829	1	74	abstract	abstract	NOUN
ap-1829	1	75	.	.	PUNCT
ap-1829	2	1	this	this	DET
ap-1829	2	2	paper	paper	NOUN
ap-1829	2	3	presents	present	VERB
ap-1829	2	4	several	several	ADJ
ap-1829	2	5	algorithms	algorithm	NOUN
ap-1829	2	6	that	that	PRON
ap-1829	2	7	were	be	AUX
ap-1829	2	8	implemented	implement	VERB
ap-1829	2	9	in	in	ADP
ap-1829	2	10	drutes	drute	NOUN
ap-1829	2	11	[	[	X
ap-1829	2	12	1	1	NUM
ap-1829	2	13	]	]	PUNCT
ap-1829	2	14	,	,	PUNCT
ap-1829	2	15	a	a	DET
ap-1829	2	16	new	new	ADJ
ap-1829	2	17	open	open	ADJ
ap-1829	2	18	source	source	NOUN
ap-1829	2	19	project	project	NOUN
ap-1829	2	20	.	.	PUNCT
ap-1829	3	1	drutes	drute	NOUN
ap-1829	3	2	is	be	AUX
ap-1829	3	3	a	a	DET
ap-1829	3	4	finite	finite	ADJ
ap-1829	3	5	element	element	NOUN
ap-1829	3	6	solver	solver	VERB
ap-1829	3	7	for	for	ADP
ap-1829	3	8	coupled	couple	VERB
ap-1829	3	9	nonlinear	nonlinear	ADJ
ap-1829	3	10	parabolic	parabolic	NOUN
ap-1829	3	11	problems	problem	NOUN
ap-1829	3	12	,	,	PUNCT
ap-1829	3	13	namely	namely	ADV
ap-1829	3	14	the	the	DET
ap-1829	3	15	richards	richard	NOUN
ap-1829	3	16	equation	equation	NOUN
ap-1829	3	17	with	with	ADP
ap-1829	3	18	the	the	DET
ap-1829	3	19	dual	dual	ADJ
ap-1829	3	20	porosity	porosity	NOUN
ap-1829	3	21	approach	approach	NOUN
ap-1829	3	22	(	(	PUNCT
ap-1829	3	23	modeling	model	VERB
ap-1829	3	24	the	the	DET
ap-1829	3	25	flow	flow	NOUN
ap-1829	3	26	of	of	ADP
ap-1829	3	27	liquids	liquid	NOUN
ap-1829	3	28	in	in	ADP
ap-1829	3	29	a	a	DET
ap-1829	3	30	porous	porous	ADJ
ap-1829	3	31	medium	medium	NOUN
ap-1829	3	32	)	)	PUNCT
ap-1829	3	33	.	.	PUNCT
ap-1829	4	1	mass	mass	ADJ
ap-1829	4	2	balance	balance	NOUN
ap-1829	4	3	consistency	consistency	NOUN
ap-1829	4	4	is	be	AUX
ap-1829	4	5	crucial	crucial	ADJ
ap-1829	4	6	in	in	ADP
ap-1829	4	7	any	any	DET
ap-1829	4	8	hydrological	hydrological	ADJ
ap-1829	4	9	balance	balance	NOUN
ap-1829	4	10	and	and	CCONJ
ap-1829	4	11	contaminant	contaminant	NOUN
ap-1829	4	12	transportation	transportation	NOUN
ap-1829	4	13	evaluations	evaluation	NOUN
ap-1829	4	14	.	.	PUNCT
ap-1829	5	1	an	an	DET
ap-1829	5	2	incorrect	incorrect	ADJ
ap-1829	5	3	approximation	approximation	NOUN
ap-1829	5	4	of	of	ADP
ap-1829	5	5	the	the	DET
ap-1829	5	6	mass	mass	ADJ
ap-1829	5	7	term	term	NOUN
ap-1829	5	8	greatly	greatly	ADV
ap-1829	5	9	depreciates	depreciate	VERB
ap-1829	5	10	the	the	DET
ap-1829	5	11	results	result	NOUN
ap-1829	5	12	that	that	PRON
ap-1829	5	13	are	be	AUX
ap-1829	5	14	obtained	obtain	VERB
ap-1829	5	15	.	.	PUNCT
ap-1829	6	1	an	an	DET
ap-1829	6	2	algorithm	algorithm	NOUN
ap-1829	6	3	for	for	ADP
ap-1829	6	4	automatic	automatic	ADJ
ap-1829	6	5	time	time	NOUN
ap-1829	6	6	step	step	NOUN
ap-1829	6	7	selection	selection	NOUN
ap-1829	6	8	is	be	AUX
ap-1829	6	9	presented	present	VERB
ap-1829	6	10	,	,	PUNCT
ap-1829	6	11	as	as	SCONJ
ap-1829	6	12	the	the	DET
ap-1829	6	13	proper	proper	ADJ
ap-1829	6	14	time	time	NOUN
ap-1829	6	15	step	step	NOUN
ap-1829	6	16	length	length	NOUN
ap-1829	6	17	is	be	AUX
ap-1829	6	18	crucial	crucial	ADJ
ap-1829	6	19	for	for	ADP
ap-1829	6	20	achieving	achieve	VERB
ap-1829	6	21	accuracy	accuracy	NOUN
ap-1829	6	22	of	of	ADP
ap-1829	6	23	the	the	DET
ap-1829	6	24	euler	euler	NOUN
ap-1829	6	25	time	time	NOUN
ap-1829	6	26	integration	integration	NOUN
ap-1829	6	27	method	method	NOUN
ap-1829	6	28	.	.	PUNCT
ap-1829	7	1	various	various	ADJ
ap-1829	7	2	problems	problem	NOUN
ap-1829	7	3	arise	arise	VERB
ap-1829	7	4	with	with	ADP
ap-1829	7	5	poor	poor	ADJ
ap-1829	7	6	conditioning	conditioning	NOUN
ap-1829	7	7	of	of	ADP
ap-1829	7	8	the	the	DET
ap-1829	7	9	richards	richard	NOUN
ap-1829	7	10	equation	equation	NOUN
ap-1829	7	11	:	:	PUNCT
ap-1829	7	12	the	the	DET
ap-1829	7	13	computational	computational	ADJ
ap-1829	7	14	domain	domain	NOUN
ap-1829	7	15	is	be	AUX
ap-1829	7	16	clustered	cluster	VERB
ap-1829	7	17	into	into	ADP
ap-1829	7	18	subregions	subregion	NOUN
ap-1829	7	19	separated	separate	VERB
ap-1829	7	20	by	by	ADP
ap-1829	7	21	a	a	DET
ap-1829	7	22	wetting	wet	VERB
ap-1829	7	23	front	front	NOUN
ap-1829	7	24	,	,	PUNCT
ap-1829	7	25	and	and	CCONJ
ap-1829	7	26	the	the	DET
ap-1829	7	27	nonlinear	nonlinear	ADJ
ap-1829	7	28	constitutive	constitutive	ADJ
ap-1829	7	29	functions	function	NOUN
ap-1829	7	30	cover	cover	VERB
ap-1829	7	31	a	a	DET
ap-1829	7	32	high	high	ADJ
ap-1829	7	33	range	range	NOUN
ap-1829	7	34	of	of	ADP
ap-1829	7	35	values	value	NOUN
ap-1829	7	36	,	,	PUNCT
ap-1829	7	37	while	while	SCONJ
ap-1829	7	38	a	a	DET
ap-1829	7	39	very	very	ADV
ap-1829	7	40	simple	simple	ADJ
ap-1829	7	41	diagonal	diagonal	ADJ
ap-1829	7	42	preconditioning	precondition	VERB
ap-1829	7	43	method	method	NOUN
ap-1829	7	44	greatly	greatly	ADV
ap-1829	7	45	improves	improve	VERB
ap-1829	7	46	the	the	DET
ap-1829	7	47	matrix	matrix	NOUN
ap-1829	7	48	properties	property	NOUN
ap-1829	7	49	.	.	PUNCT
ap-1829	8	1	the	the	DET
ap-1829	8	2	results	result	NOUN
ap-1829	8	3	are	be	AUX
ap-1829	8	4	presented	present	VERB
ap-1829	8	5	here	here	ADV
ap-1829	8	6	,	,	PUNCT
ap-1829	8	7	together	together	ADV
ap-1829	8	8	with	with	ADP
ap-1829	8	9	an	an	DET
ap-1829	8	10	analysis	analysis	NOUN
ap-1829	8	11	.	.	PUNCT
ap-1829	9	1	keywords	keyword	NOUN
ap-1829	9	2	:	:	PUNCT
ap-1829	9	3	richards	richard	NOUN
ap-1829	9	4	equation	equation	NOUN
ap-1829	9	5	,	,	PUNCT
ap-1829	9	6	time	time	NOUN
ap-1829	9	7	step	step	NOUN
ap-1829	9	8	adaptivity	adaptivity	NOUN
ap-1829	9	9	,	,	PUNCT
ap-1829	9	10	distinct	distinct	ADJ
ap-1829	9	11	unsaturated	unsaturated	ADJ
ap-1829	9	12	hydraulic	hydraulic	ADJ
ap-1829	9	13	properties	property	NOUN
ap-1829	9	14	,	,	PUNCT
ap-1829	9	15	problem	problem	NOUN
ap-1829	9	16	conditioning	conditioning	NOUN
ap-1829	9	17	,	,	PUNCT
ap-1829	9	18	diagonal	diagonal	ADJ
ap-1829	9	19	preconditioner	preconditioner	NOUN
ap-1829	9	20	.	.	PUNCT
ap-1829	10	1	1	1	X
ap-1829	10	2	.	.	X
ap-1829	10	3	introduction	introduction	NOUN
ap-1829	10	4	it	it	PRON
ap-1829	10	5	is	be	AUX
ap-1829	10	6	important	important	ADJ
ap-1829	10	7	to	to	PART
ap-1829	10	8	be	be	AUX
ap-1829	10	9	able	able	ADJ
ap-1829	10	10	to	to	PART
ap-1829	10	11	predict	predict	VERB
ap-1829	10	12	fluid	fluid	ADJ
ap-1829	10	13	movement	movement	NOUN
ap-1829	10	14	in	in	ADP
ap-1829	10	15	an	an	DET
ap-1829	10	16	unsaturated	unsaturate	VERB
ap-1829	10	17	/	/	SYM
ap-1829	10	18	saturated	saturate	VERB
ap-1829	10	19	zone	zone	NOUN
ap-1829	10	20	in	in	ADP
ap-1829	10	21	many	many	ADJ
ap-1829	10	22	fields	field	NOUN
ap-1829	10	23	,	,	PUNCT
ap-1829	10	24	ranging	range	VERB
ap-1829	10	25	from	from	ADP
ap-1829	10	26	agriculture	agriculture	NOUN
ap-1829	10	27	,	,	PUNCT
ap-1829	10	28	via	via	ADP
ap-1829	10	29	hydrology	hydrology	NOUN
ap-1829	10	30	,	,	PUNCT
ap-1829	10	31	to	to	ADP
ap-1829	10	32	technical	technical	ADJ
ap-1829	10	33	applications	application	NOUN
ap-1829	10	34	of	of	ADP
ap-1829	10	35	dangerous	dangerous	ADJ
ap-1829	10	36	waste	waste	NOUN
ap-1829	10	37	disposal	disposal	NOUN
ap-1829	10	38	in	in	ADP
ap-1829	10	39	deep	deep	ADJ
ap-1829	10	40	rock	rock	NOUN
ap-1829	10	41	formations	formation	NOUN
ap-1829	10	42	.	.	PUNCT
ap-1829	11	1	the	the	DET
ap-1829	11	2	mathematical	mathematical	ADJ
ap-1829	11	3	model	model	NOUN
ap-1829	11	4	of	of	ADP
ap-1829	11	5	unsaturated	unsaturated	ADJ
ap-1829	11	6	flow	flow	NOUN
ap-1829	11	7	was	be	AUX
ap-1829	11	8	originally	originally	ADV
ap-1829	11	9	published	publish	VERB
ap-1829	11	10	by	by	ADP
ap-1829	11	11	l.	l.	PROPN
ap-1829	11	12	a.	a.	PROPN
ap-1829	11	13	richards	richards	PROPN
ap-1829	12	1	[	[	X
ap-1829	12	2	2	2	NUM
ap-1829	12	3	]	]	PUNCT
ap-1829	12	4	.	.	PUNCT
ap-1829	13	1	the	the	DET
ap-1829	13	2	richards	richards	PROPN
ap-1829	13	3	equation	equation	NOUN
ap-1829	13	4	problem	problem	NOUN
ap-1829	13	5	has	have	AUX
ap-1829	13	6	undergone	undergo	VERB
ap-1829	13	7	various	various	ADJ
ap-1829	13	8	investigations	investigation	NOUN
ap-1829	13	9	and	and	CCONJ
ap-1829	13	10	numerical	numerical	ADJ
ap-1829	13	11	treatments	treatment	NOUN
ap-1829	13	12	.	.	PUNCT
ap-1829	14	1	its	its	PRON
ap-1829	14	2	finite	finite	ADJ
ap-1829	14	3	element	element	NOUN
ap-1829	14	4	solution	solution	NOUN
ap-1829	14	5	was	be	AUX
ap-1829	14	6	originally	originally	ADV
ap-1829	14	7	published	publish	VERB
ap-1829	14	8	by	by	ADP
ap-1829	14	9	neuman	neuman	NOUN
ap-1829	14	10	in	in	ADP
ap-1829	14	11	1970	1970	NUM
ap-1829	14	12	for	for	ADP
ap-1829	14	13	several	several	ADJ
ap-1829	14	14	engineering	engineering	NOUN
ap-1829	14	15	applications	application	NOUN
ap-1829	14	16	,	,	PUNCT
ap-1829	14	17	e.g.	e.g.	ADV
ap-1829	14	18	dam	dam	NOUN
ap-1829	14	19	seepage	seepage	NOUN
ap-1829	14	20	modeling	modeling	NOUN
ap-1829	14	21	,	,	PUNCT
ap-1829	14	22	see	see	VERB
ap-1829	14	23	[	[	X
ap-1829	14	24	3	3	NUM
ap-1829	14	25	]	]	PUNCT
ap-1829	14	26	.	.	PUNCT
ap-1829	15	1	the	the	DET
ap-1829	15	2	existence	existence	NOUN
ap-1829	15	3	and	and	CCONJ
ap-1829	15	4	the	the	DET
ap-1829	15	5	uniqueness	uniqueness	NOUN
ap-1829	15	6	of	of	ADP
ap-1829	15	7	its	its	PRON
ap-1829	15	8	solution	solution	NOUN
ap-1829	15	9	was	be	AUX
ap-1829	15	10	discovered	discover	VERB
ap-1829	15	11	10	10	NUM
ap-1829	15	12	years	year	NOUN
ap-1829	15	13	later	later	ADV
ap-1829	15	14	,	,	PUNCT
ap-1829	15	15	by	by	ADP
ap-1829	15	16	alt	alt	PROPN
ap-1829	15	17	&	&	CCONJ
ap-1829	15	18	luckhaus	luckhaus	PROPN
ap-1829	16	1	[	[	X
ap-1829	16	2	4	4	NUM
ap-1829	16	3	]	]	PUNCT
ap-1829	16	4	.	.	PUNCT
ap-1829	17	1	a	a	DET
ap-1829	17	2	fundamental	fundamental	ADJ
ap-1829	17	3	work	work	NOUN
ap-1829	17	4	analyzing	analyze	VERB
ap-1829	17	5	a	a	DET
ap-1829	17	6	mass	mass	ADJ
ap-1829	17	7	conservation	conservation	NOUN
ap-1829	17	8	numerical	numerical	ADJ
ap-1829	17	9	method	method	NOUN
ap-1829	17	10	for	for	ADP
ap-1829	17	11	the	the	DET
ap-1829	17	12	richards	richard	NOUN
ap-1829	17	13	equation	equation	NOUN
ap-1829	17	14	was	be	AUX
ap-1829	17	15	published	publish	VERB
ap-1829	17	16	in	in	ADP
ap-1829	17	17	1990	1990	NUM
ap-1829	17	18	by	by	ADP
ap-1829	17	19	celia	celia	PROPN
ap-1829	17	20	et	et	PROPN
ap-1829	17	21	al	al	PROPN
ap-1829	17	22	.	.	PUNCT
ap-1829	18	1	[	[	X
ap-1829	18	2	5].an	5].an	NUM
ap-1829	18	3	analysis	analysis	NOUN
ap-1829	18	4	of	of	ADP
ap-1829	18	5	the	the	DET
ap-1829	18	6	richards	richard	NOUN
ap-1829	18	7	equation	equation	NOUN
ap-1829	18	8	problem	problem	NOUN
ap-1829	18	9	has	have	AUX
ap-1829	18	10	been	be	AUX
ap-1829	18	11	the	the	DET
ap-1829	18	12	subject	subject	NOUN
ap-1829	18	13	of	of	ADP
ap-1829	18	14	several	several	ADJ
ap-1829	18	15	works	work	NOUN
ap-1829	18	16	by	by	ADP
ap-1829	18	17	kačur	kačur	NOUN
ap-1829	18	18	,	,	PUNCT
ap-1829	19	1	e.g.	e.g.	ADV
ap-1829	19	2	[	[	X
ap-1829	19	3	6	6	NUM
ap-1829	19	4	]	]	PUNCT
ap-1829	19	5	.	.	PUNCT
ap-1829	20	1	various	various	ADJ
ap-1829	20	2	methods	method	NOUN
ap-1829	20	3	for	for	ADP
ap-1829	20	4	numerical	numerical	ADJ
ap-1829	20	5	treatment	treatment	NOUN
ap-1829	20	6	of	of	ADP
ap-1829	20	7	the	the	DET
ap-1829	20	8	problem	problem	NOUN
ap-1829	20	9	have	have	AUX
ap-1829	20	10	recently	recently	ADV
ap-1829	20	11	been	be	AUX
ap-1829	20	12	published	publish	VERB
ap-1829	20	13	,	,	PUNCT
ap-1829	20	14	see	see	VERB
ap-1829	20	15	e.g.	e.g.	ADV
ap-1829	20	16	kees	kee	NOUN
ap-1829	20	17	et	et	PROPN
ap-1829	20	18	al	al	PROPN
ap-1829	20	19	.	.	PUNCT
ap-1829	21	1	[	[	X
ap-1829	21	2	7	7	NUM
ap-1829	21	3	]	]	PUNCT
ap-1829	21	4	,	,	PUNCT
ap-1829	21	5	šolín	šolín	PROPN
ap-1829	21	6	et	et	PROPN
ap-1829	21	7	al	al	PROPN
ap-1829	21	8	.	.	PUNCT
ap-1829	22	1	[	[	X
ap-1829	22	2	8	8	NUM
ap-1829	22	3	]	]	PUNCT
ap-1829	22	4	or	or	CCONJ
ap-1829	22	5	kuráž	kuráž	ADJ
ap-1829	22	6	et	et	PROPN
ap-1829	22	7	al	al	PROPN
ap-1829	22	8	.	.	PUNCT
ap-1829	23	1	[	[	X
ap-1829	23	2	9	9	NUM
ap-1829	23	3	,	,	PUNCT
ap-1829	23	4	10	10	NUM
ap-1829	23	5	]	]	PUNCT
ap-1829	23	6	.	.	PUNCT
ap-1829	24	1	an	an	DET
ap-1829	24	2	efficient	efficient	ADJ
ap-1829	24	3	algorithm	algorithm	NOUN
ap-1829	24	4	for	for	ADP
ap-1829	24	5	numerical	numerical	ADJ
ap-1829	24	6	solution	solution	NOUN
ap-1829	24	7	of	of	ADP
ap-1829	24	8	the	the	DET
ap-1829	24	9	richards	richard	NOUN
ap-1829	24	10	equation	equation	NOUN
ap-1829	24	11	should	should	AUX
ap-1829	24	12	handle	handle	VERB
ap-1829	24	13	temporal	temporal	ADJ
ap-1829	24	14	adaptivity	adaptivity	NOUN
ap-1829	24	15	.	.	PUNCT
ap-1829	25	1	this	this	DET
ap-1829	25	2	topic	topic	NOUN
ap-1829	25	3	has	have	AUX
ap-1829	25	4	already	already	ADV
ap-1829	25	5	been	be	AUX
ap-1829	25	6	discussed	discuss	VERB
ap-1829	25	7	by	by	ADP
ap-1829	25	8	a	a	DET
ap-1829	25	9	variety	variety	NOUN
ap-1829	25	10	of	of	ADP
ap-1829	25	11	authors	author	NOUN
ap-1829	25	12	.	.	PUNCT
ap-1829	26	1	the	the	DET
ap-1829	26	2	first	first	ADJ
ap-1829	26	3	work	work	NOUN
ap-1829	26	4	maintaining	maintain	VERB
ap-1829	26	5	the	the	DET
ap-1829	26	6	truncation	truncation	NOUN
ap-1829	26	7	error	error	NOUN
ap-1829	26	8	of	of	ADP
ap-1829	26	9	the	the	DET
ap-1829	26	10	mixed	mixed	ADJ
ap-1829	26	11	form	form	NOUN
ap-1829	26	12	of	of	ADP
ap-1829	26	13	the	the	DET
ap-1829	26	14	richards	richard	NOUN
ap-1829	26	15	equation	equation	NOUN
ap-1829	26	16	was	be	AUX
ap-1829	26	17	published	publish	VERB
ap-1829	26	18	by	by	ADP
ap-1829	26	19	kavetski	kavetski	PROPN
ap-1829	26	20	et	et	PROPN
ap-1829	26	21	al	al	PROPN
ap-1829	26	22	.	.	PUNCT
ap-1829	27	1	[	[	X
ap-1829	27	2	14	14	NUM
ap-1829	27	3	]	]	PUNCT
ap-1829	27	4	.	.	PUNCT
ap-1829	28	1	tocci	tocci	VERB
ap-1829	28	2	et	et	PROPN
ap-1829	28	3	al	al	PROPN
ap-1829	28	4	.	.	PUNCT
ap-1829	29	1	[	[	X
ap-1829	29	2	15	15	NUM
ap-1829	29	3	]	]	PUNCT
ap-1829	29	4	proved	prove	VERB
ap-1829	29	5	that	that	SCONJ
ap-1829	29	6	the	the	DET
ap-1829	29	7	h	h	NOUN
ap-1829	29	8	-	-	PUNCT
ap-1829	29	9	based	base	VERB
ap-1829	29	10	richards	richard	NOUN
ap-1829	29	11	’	'	PUNCT
ap-1829	29	12	equation	equation	NOUN
ap-1829	29	13	with	with	ADP
ap-1829	29	14	proper	proper	ADJ
ap-1829	29	15	temporal	temporal	ADJ
ap-1829	29	16	adaptivity	adaptivity	NOUN
ap-1829	29	17	can	can	AUX
ap-1829	29	18	provide	provide	VERB
ap-1829	29	19	a	a	DET
ap-1829	29	20	mass	mass	ADJ
ap-1829	29	21	conservative	conservative	ADJ
ap-1829	29	22	numerical	numerical	ADJ
ap-1829	29	23	solution	solution	NOUN
ap-1829	29	24	,	,	PUNCT
ap-1829	29	25	and	and	CCONJ
ap-1829	29	26	later	later	ADV
ap-1829	29	27	miller	miller	PROPN
ap-1829	29	28	et	et	PROPN
ap-1829	29	29	al	al	PROPN
ap-1829	29	30	.	.	PUNCT
ap-1829	30	1	[	[	X
ap-1829	30	2	16	16	NUM
ap-1829	30	3	]	]	PUNCT
ap-1829	30	4	published	publish	VERB
ap-1829	30	5	an	an	DET
ap-1829	30	6	algorithm	algorithm	NOUN
ap-1829	30	7	for	for	ADP
ap-1829	30	8	temporal	temporal	ADJ
ap-1829	30	9	adaptation	adaptation	NOUN
ap-1829	30	10	of	of	ADP
ap-1829	30	11	the	the	DET
ap-1829	30	12	step	step	NOUN
ap-1829	30	13	and	and	CCONJ
ap-1829	30	14	degree	degree	NOUN
ap-1829	30	15	of	of	ADP
ap-1829	30	16	approximation	approximation	NOUN
ap-1829	30	17	.	.	PUNCT
ap-1829	31	1	this	this	DET
ap-1829	31	2	paper	paper	NOUN
ap-1829	31	3	is	be	AUX
ap-1829	31	4	organized	organize	VERB
ap-1829	31	5	as	as	SCONJ
ap-1829	31	6	follows	follow	VERB
ap-1829	31	7	.	.	PUNCT
ap-1829	32	1	the	the	DET
ap-1829	32	2	first	first	ADJ
ap-1829	32	3	part	part	NOUN
ap-1829	32	4	discusses	discuss	VERB
ap-1829	32	5	problems	problem	NOUN
ap-1829	32	6	related	relate	VERB
ap-1829	32	7	to	to	ADP
ap-1829	32	8	inaccurate	inaccurate	ADJ
ap-1829	32	9	time	time	NOUN
ap-1829	32	10	integration	integration	NOUN
ap-1829	32	11	of	of	ADP
ap-1829	32	12	the	the	DET
ap-1829	32	13	richards	richard	NOUN
ap-1829	32	14	equation	equation	NOUN
ap-1829	32	15	.	.	PUNCT
ap-1829	33	1	a	a	DET
ap-1829	33	2	new	new	ADJ
ap-1829	33	3	and	and	CCONJ
ap-1829	33	4	efficient	efficient	ADJ
ap-1829	33	5	automated	automate	VERB
ap-1829	33	6	time	time	NOUN
ap-1829	33	7	step	step	NOUN
ap-1829	33	8	selection	selection	NOUN
ap-1829	33	9	method	method	NOUN
ap-1829	33	10	is	be	AUX
ap-1829	33	11	presented	present	VERB
ap-1829	33	12	here	here	ADV
ap-1829	33	13	,	,	PUNCT
ap-1829	33	14	and	and	CCONJ
ap-1829	33	15	its	its	PRON
ap-1829	33	16	efficiency	efficiency	NOUN
ap-1829	33	17	is	be	AUX
ap-1829	33	18	evaluated	evaluate	VERB
ap-1829	33	19	on	on	ADP
ap-1829	33	20	a	a	DET
ap-1829	33	21	simple	simple	ADJ
ap-1829	33	22	benchmark	benchmark	NOUN
ap-1829	33	23	problem	problem	NOUN
ap-1829	33	24	.	.	PUNCT
ap-1829	34	1	the	the	DET
ap-1829	34	2	second	second	ADJ
ap-1829	34	3	part	part	NOUN
ap-1829	34	4	of	of	ADP
ap-1829	34	5	the	the	DET
ap-1829	34	6	paper	paper	NOUN
ap-1829	34	7	discusses	discuss	VERB
ap-1829	34	8	poor	poor	ADJ
ap-1829	34	9	conditioning	conditioning	NOUN
ap-1829	34	10	of	of	ADP
ap-1829	34	11	the	the	DET
ap-1829	34	12	richards	richard	NOUN
ap-1829	34	13	equation	equation	NOUN
ap-1829	34	14	problem	problem	NOUN
ap-1829	34	15	.	.	PUNCT
ap-1829	35	1	a	a	DET
ap-1829	35	2	simple	simple	ADJ
ap-1829	35	3	and	and	CCONJ
ap-1829	35	4	extremely	extremely	ADV
ap-1829	35	5	efficient	efficient	ADJ
ap-1829	35	6	matrix	matrix	NOUN
ap-1829	35	7	preconditioner	preconditioner	NOUN
ap-1829	35	8	based	base	VERB
ap-1829	35	9	on	on	ADP
ap-1829	35	10	diagonal	diagonal	ADJ
ap-1829	35	11	scaling	scaling	NOUN
ap-1829	35	12	greatly	greatly	ADV
ap-1829	35	13	improves	improve	VERB
ap-1829	35	14	the	the	DET
ap-1829	35	15	conditioning	conditioning	NOUN
ap-1829	35	16	,	,	PUNCT
ap-1829	35	17	and	and	CCONJ
ap-1829	35	18	is	be	AUX
ap-1829	35	19	presented	present	VERB
ap-1829	35	20	here	here	ADV
ap-1829	35	21	.	.	PUNCT
ap-1829	36	1	diagonal	diagonal	ADJ
ap-1829	36	2	preconditioning	preconditioning	NOUN
ap-1829	36	3	,	,	PUNCT
ap-1829	36	4	or	or	CCONJ
ap-1829	36	5	more	more	ADV
ap-1829	36	6	precisely	precisely	ADV
ap-1829	36	7	jacobi	jacobi	NOUN
ap-1829	36	8	preconditioning	preconditioning	NOUN
ap-1829	36	9	,	,	PUNCT
ap-1829	36	10	is	be	AUX
ap-1829	36	11	one	one	NUM
ap-1829	36	12	of	of	ADP
ap-1829	36	13	the	the	DET
ap-1829	36	14	first	first	ADJ
ap-1829	36	15	preconditioning	precondition	VERB
ap-1829	36	16	methods	method	NOUN
ap-1829	36	17	that	that	PRON
ap-1829	36	18	ever	ever	ADV
ap-1829	36	19	appeared	appear	VERB
ap-1829	36	20	in	in	ADP
ap-1829	36	21	computational	computational	ADJ
ap-1829	36	22	history	history	NOUN
ap-1829	36	23	,	,	PUNCT
ap-1829	36	24	and	and	CCONJ
ap-1829	36	25	its	its	PRON
ap-1829	36	26	theoretical	theoretical	ADJ
ap-1829	36	27	background	background	NOUN
ap-1829	36	28	was	be	AUX
ap-1829	36	29	originally	originally	ADV
ap-1829	36	30	published	publish	VERB
ap-1829	36	31	more	more	ADJ
ap-1829	36	32	a	a	DET
ap-1829	36	33	hundred	hundred	NUM
ap-1829	36	34	years	year	NOUN
ap-1829	36	35	ago	ago	ADV
ap-1829	36	36	.	.	PUNCT
ap-1829	37	1	we	we	PRON
ap-1829	37	2	have	have	AUX
ap-1829	37	3	not	not	PART
ap-1829	37	4	succeeded	succeed	VERB
ap-1829	37	5	in	in	ADP
ap-1829	37	6	our	our	PRON
ap-1829	37	7	search	search	NOUN
ap-1829	37	8	for	for	ADP
ap-1829	37	9	the	the	DET
ap-1829	37	10	original	original	ADJ
ap-1829	37	11	reference	reference	NOUN
ap-1829	37	12	.	.	PUNCT
ap-1829	38	1	this	this	DET
ap-1829	38	2	method	method	NOUN
ap-1829	38	3	is	be	AUX
ap-1829	38	4	a	a	DET
ap-1829	38	5	very	very	ADV
ap-1829	38	6	classical	classical	ADJ
ap-1829	38	7	approach	approach	NOUN
ap-1829	38	8	,	,	PUNCT
ap-1829	38	9	and	and	CCONJ
ap-1829	38	10	it	it	PRON
ap-1829	38	11	is	be	AUX
ap-1829	38	12	even	even	ADV
ap-1829	38	13	a	a	DET
ap-1829	38	14	subject	subject	NOUN
ap-1829	38	15	of	of	ADP
ap-1829	38	16	early	early	ADJ
ap-1829	38	17	courses	course	NOUN
ap-1829	38	18	in	in	ADP
ap-1829	38	19	applied	applied	ADJ
ap-1829	38	20	mathematics	mathematic	NOUN
ap-1829	38	21	.	.	PUNCT
ap-1829	39	1	however	however	ADV
ap-1829	39	2	,	,	PUNCT
ap-1829	39	3	it	it	PRON
ap-1829	39	4	has	have	AUX
ap-1829	39	5	been	be	AUX
ap-1829	39	6	found	find	VERB
ap-1829	39	7	that	that	SCONJ
ap-1829	39	8	this	this	DET
ap-1829	39	9	standard	standard	ADJ
ap-1829	39	10	method	method	NOUN
ap-1829	39	11	is	be	AUX
ap-1829	39	12	highly	highly	ADV
ap-1829	39	13	efficient	efficient	ADJ
ap-1829	39	14	for	for	ADP
ap-1829	39	15	solving	solve	VERB
ap-1829	39	16	the	the	DET
ap-1829	39	17	systems	system	NOUN
ap-1829	39	18	of	of	ADP
ap-1829	39	19	linear	linear	ADJ
ap-1829	39	20	equations	equation	NOUN
ap-1829	39	21	that	that	PRON
ap-1829	39	22	arise	arise	VERB
ap-1829	39	23	from	from	ADP
ap-1829	39	24	numerical	numerical	ADJ
ap-1829	39	25	approximation	approximation	NOUN
ap-1829	39	26	of	of	ADP
ap-1829	39	27	the	the	DET
ap-1829	39	28	richards	richard	NOUN
ap-1829	39	29	equation	equation	NOUN
ap-1829	39	30	.	.	PUNCT
ap-1829	40	1	it	it	PRON
ap-1829	40	2	has	have	AUX
ap-1829	40	3	been	be	AUX
ap-1829	40	4	observed	observe	VERB
ap-1829	40	5	that	that	SCONJ
ap-1829	40	6	this	this	DET
ap-1829	40	7	preconditioning	precondition	VERB
ap-1829	40	8	method	method	NOUN
ap-1829	40	9	even	even	ADV
ap-1829	40	10	enables	enable	VERB
ap-1829	40	11	very	very	ADV
ap-1829	40	12	fast	fast	ADJ
ap-1829	40	13	convergence	convergence	NOUN
ap-1829	40	14	of	of	ADP
ap-1829	40	15	the	the	DET
ap-1829	40	16	conjugate	conjugate	ADJ
ap-1829	40	17	347	347	NUM
ap-1829	40	18	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-1829	40	19	michal	michal	PROPN
ap-1829	40	20	kuráž	kuráž	PROPN
ap-1829	40	21	,	,	PUNCT
ap-1829	40	22	petr	petr	PROPN
ap-1829	40	23	mayer	mayer	PROPN
ap-1829	40	24	acta	acta	PROPN
ap-1829	40	25	polytechnica	polytechnica	PROPN
ap-1829	40	26	0	0	NUM
ap-1829	40	27	0.05	0.05	NUM
ap-1829	40	28	0.1	0.1	NUM
ap-1829	40	29	0.15	0.15	NUM
ap-1829	40	30	0.2	0.2	NUM
ap-1829	40	31	0.25	0.25	NUM
ap-1829	40	32	0.3	0.3	NUM
ap-1829	40	33	0.35	0.35	NUM
ap-1829	40	34	0.4	0.4	NUM
ap-1829	40	35	0.45	0.45	NUM
ap-1829	40	36	0.5	0.5	NUM
ap-1829	40	37	-200	-200	NUM
ap-1829	40	38	-150	-150	NUM
ap-1829	40	39	-100	-100	PROPN
ap-1829	40	40	-50	-50	PUNCT
ap-1829	40	41	0	0	NUM
ap-1829	40	42	50	50	NUM
ap-1829	40	43	θ	θ	NOUN
ap-1829	40	44	[	[	PUNCT
ap-1829	40	45	-	-	PUNCT
ap-1829	40	46	]	]	X
ap-1829	40	47	capillary	capillary	ADJ
ap-1829	40	48	pressure	pressure	NOUN
ap-1829	40	49	head	head	NOUN
ap-1829	40	50	(	(	PUNCT
ap-1829	40	51	h	h	NOUN
ap-1829	40	52	)	)	PUNCT
ap-1829	41	1	[	[	X
ap-1829	41	2	cm	cm	X
ap-1829	41	3	]	]	X
ap-1829	41	4	claystone	claystone	NOUN
ap-1829	41	5	gravel	gravel	NOUN
ap-1829	41	6	concrete	concrete	ADJ
ap-1829	41	7	1e-10	1e-10	NUM
ap-1829	41	8	1e-08	1e-08	NOUN
ap-1829	41	9	1e-06	1e-06	NUM
ap-1829	41	10	0.0001	0.0001	NUM
ap-1829	41	11	0.01	0.01	NUM
ap-1829	41	12	1	1	NUM
ap-1829	41	13	100	100	NUM
ap-1829	41	14	10000	10000	NUM
ap-1829	42	1	-200	-200	NUM
ap-1829	43	1	-150	-150	NUM
ap-1829	43	2	-100	-100	PROPN
ap-1829	43	3	-50	-50	PUNCT
ap-1829	43	4	0	0	NUM
ap-1829	44	1	50	50	NUM
ap-1829	44	2	k	k	NOUN
ap-1829	44	3	(	(	PUNCT
ap-1829	44	4	h	h	NOUN
ap-1829	44	5	)	)	PUNCT
ap-1829	45	1	[	[	X
ap-1829	45	2	c	c	X
ap-1829	45	3	m	m	VERB
ap-1829	45	4	.d	.d	ADJ
ap-1829	45	5	-1	-1	PUNCT
ap-1829	45	6	]	]	PUNCT
ap-1829	45	7	capillary	capillary	ADJ
ap-1829	45	8	pressure	pressure	NOUN
ap-1829	45	9	head	head	NOUN
ap-1829	45	10	(	(	PUNCT
ap-1829	45	11	h	h	NOUN
ap-1829	45	12	)	)	PUNCT
ap-1829	46	1	[	[	X
ap-1829	46	2	cm	cm	X
ap-1829	46	3	]	]	X
ap-1829	46	4	claystone	claystone	NOUN
ap-1829	46	5	gravel	gravel	NOUN
ap-1829	46	6	concrete	concrete	ADJ
ap-1829	46	7	figure	figure	NOUN
ap-1829	46	8	1	1	NUM
ap-1829	46	9	.	.	PUNCT
ap-1829	47	1	plot	plot	NOUN
ap-1829	47	2	of	of	ADP
ap-1829	47	3	the	the	DET
ap-1829	47	4	constitutive	constitutive	ADJ
ap-1829	47	5	functions	function	NOUN
ap-1829	47	6	for	for	ADP
ap-1829	47	7	the	the	DET
ap-1829	47	8	richards	richard	NOUN
ap-1829	47	9	equation	equation	NOUN
ap-1829	47	10	(	(	PUNCT
ap-1829	47	11	1	1	NUM
ap-1829	47	12	)	)	PUNCT
ap-1829	47	13	.	.	PUNCT
ap-1829	48	1	left	leave	VERB
ap-1829	48	2	–	–	PUNCT
ap-1829	48	3	the	the	DET
ap-1829	48	4	van	van	PROPN
ap-1829	48	5	genuchten	genuchten	VERB
ap-1829	48	6	function	function	NOUN
ap-1829	48	7	–	–	PUNCT
ap-1829	48	8	retention	retention	NOUN
ap-1829	48	9	curve	curve	NOUN
ap-1829	48	10	–	–	PUNCT
ap-1829	48	11	relation	relation	NOUN
ap-1829	48	12	between	between	ADP
ap-1829	48	13	water	water	NOUN
ap-1829	48	14	content	content	NOUN
ap-1829	48	15	θ	θ	PROPN
ap-1829	48	16	and	and	CCONJ
ap-1829	48	17	the	the	DET
ap-1829	48	18	capillary	capillary	ADJ
ap-1829	48	19	pressure	pressure	NOUN
ap-1829	48	20	head	head	NOUN
ap-1829	48	21	h	h	NOUN
ap-1829	48	22	(	(	PUNCT
ap-1829	48	23	mass	mass	NOUN
ap-1829	48	24	function	function	NOUN
ap-1829	48	25	)	)	PUNCT
ap-1829	48	26	.	.	PUNCT
ap-1829	49	1	right	right	INTJ
ap-1829	49	2	–	–	PUNCT
ap-1829	49	3	the	the	DET
ap-1829	49	4	mualem	mualem	NOUN
ap-1829	49	5	function	function	VERB
ap-1829	49	6	–	–	PUNCT
ap-1829	49	7	unsaturated	unsaturate	VERB
ap-1829	49	8	hydraulic	hydraulic	ADJ
ap-1829	49	9	conductivity	conductivity	NOUN
ap-1829	49	10	)	)	PUNCT
ap-1829	49	11	gradient	gradient	NOUN
ap-1829	49	12	method	method	NOUN
ap-1829	49	13	for	for	ADP
ap-1829	49	14	normal	normal	ADJ
ap-1829	49	15	equations	equation	NOUN
ap-1829	49	16	,	,	PUNCT
ap-1829	49	17	despite	despite	SCONJ
ap-1829	49	18	powering	power	VERB
ap-1829	49	19	the	the	DET
ap-1829	49	20	condition	condition	NOUN
ap-1829	49	21	number	number	NOUN
ap-1829	49	22	.	.	PUNCT
ap-1829	50	1	several	several	ADJ
ap-1829	50	2	more	more	ADJ
ap-1829	50	3	or	or	CCONJ
ap-1829	50	4	less	less	ADV
ap-1829	50	5	recent	recent	ADJ
ap-1829	50	6	remarks	remark	NOUN
ap-1829	50	7	on	on	ADP
ap-1829	50	8	using	use	VERB
ap-1829	50	9	the	the	DET
ap-1829	50	10	diagonal	diagonal	ADJ
ap-1829	50	11	preconditioner	preconditioner	NOUN
ap-1829	50	12	for	for	ADP
ap-1829	50	13	cfd	cfd	NOUN
ap-1829	50	14	and	and	CCONJ
ap-1829	50	15	porous	porous	ADJ
ap-1829	50	16	media	medium	NOUN
ap-1829	50	17	transport	transport	NOUN
ap-1829	50	18	problems	problem	NOUN
ap-1829	50	19	can	can	AUX
ap-1829	50	20	be	be	AUX
ap-1829	50	21	found	find	VERB
ap-1829	50	22	in	in	ADP
ap-1829	50	23	[	[	X
ap-1829	50	24	20	20	NUM
ap-1829	50	25	]	]	PUNCT
ap-1829	50	26	and	and	CCONJ
ap-1829	50	27	[	[	X
ap-1829	50	28	21],but	21],but	NUM
ap-1829	50	29	we	we	PRON
ap-1829	50	30	have	have	AUX
ap-1829	50	31	not	not	PART
ap-1829	50	32	succeeded	succeed	VERB
ap-1829	50	33	in	in	ADP
ap-1829	50	34	a	a	DET
ap-1829	50	35	search	search	NOUN
ap-1829	50	36	for	for	ADP
ap-1829	50	37	a	a	DET
ap-1829	50	38	publication	publication	NOUN
ap-1829	50	39	demonstrating	demonstrate	VERB
ap-1829	50	40	the	the	DET
ap-1829	50	41	high	high	ADJ
ap-1829	50	42	efficiency	efficiency	NOUN
ap-1829	50	43	of	of	ADP
ap-1829	50	44	this	this	DET
ap-1829	50	45	algorithm	algorithm	NOUN
ap-1829	50	46	as	as	SCONJ
ap-1829	50	47	observed	observe	VERB
ap-1829	50	48	.	.	PUNCT
ap-1829	51	1	the	the	DET
ap-1829	51	2	efficiency	efficiency	NOUN
ap-1829	51	3	of	of	ADP
ap-1829	51	4	this	this	DET
ap-1829	51	5	method	method	NOUN
ap-1829	51	6	will	will	AUX
ap-1829	51	7	be	be	AUX
ap-1829	51	8	presented	present	VERB
ap-1829	51	9	on	on	ADP
ap-1829	51	10	the	the	DET
ap-1829	51	11	basis	basis	NOUN
ap-1829	51	12	of	of	ADP
ap-1829	51	13	one	one	NUM
ap-1829	51	14	theoretical	theoretical	ADJ
ap-1829	51	15	application	application	NOUN
ap-1829	51	16	and	and	CCONJ
ap-1829	51	17	one	one	NUM
ap-1829	51	18	practical	practical	ADJ
ap-1829	51	19	application	application	NOUN
ap-1829	51	20	.	.	PUNCT
ap-1829	52	1	however	however	ADV
ap-1829	52	2	,	,	PUNCT
ap-1829	52	3	during	during	ADP
ap-1829	52	4	the	the	DET
ap-1829	52	5	last	last	ADJ
ap-1829	52	6	two	two	NUM
ap-1829	52	7	years	year	NOUN
ap-1829	52	8	we	we	PRON
ap-1829	52	9	have	have	AUX
ap-1829	52	10	not	not	PART
ap-1829	52	11	discovered	discover	VERB
ap-1829	52	12	any	any	DET
ap-1829	52	13	richards	richard	NOUN
ap-1829	52	14	equation	equation	NOUN
ap-1829	52	15	problem	problem	NOUN
ap-1829	52	16	where	where	SCONJ
ap-1829	52	17	this	this	DET
ap-1829	52	18	preconditioning	precondition	VERB
ap-1829	52	19	method	method	NOUN
ap-1829	52	20	performed	perform	VERB
ap-1829	52	21	in	in	ADP
ap-1829	52	22	a	a	DET
ap-1829	52	23	significantly	significantly	ADV
ap-1829	52	24	different	different	ADJ
ap-1829	52	25	way	way	NOUN
ap-1829	52	26	than	than	SCONJ
ap-1829	52	27	as	as	SCONJ
ap-1829	52	28	presented	present	VERB
ap-1829	52	29	here	here	ADV
ap-1829	52	30	.	.	PUNCT
ap-1829	53	1	2	2	X
ap-1829	53	2	.	.	X
ap-1829	53	3	mathematical	mathematical	ADJ
ap-1829	53	4	model	model	NOUN
ap-1829	53	5	the	the	DET
ap-1829	53	6	problem	problem	NOUN
ap-1829	53	7	of	of	ADP
ap-1829	53	8	darcian	darcian	ADJ
ap-1829	53	9	flow	flow	NOUN
ap-1829	53	10	in	in	ADP
ap-1829	53	11	a	a	DET
ap-1829	53	12	structured	structured	ADJ
ap-1829	53	13	porous	porous	ADJ
ap-1829	53	14	medium	medium	NOUN
ap-1829	53	15	is	be	AUX
ap-1829	53	16	usually	usually	ADV
ap-1829	53	17	expressed	express	VERB
ap-1829	53	18	by	by	ADP
ap-1829	53	19	the	the	DET
ap-1829	53	20	dual	dual	ADJ
ap-1829	53	21	porosity	porosity	NOUN
ap-1829	53	22	conceptual	conceptual	ADJ
ap-1829	53	23	approach	approach	NOUN
ap-1829	53	24	.	.	PUNCT
ap-1829	54	1	the	the	DET
ap-1829	54	2	governing	govern	VERB
ap-1829	54	3	equations	equation	NOUN
ap-1829	54	4	for	for	ADP
ap-1829	54	5	variably	variably	ADV
ap-1829	54	6	saturated	saturate	VERB
ap-1829	54	7	darcian	darcian	NOUN
ap-1829	54	8	flow	flow	NOUN
ap-1829	54	9	and	and	CCONJ
ap-1829	54	10	contaminant	contaminant	NOUN
ap-1829	54	11	transport	transport	NOUN
ap-1829	54	12	in	in	ADP
ap-1829	54	13	the	the	DET
ap-1829	54	14	dual	dual	ADJ
ap-1829	54	15	flow	flow	NOUN
ap-1829	54	16	regime	regime	NOUN
ap-1829	54	17	were	be	AUX
ap-1829	54	18	originally	originally	ADV
ap-1829	54	19	published	publish	VERB
ap-1829	54	20	by	by	ADP
ap-1829	54	21	gerke	gerke	NOUN
ap-1829	54	22	,	,	PUNCT
ap-1829	54	23	et	et	PROPN
ap-1829	54	24	al	al	PROPN
ap-1829	54	25	.	.	PUNCT
ap-1829	55	1	[	[	X
ap-1829	55	2	11	11	NUM
ap-1829	55	3	]	]	PUNCT
ap-1829	55	4	.	.	PUNCT
ap-1829	56	1	the	the	DET
ap-1829	56	2	following	follow	VERB
ap-1829	56	3	section	section	NOUN
ap-1829	56	4	introduces	introduce	VERB
ap-1829	56	5	the	the	DET
ap-1829	56	6	strong	strong	ADJ
ap-1829	56	7	and	and	CCONJ
ap-1829	56	8	weak	weak	ADJ
ap-1829	56	9	formulation	formulation	NOUN
ap-1829	56	10	of	of	ADP
ap-1829	56	11	dual	dual	ADJ
ap-1829	56	12	porosity	porosity	NOUN
ap-1829	56	13	variably	variably	ADV
ap-1829	56	14	saturated	saturate	VERB
ap-1829	56	15	flow	flow	NOUN
ap-1829	56	16	.	.	PUNCT
ap-1829	57	1	a	a	DET
ap-1829	57	2	very	very	ADV
ap-1829	57	3	brief	brief	ADJ
ap-1829	57	4	description	description	NOUN
ap-1829	57	5	is	be	AUX
ap-1829	57	6	given	give	VERB
ap-1829	57	7	of	of	ADP
ap-1829	57	8	the	the	DET
ap-1829	57	9	constitutive	constitutive	ADJ
ap-1829	57	10	relations	relation	NOUN
ap-1829	57	11	and	and	CCONJ
ap-1829	57	12	coefficients	coefficient	NOUN
ap-1829	57	13	involved	involve	VERB
ap-1829	57	14	in	in	ADP
ap-1829	57	15	this	this	DET
ap-1829	57	16	problem	problem	NOUN
ap-1829	57	17	,	,	PUNCT
ap-1829	57	18	and	and	CCONJ
ap-1829	57	19	an	an	DET
ap-1829	57	20	interested	interested	ADJ
ap-1829	57	21	reader	reader	NOUN
ap-1829	57	22	can	can	AUX
ap-1829	57	23	find	find	VERB
ap-1829	57	24	more	more	ADJ
ap-1829	57	25	information	information	NOUN
ap-1829	57	26	in	in	ADP
ap-1829	57	27	the	the	DET
ap-1829	57	28	references	reference	NOUN
ap-1829	57	29	provided	provide	VERB
ap-1829	57	30	below	below	ADV
ap-1829	57	31	.	.	PUNCT
ap-1829	58	1	2.1	2.1	NUM
ap-1829	58	2	.	.	PUNCT
ap-1829	59	1	strong	strong	ADJ
ap-1829	59	2	and	and	CCONJ
ap-1829	59	3	weak	weak	ADJ
ap-1829	59	4	formulations	formulation	NOUN
ap-1829	59	5	the	the	DET
ap-1829	59	6	mathematical	mathematical	ADJ
ap-1829	59	7	problem	problem	NOUN
ap-1829	59	8	to	to	PART
ap-1829	59	9	be	be	AUX
ap-1829	59	10	solved	solve	VERB
ap-1829	59	11	is	be	AUX
ap-1829	59	12	the	the	DET
ap-1829	59	13	richards	richard	NOUN
ap-1829	59	14	equation	equation	NOUN
ap-1829	59	15	with	with	ADP
ap-1829	59	16	the	the	DET
ap-1829	59	17	dual	dual	ADJ
ap-1829	59	18	porosity	porosity	NOUN
ap-1829	59	19	conceptual	conceptual	ADJ
ap-1829	59	20	approach	approach	NOUN
ap-1829	59	21	.	.	PUNCT
ap-1829	60	1	let	let	VERB
ap-1829	60	2	ω	ω	PRON
ap-1829	60	3	be	be	AUX
ap-1829	60	4	a	a	DET
ap-1829	60	5	bounded	bounded	ADJ
ap-1829	60	6	domain	domain	NOUN
ap-1829	60	7	in	in	ADP
ap-1829	60	8	<	<	X
ap-1829	60	9	n	n	X
ap-1829	60	10	(	(	PUNCT
ap-1829	60	11	n	n	NOUN
ap-1829	60	12	=	=	SYM
ap-1829	60	13	1	1	NUM
ap-1829	60	14	,	,	PUNCT
ap-1829	60	15	2	2	NUM
ap-1829	60	16	)	)	PUNCT
ap-1829	60	17	,	,	PUNCT
ap-1829	60	18	with	with	ADP
ap-1829	60	19	a	a	DET
ap-1829	60	20	lipschitz	lipschitz	ADJ
ap-1829	60	21	boundary	boundary	ADJ
ap-1829	60	22	∂ω	∂ω	PROPN
ap-1829	60	23	for	for	ADP
ap-1829	60	24	n	n	NOUN
ap-1829	60	25	=	=	SYM
ap-1829	60	26	2	2	X
ap-1829	60	27	.	.	PUNCT
ap-1829	61	1	let	let	VERB
ap-1829	61	2	γdm	γdm	NOUN
ap-1829	61	3	and	and	CCONJ
ap-1829	61	4	γnm	γnm	ADJ
ap-1829	61	5	be	be	AUX
ap-1829	61	6	open	open	ADJ
ap-1829	61	7	disjoint	disjoint	NOUN
ap-1829	61	8	subsets	subset	NOUN
ap-1829	61	9	of	of	ADP
ap-1829	61	10	∂ω	∂ω	PROPN
ap-1829	61	11	(	(	PUNCT
ap-1829	61	12	not	not	PART
ap-1829	61	13	necessarily	necessarily	ADV
ap-1829	61	14	connected	connect	VERB
ap-1829	61	15	)	)	PUNCT
ap-1829	62	1	such	such	ADJ
ap-1829	62	2	that	that	PRON
ap-1829	62	3	∂ω	∂ω	ADJ
ap-1829	62	4	=	=	SYM
ap-1829	62	5	γdm∪γnm	γdm∪γnm	X
ap-1829	62	6	,	,	PUNCT
ap-1829	62	7	measn−1(∂ω\(γdm∪γnm	measn−1(∂ω\(γdm∪γnm	NOUN
ap-1829	62	8	)	)	PUNCT
ap-1829	62	9	)	)	PUNCT
ap-1829	63	1	=	=	SYM
ap-1829	63	2	0	0	NUM
ap-1829	63	3	and	and	CCONJ
ap-1829	63	4	measn−1(γdm	measn−1(γdm	PROPN
ap-1829	63	5	)	)	PUNCT
ap-1829	63	6	>	>	X
ap-1829	63	7	0	0	PUNCT
ap-1829	63	8	and	and	CCONJ
ap-1829	63	9	measn−1(γnm	measn−1(γnm	NUM
ap-1829	63	10	)	)	PUNCT
ap-1829	64	1	>	>	X
ap-1829	64	2	0	0	X
ap-1829	64	3	.	.	PUNCT
ap-1829	65	1	let	let	VERB
ap-1829	65	2	the	the	DET
ap-1829	65	3	same	same	ADJ
ap-1829	65	4	hold	hold	NOUN
ap-1829	65	5	for	for	SCONJ
ap-1829	65	6	the	the	DET
ap-1829	65	7	pair	pair	NOUN
ap-1829	65	8	γdf	γdf	X
ap-1829	65	9	,	,	PUNCT
ap-1829	65	10	γnf	γnf	ADV
ap-1829	65	11	.	.	PUNCT
ap-1829	66	1	let	let	VERB
ap-1829	66	2	n	n	PRON
ap-1829	66	3	denotes	denote	VERB
ap-1829	66	4	the	the	DET
ap-1829	66	5	outer	outer	ADJ
ap-1829	66	6	unit	unit	NOUN
ap-1829	66	7	normal	normal	ADJ
ap-1829	66	8	to	to	ADP
ap-1829	66	9	∂ω	∂ω	PROPN
ap-1829	66	10	.	.	PUNCT
ap-1829	67	1	for	for	ADP
ap-1829	67	2	positive	positive	ADJ
ap-1829	67	3	t	t	NOUN
ap-1829	67	4	let	let	VERB
ap-1829	67	5	qt	qt	VERB
ap-1829	67	6	=	=	VERB
ap-1829	67	7	ω×	ω×	PUNCT
ap-1829	68	1	[	[	X
ap-1829	68	2	0	0	NUM
ap-1829	68	3	,	,	PUNCT
ap-1829	68	4	t	t	NOUN
ap-1829	68	5	)	)	PUNCT
ap-1829	68	6	.	.	PUNCT
ap-1829	69	1	the	the	DET
ap-1829	69	2	richards	richard	NOUN
ap-1829	69	3	equation	equation	NOUN
ap-1829	69	4	in	in	ADP
ap-1829	69	5	the	the	DET
ap-1829	69	6	dual	dual	ADJ
ap-1829	69	7	regime	regime	NOUN
ap-1829	69	8	was	be	AUX
ap-1829	69	9	presumed	presume	VERB
ap-1829	69	10	by	by	ADP
ap-1829	69	11	gerke	gerke	NOUN
ap-1829	69	12	&	&	CCONJ
ap-1829	69	13	genuchten	genuchten	ADJ
ap-1829	69	14	[	[	X
ap-1829	69	15	11	11	NUM
ap-1829	69	16	]	]	PUNCT
ap-1829	69	17	as	as	ADP
ap-1829	69	18	cm(hm)∂hm	cm(hm)∂hm	ADP
ap-1829	69	19	∂t	∂t	PROPN
ap-1829	69	20	=	=	SYM
ap-1829	69	21	∇.	∇.	PROPN
ap-1829	69	22	(	(	PUNCT
ap-1829	69	23	km(hm)∇hm	km(hm)∇hm	NOUN
ap-1829	69	24	)	)	PUNCT
ap-1829	69	25	+	+	SYM
ap-1829	69	26	∂km(hm	∂km(hm	NOUN
ap-1829	69	27	)	)	PUNCT
ap-1829	69	28	∂z	∂z	PROPN
ap-1829	70	1	+	+	CCONJ
ap-1829	70	2	γw	γw	PROPN
ap-1829	70	3	1−	1−	NUM
ap-1829	70	4	ωf	ωf	ADV
ap-1829	70	5	,	,	PUNCT
ap-1829	70	6	(	(	PUNCT
ap-1829	70	7	x	x	X
ap-1829	70	8	,	,	PUNCT
ap-1829	70	9	t	t	PROPN
ap-1829	70	10	)	)	PUNCT
ap-1829	70	11	∈	∈	PROPN
ap-1829	70	12	qt	qt	NOUN
ap-1829	70	13	,	,	PUNCT
ap-1829	71	1	cf	cf	INTJ
ap-1829	71	2	(	(	PUNCT
ap-1829	71	3	hf	hf	NOUN
ap-1829	71	4	)	)	PUNCT
ap-1829	71	5	∂hf	∂hf	PROPN
ap-1829	71	6	∂t	∂t	PROPN
ap-1829	71	7	=	=	PUNCT
ap-1829	71	8	∇.	∇.	PROPN
ap-1829	71	9	(	(	PUNCT
ap-1829	71	10	kf	kf	INTJ
ap-1829	71	11	(	(	PUNCT
ap-1829	71	12	hf	hf	NOUN
ap-1829	71	13	)	)	PUNCT
ap-1829	71	14	∇hf	∇hf	PROPN
ap-1829	71	15	)	)	PUNCT
ap-1829	72	1	+	+	CCONJ
ap-1829	72	2	∂kf	∂kf	PROPN
ap-1829	72	3	(	(	PUNCT
ap-1829	72	4	hf	hf	NOUN
ap-1829	72	5	)	)	PUNCT
ap-1829	72	6	∂z	∂z	PROPN
ap-1829	73	1	−	−	NOUN
ap-1829	73	2	γw	γw	VERB
ap-1829	73	3	ωf	ωf	PRON
ap-1829	73	4	,	,	PUNCT
ap-1829	73	5	(	(	PUNCT
ap-1829	73	6	x	x	X
ap-1829	73	7	,	,	PUNCT
ap-1829	73	8	t	t	PROPN
ap-1829	73	9	)	)	PUNCT
ap-1829	73	10	∈	∈	PROPN
ap-1829	73	11	qt	qt	NOUN
ap-1829	73	12	,	,	PUNCT
ap-1829	73	13	γw	γw	PROPN
ap-1829	73	14	=	=	PUNCT
ap-1829	73	15	αw(hf	αw(hf	PROPN
ap-1829	73	16	−	−	PROPN
ap-1829	73	17	hm	hm	INTJ
ap-1829	73	18	)	)	PUNCT
ap-1829	73	19	,	,	PUNCT
ap-1829	73	20	(	(	PUNCT
ap-1829	73	21	1	1	X
ap-1829	73	22	)	)	PUNCT
ap-1829	73	23	where	where	SCONJ
ap-1829	73	24	the	the	DET
ap-1829	73	25	subscripts	subscript	NOUN
ap-1829	73	26	f	f	NOUN
ap-1829	73	27	and	and	CCONJ
ap-1829	73	28	m	m	PROPN
ap-1829	73	29	denote	denote	VERB
ap-1829	73	30	the	the	DET
ap-1829	73	31	subsystem	subsystem	NOUN
ap-1829	73	32	of	of	ADP
ap-1829	73	33	fractures	fracture	NOUN
ap-1829	73	34	(	(	PUNCT
ap-1829	73	35	macropores	macropore	NOUN
ap-1829	73	36	)	)	PUNCT
ap-1829	73	37	and	and	CCONJ
ap-1829	73	38	matrix	matrix	NOUN
ap-1829	73	39	blocks	block	NOUN
ap-1829	73	40	(	(	PUNCT
ap-1829	73	41	micropores	micropore	NOUN
ap-1829	73	42	)	)	PUNCT
ap-1829	73	43	,	,	PUNCT
ap-1829	73	44	h	h	NOUN
ap-1829	73	45	is	be	AUX
ap-1829	73	46	the	the	DET
ap-1829	73	47	capillary	capillary	ADJ
ap-1829	73	48	pressure	pressure	NOUN
ap-1829	73	49	head	head	NOUN
ap-1829	73	50	function	function	VERB
ap-1829	73	51	[	[	X
ap-1829	73	52	l	l	X
ap-1829	73	53	]	]	X
ap-1829	73	54	,	,	PUNCT
ap-1829	73	55	k(h	k(h	PROPN
ap-1829	73	56	)	)	PUNCT
ap-1829	73	57	is	be	AUX
ap-1829	73	58	the	the	DET
ap-1829	73	59	unsaturated	unsaturated	ADJ
ap-1829	73	60	hydraulic	hydraulic	ADJ
ap-1829	73	61	conductivity	conductivity	NOUN
ap-1829	74	1	[	[	X
ap-1829	74	2	lt−1	lt−1	PROPN
ap-1829	74	3	]	]	X
ap-1829	74	4	,	,	PUNCT
ap-1829	74	5	c(h	c(h	PROPN
ap-1829	74	6	)	)	PUNCT
ap-1829	74	7	is	be	AUX
ap-1829	74	8	the	the	DET
ap-1829	74	9	water	water	NOUN
ap-1829	74	10	retention	retention	NOUN
ap-1829	74	11	capacity	capacity	NOUN
ap-1829	74	12	[	[	X
ap-1829	74	13	l−1	l−1	NOUN
ap-1829	74	14	]	]	PUNCT
ap-1829	74	15	,	,	PUNCT
ap-1829	74	16	usually	usually	ADV
ap-1829	74	17	defined	define	VERB
ap-1829	74	18	as	as	ADP
ap-1829	74	19	c(h	c(h	VERB
ap-1829	74	20	)	)	PUNCT
ap-1829	74	21	=	=	PUNCT
ap-1829	74	22	θ(h)′	θ(h)′	PROPN
ap-1829	74	23	+	+	CCONJ
ap-1829	74	24	θ(h	θ(h	PROPN
ap-1829	74	25	)	)	PUNCT
ap-1829	74	26	θs	θs	PROPN
ap-1829	74	27	ss	ss	PROPN
ap-1829	74	28	,	,	PUNCT
ap-1829	74	29	where	where	SCONJ
ap-1829	74	30	θ(h	θ(h	PROPN
ap-1829	74	31	)	)	PUNCT
ap-1829	74	32	is	be	AUX
ap-1829	74	33	the	the	DET
ap-1829	74	34	water	water	NOUN
ap-1829	74	35	content	content	NOUN
ap-1829	74	36	function	function	VERB
ap-1829	74	37	[	[	X
ap-1829	74	38	–	–	PUNCT
ap-1829	74	39	]	]	PUNCT
ap-1829	74	40	,	,	PUNCT
ap-1829	74	41	ss	ss	PROPN
ap-1829	74	42	is	be	AUX
ap-1829	74	43	the	the	DET
ap-1829	74	44	specific	specific	ADJ
ap-1829	74	45	aquifer	aquifer	NOUN
ap-1829	74	46	storage	storage	NOUN
ap-1829	74	47	[	[	X
ap-1829	74	48	l−1	l−1	NOUN
ap-1829	74	49	]	]	PUNCT
ap-1829	74	50	,	,	PUNCT
ap-1829	74	51	θs	θs	PRON
ap-1829	74	52	is	be	AUX
ap-1829	74	53	the	the	DET
ap-1829	74	54	saturated	saturate	VERB
ap-1829	74	55	water	water	NOUN
ap-1829	74	56	content	content	NOUN
ap-1829	74	57	[	[	X
ap-1829	74	58	–	–	PUNCT
ap-1829	74	59	]	]	PUNCT
ap-1829	74	60	,	,	PUNCT
ap-1829	74	61	ωf	ωf	PROPN
ap-1829	74	62	denotes	denote	VERB
ap-1829	74	63	the	the	DET
ap-1829	74	64	volume	volume	NOUN
ap-1829	74	65	ratio	ratio	NOUN
ap-1829	74	66	of	of	ADP
ap-1829	74	67	the	the	DET
ap-1829	74	68	fracture	fracture	ADJ
ap-1829	74	69	pore	pore	ADJ
ap-1829	74	70	system	system	NOUN
ap-1829	74	71	related	relate	VERB
ap-1829	74	72	to	to	ADP
ap-1829	74	73	the	the	DET
ap-1829	74	74	total	total	ADJ
ap-1829	74	75	pore	pore	ADJ
ap-1829	74	76	system	system	NOUN
ap-1829	74	77	,	,	PUNCT
ap-1829	74	78	and	and	CCONJ
ap-1829	74	79	αw	αw	PRON
ap-1829	74	80	is	be	AUX
ap-1829	74	81	the	the	DET
ap-1829	74	82	first	first	ADJ
ap-1829	74	83	order	order	NOUN
ap-1829	74	84	mass	mass	NOUN
ap-1829	74	85	transfer	transfer	NOUN
ap-1829	74	86	coefficient	coefficient	NOUN
ap-1829	74	87	[	[	X
ap-1829	74	88	l−1	l−1	PROPN
ap-1829	74	89	t−1	t−1	PROPN
ap-1829	74	90	]	]	PUNCT
ap-1829	74	91	presumed	presume	VERB
ap-1829	74	92	as	as	ADP
ap-1829	74	93	αw	αw	ADP
ap-1829	74	94	=	=	NOUN
ap-1829	74	95	β	β	X
ap-1829	74	96	α2	α2	ADJ
ap-1829	74	97	dp	dp	PROPN
ap-1829	74	98	kaγw	kaγw	NOUN
ap-1829	74	99	,	,	PUNCT
ap-1829	74	100	(	(	PUNCT
ap-1829	74	101	2	2	X
ap-1829	74	102	)	)	PUNCT
ap-1829	74	103	where	where	SCONJ
ap-1829	74	104	β	β	PROPN
ap-1829	74	105	is	be	AUX
ap-1829	74	106	the	the	DET
ap-1829	74	107	dimensionless	dimensionless	NOUN
ap-1829	74	108	geometry	geometry	NOUN
ap-1829	74	109	coefficient	coefficient	NOUN
ap-1829	74	110	,	,	PUNCT
ap-1829	74	111	αdp	αdp	PROPN
ap-1829	74	112	is	be	AUX
ap-1829	74	113	the	the	DET
ap-1829	74	114	characteristic	characteristic	ADJ
ap-1829	74	115	half	half	ADJ
ap-1829	74	116	width	width	NOUN
ap-1829	75	1	[	[	X
ap-1829	75	2	l	l	X
ap-1829	75	3	]	]	X
ap-1829	75	4	of	of	ADP
ap-1829	75	5	the	the	DET
ap-1829	75	6	matrix	matrix	NOUN
ap-1829	75	7	block	block	NOUN
ap-1829	75	8	,	,	PUNCT
ap-1829	75	9	ka	ka	PROPN
ap-1829	75	10	is	be	AUX
ap-1829	75	11	the	the	DET
ap-1829	75	12	effective	effective	ADJ
ap-1829	75	13	hydraulic	hydraulic	ADJ
ap-1829	75	14	conductivity	conductivity	NOUN
ap-1829	76	1	[	[	X
ap-1829	76	2	lt−1	lt−1	NOUN
ap-1829	76	3	]	]	PUNCT
ap-1829	76	4	of	of	ADP
ap-1829	76	5	the	the	DET
ap-1829	76	6	matrix	matrix	NOUN
ap-1829	76	7	at	at	ADP
ap-1829	76	8	or	or	CCONJ
ap-1829	76	9	near	near	ADP
ap-1829	76	10	the	the	DET
ap-1829	76	11	fracture	fracture	NOUN
ap-1829	76	12	/	/	SYM
ap-1829	76	13	matrix	matrix	NOUN
ap-1829	76	14	interface	interface	NOUN
ap-1829	76	15	,	,	PUNCT
ap-1829	76	16	and	and	CCONJ
ap-1829	76	17	γw	γw	PROPN
ap-1829	76	18	is	be	AUX
ap-1829	76	19	the	the	DET
ap-1829	76	20	dimensionless	dimensionless	NOUN
ap-1829	76	21	scaling	scale	VERB
ap-1829	76	22	factor	factor	NOUN
ap-1829	76	23	.	.	PUNCT
ap-1829	77	1	the	the	DET
ap-1829	77	2	constitutive	constitutive	ADJ
ap-1829	77	3	relation	relation	NOUN
ap-1829	77	4	for	for	ADP
ap-1829	77	5	function	function	NOUN
ap-1829	77	6	θ(h	θ(h	PROPN
ap-1829	77	7	)	)	PUNCT
ap-1829	77	8	was	be	AUX
ap-1829	77	9	supplied	supply	VERB
ap-1829	77	10	by	by	ADP
ap-1829	77	11	the	the	DET
ap-1829	77	12	van	van	PROPN
ap-1829	77	13	genuchten	genuchten	ADJ
ap-1829	77	14	law	law	NOUN
ap-1829	77	15	[	[	X
ap-1829	77	16	12	12	NUM
ap-1829	77	17	]	]	PUNCT
ap-1829	77	18	,	,	PUNCT
ap-1829	77	19	and	and	CCONJ
ap-1829	77	20	for	for	ADP
ap-1829	77	21	the	the	DET
ap-1829	77	22	k(h	k(h	PROPN
ap-1829	77	23	)	)	PUNCT
ap-1829	77	24	function	function	NOUN
ap-1829	77	25	it	it	PRON
ap-1829	77	26	was	be	AUX
ap-1829	77	27	supplied	supply	VERB
ap-1829	77	28	by	by	ADP
ap-1829	77	29	the	the	DET
ap-1829	77	30	mualem	mualem	NOUN
ap-1829	77	31	law	law	NOUN
ap-1829	78	1	[	[	X
ap-1829	78	2	13	13	NUM
ap-1829	78	3	]	]	PUNCT
ap-1829	78	4	,	,	PUNCT
ap-1829	78	5	see	see	VERB
ap-1829	78	6	figure	figure	NOUN
ap-1829	78	7	1	1	NUM
ap-1829	78	8	for	for	ADP
ap-1829	78	9	a	a	DET
ap-1829	78	10	plot	plot	NOUN
ap-1829	78	11	of	of	ADP
ap-1829	78	12	these	these	DET
ap-1829	78	13	functions	function	NOUN
ap-1829	78	14	.	.	PUNCT
ap-1829	79	1	the	the	DET
ap-1829	79	2	initial	initial	ADJ
ap-1829	79	3	conditions	condition	NOUN
ap-1829	79	4	are	be	AUX
ap-1829	79	5	stated	state	VERB
ap-1829	79	6	as	as	ADP
ap-1829	79	7	hm(x	hm(x	X
ap-1829	79	8	,	,	PUNCT
ap-1829	79	9	0	0	NUM
ap-1829	79	10	)	)	PUNCT
ap-1829	80	1	=	=	SYM
ap-1829	80	2	h0	h0	NOUN
ap-1829	80	3	m(x	m(x	PROPN
ap-1829	80	4	)	)	PUNCT
ap-1829	80	5	∀x	∀x	X
ap-1829	80	6	∈	∈	PROPN
ap-1829	80	7	ω	ω	NOUN
ap-1829	80	8	,	,	PUNCT
ap-1829	80	9	hf	hf	X
ap-1829	80	10	(	(	PUNCT
ap-1829	80	11	x	x	X
ap-1829	80	12	,	,	PUNCT
ap-1829	80	13	0	0	NUM
ap-1829	80	14	)	)	PUNCT
ap-1829	81	1	=	=	SYM
ap-1829	81	2	h0	h0	NOUN
ap-1829	81	3	f	f	PROPN
ap-1829	81	4	(	(	PUNCT
ap-1829	81	5	x	x	X
ap-1829	81	6	)	)	PUNCT
ap-1829	81	7	∀x	∀x	PROPN
ap-1829	81	8	∈	∈	PROPN
ap-1829	81	9	ω	ω	NOUN
ap-1829	81	10	,	,	PUNCT
ap-1829	81	11	(	(	PUNCT
ap-1829	81	12	3	3	NUM
ap-1829	81	13	)	)	PUNCT
ap-1829	81	14	348	348	NUM
ap-1829	81	15	vol	vol	NOUN
ap-1829	81	16	.	.	PUNCT
ap-1829	82	1	53	53	NUM
ap-1829	82	2	no	no	NOUN
ap-1829	82	3	.	.	PUNCT
ap-1829	83	1	4/2013	4/2013	NOUN
ap-1829	83	2	algorithms	algorithm	NOUN
ap-1829	83	3	for	for	ADP
ap-1829	83	4	solving	solve	VERB
ap-1829	83	5	darcian	darcian	NOUN
ap-1829	83	6	flow	flow	NOUN
ap-1829	83	7	in	in	ADP
ap-1829	83	8	structured	structured	ADJ
ap-1829	83	9	porous	porous	ADJ
ap-1829	83	10	media	medium	NOUN
ap-1829	83	11	and	and	CCONJ
ap-1829	83	12	the	the	DET
ap-1829	83	13	boundary	boundary	ADJ
ap-1829	83	14	conditions	condition	NOUN
ap-1829	83	15	hm(x	hm(x	X
ap-1829	83	16	,	,	PUNCT
ap-1829	83	17	t	t	PROPN
ap-1829	83	18	)	)	PUNCT
ap-1829	83	19	=	=	SYM
ap-1829	83	20	hdm(x	hdm(x	PROPN
ap-1829	83	21	,	,	PUNCT
ap-1829	83	22	t	t	PROPN
ap-1829	83	23	)	)	PUNCT
ap-1829	83	24	,	,	PUNCT
ap-1829	83	25	(	(	PUNCT
ap-1829	83	26	x	x	X
ap-1829	83	27	,	,	PUNCT
ap-1829	83	28	t	t	PROPN
ap-1829	83	29	)	)	PUNCT
ap-1829	83	30	∈	∈	PROPN
ap-1829	84	1	γdm	γdm	PROPN
ap-1829	84	2	×	×	NOUN
ap-1829	85	1	[	[	X
ap-1829	85	2	0	0	NUM
ap-1829	85	3	,	,	PUNCT
ap-1829	85	4	t	t	NOUN
ap-1829	85	5	)	)	PUNCT
ap-1829	85	6	,	,	PUNCT
ap-1829	85	7	∂hm	∂hm	PROPN
ap-1829	85	8	∂n	∂n	PROPN
ap-1829	85	9	=	=	SYM
ap-1829	85	10	hnm(x	hnm(x	PROPN
ap-1829	85	11	,	,	PUNCT
ap-1829	85	12	t	t	PROPN
ap-1829	85	13	)	)	PUNCT
ap-1829	85	14	,	,	PUNCT
ap-1829	85	15	(	(	PUNCT
ap-1829	85	16	x	x	X
ap-1829	85	17	,	,	PUNCT
ap-1829	85	18	t	t	PROPN
ap-1829	85	19	)	)	PUNCT
ap-1829	85	20	∈	∈	PROPN
ap-1829	85	21	γnm	γnm	VERB
ap-1829	85	22	×	×	X
ap-1829	85	23	[	[	X
ap-1829	85	24	0	0	NUM
ap-1829	85	25	,	,	PUNCT
ap-1829	85	26	t	t	NOUN
ap-1829	85	27	)	)	PUNCT
ap-1829	85	28	,	,	PUNCT
ap-1829	85	29	hf	hf	INTJ
ap-1829	85	30	(	(	PUNCT
ap-1829	85	31	x	x	NOUN
ap-1829	85	32	,	,	PUNCT
ap-1829	85	33	t	t	PROPN
ap-1829	85	34	)	)	PUNCT
ap-1829	85	35	=	=	SYM
ap-1829	85	36	hdf	hdf	PROPN
ap-1829	85	37	(	(	PUNCT
ap-1829	85	38	x	x	PROPN
ap-1829	85	39	,	,	PUNCT
ap-1829	85	40	t	t	PROPN
ap-1829	85	41	)	)	PUNCT
ap-1829	85	42	,	,	PUNCT
ap-1829	85	43	(	(	PUNCT
ap-1829	85	44	x	x	X
ap-1829	85	45	,	,	PUNCT
ap-1829	85	46	t	t	PROPN
ap-1829	85	47	)	)	PUNCT
ap-1829	85	48	∈	∈	PROPN
ap-1829	86	1	γdf	γdf	X
ap-1829	86	2	×	×	NOUN
ap-1829	87	1	[	[	X
ap-1829	87	2	0	0	NUM
ap-1829	87	3	,	,	PUNCT
ap-1829	87	4	t	t	NOUN
ap-1829	87	5	)	)	PUNCT
ap-1829	87	6	,	,	PUNCT
ap-1829	87	7	∂hf	∂hf	PROPN
ap-1829	87	8	∂n	∂n	PROPN
ap-1829	87	9	=	=	PUNCT
ap-1829	87	10	hnf	hnf	NOUN
ap-1829	87	11	(	(	PUNCT
ap-1829	87	12	x	x	NOUN
ap-1829	87	13	,	,	PUNCT
ap-1829	87	14	t	t	PROPN
ap-1829	87	15	)	)	PUNCT
ap-1829	87	16	,	,	PUNCT
ap-1829	87	17	(	(	PUNCT
ap-1829	87	18	x	x	X
ap-1829	87	19	,	,	PUNCT
ap-1829	87	20	t	t	PROPN
ap-1829	87	21	)	)	PUNCT
ap-1829	87	22	∈	∈	PROPN
ap-1829	88	1	γnf	γnf	NOUN
ap-1829	88	2	×	×	NOUN
ap-1829	89	1	[	[	X
ap-1829	89	2	0	0	NUM
ap-1829	89	3	,	,	PUNCT
ap-1829	89	4	t	t	NOUN
ap-1829	89	5	)	)	PUNCT
ap-1829	89	6	.	.	PUNCT
ap-1829	90	1	(	(	PUNCT
ap-1829	90	2	4	4	X
ap-1829	90	3	)	)	PUNCT
ap-1829	90	4	we	we	PRON
ap-1829	90	5	assume	assume	VERB
ap-1829	90	6	that	that	SCONJ
ap-1829	90	7	all	all	DET
ap-1829	90	8	coefficients	coefficient	NOUN
ap-1829	90	9	are	be	AUX
ap-1829	90	10	sufficiently	sufficiently	ADV
ap-1829	90	11	smooth	smooth	ADJ
ap-1829	90	12	.	.	PUNCT
ap-1829	91	1	let	let	VERB
ap-1829	91	2	e1(ω	e1(ω	VERB
ap-1829	91	3	)	)	PUNCT
ap-1829	91	4	:	:	PUNCT
ap-1829	92	1	=	=	SYM
ap-1829	92	2	{	{	PUNCT
ap-1829	92	3	v	v	NUM
ap-1829	92	4	∈	∈	PROPN
ap-1829	92	5	c∞(ω)n	c∞(ω)n	NOUN
ap-1829	92	6	;	;	PUNCT
ap-1829	92	7	supp	supp	PROPN
ap-1829	92	8	v	v	ADP
ap-1829	92	9	∩	∩	ADJ
ap-1829	92	10	γdm	γdm	NOUN
ap-1829	92	11	=	=	NOUN
ap-1829	92	12	∅	∅	NOUN
ap-1829	92	13	}	}	PUNCT
ap-1829	92	14	,	,	PUNCT
ap-1829	92	15	e2(ω	e2(ω	ADV
ap-1829	92	16	)	)	PUNCT
ap-1829	92	17	:	:	PUNCT
ap-1829	92	18	=	=	SYM
ap-1829	92	19	{	{	PUNCT
ap-1829	92	20	v	v	NUM
ap-1829	92	21	∈	∈	PROPN
ap-1829	92	22	c∞(ω)n	c∞(ω)n	NOUN
ap-1829	92	23	;	;	PUNCT
ap-1829	92	24	supp	supp	PROPN
ap-1829	92	25	v	v	ADP
ap-1829	92	26	∩	∩	X
ap-1829	92	27	γdf	γdf	NOUN
ap-1829	92	28	=	=	SYM
ap-1829	92	29	∅	∅	NOUN
ap-1829	92	30	}	}	PUNCT
ap-1829	92	31	.	.	PUNCT
ap-1829	93	1	(	(	PUNCT
ap-1829	93	2	5	5	X
ap-1829	93	3	)	)	PUNCT
ap-1829	93	4	let	let	VERB
ap-1829	93	5	the	the	DET
ap-1829	93	6	linear	linear	ADJ
ap-1829	93	7	space	space	NOUN
ap-1829	93	8	v1	v1	NOUN
ap-1829	93	9	be	be	AUX
ap-1829	93	10	a	a	DET
ap-1829	93	11	closure	closure	NOUN
ap-1829	93	12	of	of	ADP
ap-1829	93	13	e1(ω	e1(ω	NOUN
ap-1829	93	14	)	)	PUNCT
ap-1829	93	15	,	,	PUNCT
ap-1829	93	16	and	and	CCONJ
ap-1829	93	17	let	let	VERB
ap-1829	93	18	v2	v2	NOUN
ap-1829	93	19	be	be	AUX
ap-1829	93	20	a	a	DET
ap-1829	93	21	closure	closure	NOUN
ap-1829	93	22	of	of	ADP
ap-1829	93	23	e2(ω	e2(ω	NOUN
ap-1829	93	24	)	)	PUNCT
ap-1829	93	25	,	,	PUNCT
ap-1829	93	26	in	in	ADP
ap-1829	93	27	the	the	DET
ap-1829	93	28	norm	norm	NOUN
ap-1829	93	29	of	of	ADP
ap-1829	93	30	w	w	PROPN
ap-1829	93	31	1,2(ω	1,2(ω	NUM
ap-1829	93	32	)	)	PUNCT
ap-1829	93	33	.	.	PUNCT
ap-1829	94	1	functions	function	NOUN
ap-1829	94	2	hm	hm	INTJ
ap-1829	94	3	,	,	PUNCT
ap-1829	94	4	hf	hf	PROPN
ap-1829	94	5	∈	∈	PROPN
ap-1829	94	6	c([0	c([0	PROPN
ap-1829	94	7	,	,	PUNCT
ap-1829	94	8	t	t	PROPN
ap-1829	94	9	)	)	PUNCT
ap-1829	94	10	;	;	PUNCT
ap-1829	95	1	w	w	PROPN
ap-1829	95	2	1,2(ω	1,2(ω	NUM
ap-1829	95	3	)	)	PUNCT
ap-1829	95	4	)	)	PUNCT
ap-1829	95	5	∩	∩	NOUN
ap-1829	95	6	c([0	c([0	NOUN
ap-1829	95	7	,	,	PUNCT
ap-1829	95	8	t	t	PROPN
ap-1829	95	9	)	)	PUNCT
ap-1829	95	10	;	;	PUNCT
ap-1829	95	11	l∞(ω))∩	l∞(ω))∩	PROPN
ap-1829	95	12	c1([0	c1([0	PROPN
ap-1829	95	13	,	,	PUNCT
ap-1829	95	14	t	t	NOUN
ap-1829	95	15	)	)	PUNCT
ap-1829	95	16	;	;	PUNCT
ap-1829	95	17	l2(ω	l2(ω	X
ap-1829	95	18	)	)	PUNCT
ap-1829	95	19	)	)	PUNCT
ap-1829	95	20	,	,	PUNCT
ap-1829	95	21	such	such	ADJ
ap-1829	95	22	that	that	DET
ap-1829	95	23	hm(x	hm(x	NOUN
ap-1829	95	24	,	,	PUNCT
ap-1829	95	25	0	0	NUM
ap-1829	95	26	)	)	PUNCT
ap-1829	95	27	=	=	SYM
ap-1829	95	28	h0	h0	NOUN
ap-1829	95	29	m	m	PROPN
ap-1829	95	30	,	,	PUNCT
ap-1829	95	31	hf	hf	INTJ
ap-1829	95	32	(	(	PUNCT
ap-1829	95	33	x	x	X
ap-1829	95	34	,	,	PUNCT
ap-1829	95	35	0	0	NUM
ap-1829	95	36	)	)	PUNCT
ap-1829	95	37	=	=	SYM
ap-1829	95	38	h0	h0	PROPN
ap-1829	95	39	f	f	PROPN
ap-1829	95	40	,	,	PUNCT
ap-1829	95	41	for	for	ADP
ap-1829	95	42	x	x	PROPN
ap-1829	95	43	∈	∈	PROPN
ap-1829	95	44	ω	ω	PROPN
ap-1829	95	45	and	and	CCONJ
ap-1829	95	46	hm(x	hm(x	PROPN
ap-1829	95	47	,	,	PUNCT
ap-1829	95	48	t	t	PROPN
ap-1829	95	49	)	)	PUNCT
ap-1829	95	50	=	=	SYM
ap-1829	95	51	hdm	hdm	PROPN
ap-1829	95	52	for	for	ADP
ap-1829	95	53	x	x	PROPN
ap-1829	95	54	∈	∈	PROPN
ap-1829	95	55	γdm	γdm	PROPN
ap-1829	95	56	×	×	NOUN
ap-1829	96	1	[	[	X
ap-1829	96	2	0	0	NUM
ap-1829	96	3	,	,	PUNCT
ap-1829	96	4	t	t	NOUN
ap-1829	96	5	)	)	PUNCT
ap-1829	96	6	and	and	CCONJ
ap-1829	96	7	similarly	similarly	ADV
ap-1829	96	8	for	for	ADP
ap-1829	96	9	hf	hf	NOUN
ap-1829	96	10	,	,	PUNCT
ap-1829	96	11	constitute	constitute	VERB
ap-1829	96	12	a	a	DET
ap-1829	96	13	variational	variational	ADJ
ap-1829	96	14	solution	solution	NOUN
ap-1829	96	15	of	of	ADP
ap-1829	96	16	system	system	NOUN
ap-1829	96	17	(	(	PUNCT
ap-1829	96	18	1	1	NUM
ap-1829	96	19	)	)	PUNCT
ap-1829	96	20	together	together	ADV
ap-1829	96	21	with	with	ADP
ap-1829	96	22	initial	initial	ADJ
ap-1829	96	23	condition	condition	NOUN
ap-1829	96	24	and	and	CCONJ
ap-1829	96	25	boundary	boundary	ADJ
ap-1829	96	26	conditions	condition	NOUN
ap-1829	96	27	(	(	PUNCT
ap-1829	96	28	3)–(4	3)–(4	NUM
ap-1829	96	29	)	)	PUNCT
ap-1829	96	30	iff∫	iff∫	NOUN
ap-1829	96	31	ω	ω	X
ap-1829	96	32	cm(hm)∂hm	cm(hm)∂hm	NOUN
ap-1829	97	1	∂t	∂t	PROPN
ap-1829	97	2	ϕ1dω	ϕ1dω	X
ap-1829	98	1	+	+	NUM
ap-1829	98	2	∫	∫	PROPN
ap-1829	98	3	ω	ω	PROPN
ap-1829	98	4	(	(	PUNCT
ap-1829	98	5	km(hm)∇hm)∇ϕ1dω	km(hm)∇hm)∇ϕ1dω	PROPN
ap-1829	98	6	−	−	PROPN
ap-1829	98	7	∫	∫	PROPN
ap-1829	98	8	ω	ω	PROPN
ap-1829	98	9	∂km(hm	∂km(hm	PROPN
ap-1829	98	10	)	)	PUNCT
ap-1829	98	11	∂z	∂z	PROPN
ap-1829	98	12	ϕ1dω	ϕ1dω	X
ap-1829	99	1	−	−	PROPN
ap-1829	99	2	∫	∫	PROPN
ap-1829	99	3	ω	ω	NUM
ap-1829	99	4	γw	γw	PROPN
ap-1829	99	5	1−	1−	NUM
ap-1829	99	6	ωf	ωf	ADV
ap-1829	99	7	ϕ1dω	ϕ1dω	X
ap-1829	99	8	=	=	SYM
ap-1829	99	9	∫	∫	PROPN
ap-1829	100	1	γn	γn	NUM
ap-1829	100	2	m	m	PROPN
ap-1829	100	3	hnmϕ1dγnm	hnmϕ1dγnm	NOUN
ap-1829	100	4	(	(	PUNCT
ap-1829	100	5	6	6	NUM
ap-1829	100	6	)	)	PUNCT
ap-1829	100	7	and∫	and∫	NOUN
ap-1829	101	1	ω	ω	NUM
ap-1829	101	2	cf	cf	NOUN
ap-1829	101	3	(	(	PUNCT
ap-1829	101	4	hf	hf	NOUN
ap-1829	101	5	)	)	PUNCT
ap-1829	101	6	∂hf	∂hf	PROPN
ap-1829	101	7	∂t	∂t	PROPN
ap-1829	101	8	ϕ2dω	ϕ2dω	PUNCT
ap-1829	102	1	+	+	NUM
ap-1829	102	2	∫	∫	PROPN
ap-1829	102	3	ω	ω	PROPN
ap-1829	102	4	(	(	PUNCT
ap-1829	102	5	kf	kf	PROPN
ap-1829	102	6	(	(	PUNCT
ap-1829	102	7	hf	hf	NOUN
ap-1829	102	8	)	)	PUNCT
ap-1829	102	9	∇hf	∇hf	X
ap-1829	102	10	)	)	PUNCT
ap-1829	102	11	∇ϕ2dω	∇ϕ2dω	PROPN
ap-1829	102	12	−	−	PROPN
ap-1829	103	1	∫	∫	PROPN
ap-1829	104	1	ω	ω	NUM
ap-1829	105	1	∂kf	∂kf	PROPN
ap-1829	106	1	(	(	PUNCT
ap-1829	106	2	hf	hf	PROPN
ap-1829	106	3	)	)	PUNCT
ap-1829	107	1	∂z	∂z	PROPN
ap-1829	107	2	ϕ2dω	ϕ2dω	PUNCT
ap-1829	108	1	+	+	NUM
ap-1829	109	1	∫	∫	PROPN
ap-1829	109	2	ω	ω	NUM
ap-1829	109	3	γw	γw	VERB
ap-1829	109	4	ωf	ωf	ADV
ap-1829	109	5	ϕ2dω	ϕ2dω	PUNCT
ap-1829	109	6	=	=	PUNCT
ap-1829	110	1	∫	∫	PROPN
ap-1829	111	1	γn	γn	ADP
ap-1829	111	2	f	f	PROPN
ap-1829	111	3	hnf	hnf	PUNCT
ap-1829	111	4	ϕ2dγnf	ϕ2dγnf	PROPN
ap-1829	111	5	(	(	PUNCT
ap-1829	111	6	7	7	X
ap-1829	111	7	)	)	PUNCT
ap-1829	111	8	hold	hold	NOUN
ap-1829	111	9	for	for	ADP
ap-1829	111	10	every	every	DET
ap-1829	111	11	ϕ1	ϕ1	NOUN
ap-1829	111	12	∈	∈	NOUN
ap-1829	111	13	v1	v1	NOUN
ap-1829	111	14	,	,	PUNCT
ap-1829	111	15	ϕ2	ϕ2	ADV
ap-1829	111	16	∈	∈	NOUN
ap-1829	111	17	v2	v2	NOUN
ap-1829	111	18	,	,	PUNCT
ap-1829	111	19	and	and	CCONJ
ap-1829	111	20	t	t	PROPN
ap-1829	111	21	∈	∈	PROPN
ap-1829	112	1	[	[	X
ap-1829	112	2	0	0	NUM
ap-1829	112	3	,	,	PUNCT
ap-1829	112	4	t	t	NOUN
ap-1829	112	5	)	)	PUNCT
ap-1829	112	6	.	.	PUNCT
ap-1829	113	1	the	the	DET
ap-1829	113	2	time	time	NOUN
ap-1829	113	3	derivative	derivative	ADJ
ap-1829	113	4	in	in	ADP
ap-1829	113	5	equations	equation	NOUN
ap-1829	113	6	(	(	PUNCT
ap-1829	113	7	6)–(7	6)–(7	NUM
ap-1829	113	8	)	)	PUNCT
ap-1829	113	9	was	be	AUX
ap-1829	113	10	handled	handle	VERB
ap-1829	113	11	with	with	ADP
ap-1829	113	12	the	the	DET
ap-1829	113	13	backward	backward	ADJ
ap-1829	113	14	time	time	NOUN
ap-1829	113	15	difference	difference	NOUN
ap-1829	113	16	.	.	PUNCT
ap-1829	114	1	the	the	DET
ap-1829	114	2	continuous	continuous	ADJ
ap-1829	114	3	unknown	unknown	ADJ
ap-1829	114	4	hn+1	hn+1	PROPN
ap-1829	114	5	m	m	PROPN
ap-1829	114	6	,	,	PUNCT
ap-1829	114	7	f	f	PROPN
ap-1829	114	8	will	will	AUX
ap-1829	114	9	be	be	AUX
ap-1829	114	10	replaced	replace	VERB
ap-1829	114	11	by	by	ADP
ap-1829	114	12	a	a	DET
ap-1829	114	13	piecewisepolynomial	piecewisepolynomial	ADJ
ap-1829	114	14	function	function	NOUN
ap-1829	114	15	(	(	PUNCT
ap-1829	114	16	in	in	ADP
ap-1829	114	17	our	our	PRON
ap-1829	114	18	implementation	implementation	NOUN
ap-1829	114	19	the	the	DET
ap-1829	114	20	degree	degree	NOUN
ap-1829	114	21	of	of	ADP
ap-1829	114	22	the	the	DET
ap-1829	114	23	polynomial	polynomial	NOUN
ap-1829	114	24	is	be	AUX
ap-1829	114	25	p	p	NOUN
ap-1829	114	26	=	=	ADJ
ap-1829	114	27	1	1	NUM
ap-1829	114	28	)	)	PUNCT
ap-1829	114	29	hn+1	hn+1	PROPN
ap-1829	114	30	m	m	NOUN
ap-1829	114	31	=	=	NOUN
ap-1829	114	32	dm∑	dm∑	NOUN
ap-1829	114	33	j=1	j=1	PROPN
ap-1829	114	34	am	be	AUX
ap-1829	114	35	,	,	PUNCT
ap-1829	114	36	jϕ1,j	jϕ1,j	NOUN
ap-1829	114	37	,	,	PUNCT
ap-1829	115	1	hn+1	hn+1	PROPN
ap-1829	115	2	f	f	NOUN
ap-1829	115	3	=	=	PUNCT
ap-1829	115	4	df∑	df∑	VERB
ap-1829	115	5	j=1	j=1	PROPN
ap-1829	115	6	af	af	PROPN
ap-1829	115	7	,	,	PUNCT
ap-1829	115	8	jϕ2,j	jϕ2,j	NOUN
ap-1829	115	9	(	(	PUNCT
ap-1829	115	10	8)	8)	NUM
ap-1829	115	11	and	and	CCONJ
ap-1829	115	12	the	the	DET
ap-1829	115	13	test	test	NOUN
ap-1829	115	14	functions	function	NOUN
ap-1829	115	15	ϕ1	ϕ1	NOUN
ap-1829	115	16	and	and	CCONJ
ap-1829	115	17	ϕ2	ϕ2	ADV
ap-1829	115	18	with	with	ADP
ap-1829	115	19	finite	finite	PROPN
ap-1829	115	20	element	element	NOUN
ap-1829	115	21	test	test	NOUN
ap-1829	115	22	functions	function	NOUN
ap-1829	115	23	ϕi1	ϕi1	PROPN
ap-1829	115	24	and	and	CCONJ
ap-1829	115	25	ϕi2	ϕi2	VERB
ap-1829	115	26	to	to	PART
ap-1829	115	27	obtain∫	obtain∫	VERB
ap-1829	115	28	ω	ω	PROPN
ap-1829	115	29	cm(hn+1	cm(hn+1	PROPN
ap-1829	115	30	m	m	PROPN
ap-1829	115	31	)	)	PUNCT
ap-1829	116	1	h	h	PROPN
ap-1829	117	1	n+1	n+1	NUM
ap-1829	117	2	m	m	VERB
ap-1829	117	3	−	−	NOUN
ap-1829	117	4	hnm	hnm	PROPN
ap-1829	117	5	∆t	∆t	PROPN
ap-1829	117	6	ϕi1dω	ϕi1dω	PROPN
ap-1829	118	1	+	+	CCONJ
ap-1829	118	2	∫	∫	PROPN
ap-1829	118	3	ω	ω	PROPN
ap-1829	118	4	(	(	PUNCT
ap-1829	118	5	km(hn+1	km(hn+1	PROPN
ap-1829	118	6	m	m	PROPN
ap-1829	118	7	)	)	PUNCT
ap-1829	118	8	∇hn+1	∇hn+1	PROPN
ap-1829	118	9	m	m	NOUN
ap-1829	118	10	)	)	PUNCT
ap-1829	119	1	∇ϕi1dω	∇ϕi1dω	PROPN
ap-1829	119	2	−	−	PROPN
ap-1829	120	1	∫	∫	PROPN
ap-1829	120	2	ω	ω	PROPN
ap-1829	120	3	k	k	PROPN
ap-1829	120	4	′m(hn+1	′m(hn+1	PROPN
ap-1829	120	5	m	m	VERB
ap-1829	120	6	)	)	PUNCT
ap-1829	121	1	∂h	∂h	PROPN
ap-1829	122	1	n+1	n+1	NUM
ap-1829	122	2	m	m	NOUN
ap-1829	122	3	∂z	∂z	PROPN
ap-1829	123	1	ϕi1dω	ϕi1dω	NUM
ap-1829	123	2	−	−	PROPN
ap-1829	124	1	∫	∫	PROPN
ap-1829	124	2	ω	ω	NUM
ap-1829	124	3	γw	γw	PROPN
ap-1829	124	4	1−	1−	NUM
ap-1829	124	5	ωf	ωf	PRON
ap-1829	124	6	ϕi1dω	ϕi1dω	PROPN
ap-1829	124	7	=	=	SYM
ap-1829	124	8	∫	∫	PROPN
ap-1829	125	1	γn	γn	NUM
ap-1829	125	2	m	m	PROPN
ap-1829	125	3	hn+1,n	hn+1,n	PROPN
ap-1829	125	4	m	m	PROPN
ap-1829	125	5	ϕi1dγnm	ϕi1dγnm	NOUN
ap-1829	125	6	(	(	PUNCT
ap-1829	125	7	9	9	NUM
ap-1829	125	8	)	)	PUNCT
ap-1829	125	9	for	for	ADP
ap-1829	125	10	all	all	DET
ap-1829	125	11	i	i	PRON
ap-1829	125	12	=	=	NOUN
ap-1829	125	13	1	1	NUM
ap-1829	125	14	;	;	PUNCT
ap-1829	125	15	2	2	NUM
ap-1829	125	16	;	;	PUNCT
ap-1829	125	17	.	.	PUNCT
ap-1829	125	18	.	.	PUNCT
ap-1829	125	19	.	.	PUNCT
ap-1829	126	1	;	;	PUNCT
ap-1829	126	2	dm	dm	X
ap-1829	126	3	,	,	PUNCT
ap-1829	126	4	dm	dm	PROPN
ap-1829	126	5	is	be	AUX
ap-1829	126	6	the	the	DET
ap-1829	126	7	dimension	dimension	NOUN
ap-1829	126	8	of	of	ADP
ap-1829	126	9	the	the	DET
ap-1829	126	10	finite	finite	ADJ
ap-1829	126	11	element	element	NOUN
ap-1829	126	12	subspace	subspace	NOUN
ap-1829	126	13	of	of	ADP
ap-1829	126	14	v1	v1	NOUN
ap-1829	126	15	,	,	PUNCT
ap-1829	126	16	and∫	and∫	PROPN
ap-1829	126	17	ω	ω	NUM
ap-1829	126	18	cf	cf	NOUN
ap-1829	126	19	(	(	PUNCT
ap-1829	126	20	hn+1	hn+1	PROPN
ap-1829	126	21	f	f	PROPN
ap-1829	126	22	)	)	PUNCT
ap-1829	126	23	hn+1	hn+1	PROPN
ap-1829	127	1	f	f	PROPN
ap-1829	127	2	−	−	PROPN
ap-1829	127	3	hnf	hnf	NOUN
ap-1829	127	4	∆t	∆t	PROPN
ap-1829	127	5	ϕi2dω	ϕi2dω	PROPN
ap-1829	127	6	+	+	CCONJ
ap-1829	127	7	∫	∫	PROPN
ap-1829	127	8	ω	ω	PROPN
ap-1829	127	9	(	(	PUNCT
ap-1829	127	10	kf	kf	PROPN
ap-1829	127	11	(	(	PUNCT
ap-1829	127	12	hn+1	hn+1	PROPN
ap-1829	127	13	f	f	PROPN
ap-1829	127	14	)	)	PUNCT
ap-1829	127	15	∇hn+1	∇hn+1	PROPN
ap-1829	127	16	f	f	PROPN
ap-1829	127	17	)	)	PUNCT
ap-1829	128	1	∇ϕi2dω	∇ϕi2dω	PROPN
ap-1829	128	2	−	−	PROPN
ap-1829	129	1	∫	∫	PROPN
ap-1829	129	2	ω	ω	PROPN
ap-1829	129	3	k	k	PROPN
ap-1829	129	4	′f	′f	PROPN
ap-1829	129	5	(	(	PUNCT
ap-1829	129	6	hn+1	hn+1	PROPN
ap-1829	129	7	f	f	PROPN
ap-1829	129	8	)	)	PUNCT
ap-1829	129	9	∂hn+1	∂hn+1	PROPN
ap-1829	129	10	f	f	PROPN
ap-1829	130	1	∂z	∂z	PROPN
ap-1829	130	2	ϕi2dω	ϕi2dω	PROPN
ap-1829	131	1	−	−	PROPN
ap-1829	131	2	∫	∫	PROPN
ap-1829	132	1	ω	ω	NUM
ap-1829	132	2	γw	γw	PROPN
ap-1829	132	3	ωf	ωf	PROPN
ap-1829	132	4	ϕi2dω	ϕi2dω	PROPN
ap-1829	132	5	=	=	SYM
ap-1829	132	6	∫	∫	PROPN
ap-1829	132	7	γn	γn	ADP
ap-1829	132	8	f	f	PROPN
ap-1829	132	9	hn+1,n	hn+1,n	PROPN
ap-1829	132	10	f	f	PROPN
ap-1829	132	11	ϕi2dγnf	ϕi2dγnf	PROPN
ap-1829	132	12	(	(	PUNCT
ap-1829	132	13	10	10	NUM
ap-1829	132	14	)	)	PUNCT
ap-1829	132	15	for	for	ADP
ap-1829	132	16	all	all	DET
ap-1829	132	17	i	i	PRON
ap-1829	132	18	=	=	NOUN
ap-1829	132	19	1	1	NUM
ap-1829	132	20	;	;	PUNCT
ap-1829	132	21	2	2	NUM
ap-1829	132	22	;	;	PUNCT
ap-1829	132	23	.	.	PUNCT
ap-1829	132	24	.	.	PUNCT
ap-1829	132	25	.	.	PUNCT
ap-1829	133	1	;	;	PUNCT
ap-1829	133	2	df	df	PROPN
ap-1829	133	3	,	,	PUNCT
ap-1829	133	4	df	df	PROPN
ap-1829	133	5	is	be	AUX
ap-1829	133	6	the	the	DET
ap-1829	133	7	dimension	dimension	NOUN
ap-1829	133	8	of	of	ADP
ap-1829	133	9	the	the	DET
ap-1829	133	10	finite	finite	ADJ
ap-1829	133	11	element	element	NOUN
ap-1829	133	12	subspace	subspace	NOUN
ap-1829	133	13	of	of	ADP
ap-1829	133	14	v2	v2	PROPN
ap-1829	133	15	.	.	PUNCT
ap-1829	134	1	the	the	DET
ap-1829	134	2	superscript	superscript	PROPN
ap-1829	134	3	n	n	PART
ap-1829	134	4	enumerates	enumerate	VERB
ap-1829	134	5	the	the	DET
ap-1829	134	6	time	time	NOUN
ap-1829	134	7	steps	step	NOUN
ap-1829	134	8	,	,	PUNCT
ap-1829	134	9	and	and	CCONJ
ap-1829	134	10	∆t	∆t	PROPN
ap-1829	134	11	is	be	AUX
ap-1829	134	12	the	the	DET
ap-1829	134	13	length	length	NOUN
ap-1829	134	14	of	of	ADP
ap-1829	134	15	the	the	DET
ap-1829	134	16	time	time	NOUN
ap-1829	134	17	step	step	NOUN
ap-1829	134	18	.	.	PUNCT
ap-1829	135	1	the	the	DET
ap-1829	135	2	nonlinear	nonlinear	ADJ
ap-1829	135	3	operator	operator	NOUN
ap-1829	135	4	was	be	AUX
ap-1829	135	5	treated	treat	VERB
ap-1829	135	6	by	by	ADP
ap-1829	135	7	the	the	DET
ap-1829	135	8	standard	standard	ADJ
ap-1829	135	9	picard	picard	NOUN
ap-1829	135	10	method	method	NOUN
ap-1829	135	11	.	.	PUNCT
ap-1829	136	1	this	this	DET
ap-1829	136	2	method	method	NOUN
ap-1829	136	3	performs	perform	VERB
ap-1829	136	4	a	a	DET
ap-1829	136	5	simple	simple	ADJ
ap-1829	136	6	linearization	linearization	NOUN
ap-1829	136	7	of	of	ADP
ap-1829	136	8	nonlinear	nonlinear	ADJ
ap-1829	136	9	product	product	NOUN
ap-1829	136	10	terms	term	NOUN
ap-1829	136	11	by	by	ADP
ap-1829	136	12	moving	move	VERB
ap-1829	136	13	all	all	PRON
ap-1829	136	14	of	of	ADP
ap-1829	136	15	them	they	PRON
ap-1829	136	16	but	but	CCONJ
ap-1829	136	17	one	one	NUM
ap-1829	136	18	to	to	ADP
ap-1829	136	19	the	the	DET
ap-1829	136	20	previous	previous	ADJ
ap-1829	136	21	iteration	iteration	NOUN
ap-1829	136	22	level	level	NOUN
ap-1829	136	23	.	.	PUNCT
ap-1829	137	1	for	for	ADP
ap-1829	137	2	equations	equation	NOUN
ap-1829	137	3	(	(	PUNCT
ap-1829	137	4	9)–(10	9)–(10	NUM
ap-1829	137	5	)	)	PUNCT
ap-1829	137	6	the	the	DET
ap-1829	137	7	following	follow	VERB
ap-1829	137	8	set	set	NOUN
ap-1829	137	9	is	be	AUX
ap-1829	137	10	obtained∫	obtained∫	VERB
ap-1829	137	11	ω	ω	NUM
ap-1829	137	12	cm(hn+1	cm(hn+1	PROPN
ap-1829	137	13	m	m	PROPN
ap-1829	137	14	,	,	PUNCT
ap-1829	137	15	k	k	PROPN
ap-1829	137	16	)	)	PUNCT
ap-1829	137	17	hn+1	hn+1	PROPN
ap-1829	138	1	m	m	PROPN
ap-1829	138	2	,	,	PUNCT
ap-1829	138	3	k+1	k+1	X
ap-1829	138	4	−	−	PROPN
ap-1829	138	5	hnm	hnm	PROPN
ap-1829	138	6	∆t	∆t	PROPN
ap-1829	138	7	ϕi1dω	ϕi1dω	PROPN
ap-1829	139	1	+	+	CCONJ
ap-1829	139	2	∫	∫	PROPN
ap-1829	139	3	ω	ω	PROPN
ap-1829	139	4	(	(	PUNCT
ap-1829	139	5	km(hn+1	km(hn+1	PROPN
ap-1829	139	6	m	m	PROPN
ap-1829	139	7	,	,	PUNCT
ap-1829	139	8	k	k	PROPN
ap-1829	139	9	)	)	PUNCT
ap-1829	139	10	∇hn+1	∇hn+1	PROPN
ap-1829	139	11	m	m	PROPN
ap-1829	139	12	,	,	PUNCT
ap-1829	139	13	k+1	k+1	X
ap-1829	139	14	)	)	PUNCT
ap-1829	140	1	∇ϕi1dω	∇ϕi1dω	PROPN
ap-1829	140	2	−	−	PROPN
ap-1829	140	3	∫	∫	PROPN
ap-1829	140	4	ω	ω	PROPN
ap-1829	140	5	k	k	PROPN
ap-1829	140	6	′m(hn+1	′m(hn+1	PROPN
ap-1829	140	7	m	m	PROPN
ap-1829	140	8	,	,	PUNCT
ap-1829	140	9	k	k	PROPN
ap-1829	140	10	)	)	PUNCT
ap-1829	140	11	∂hn+1	∂hn+1	PROPN
ap-1829	140	12	m	m	PROPN
ap-1829	140	13	,	,	PUNCT
ap-1829	140	14	k+1	k+1	PROPN
ap-1829	140	15	∂z	∂z	PROPN
ap-1829	140	16	ϕi1dω	ϕi1dω	PROPN
ap-1829	140	17	−	−	PROPN
ap-1829	140	18	∫	∫	PROPN
ap-1829	141	1	ω	ω	NUM
ap-1829	141	2	γw	γw	PROPN
ap-1829	141	3	1−	1−	NUM
ap-1829	141	4	ωf	ωf	PRON
ap-1829	141	5	ϕi1dω	ϕi1dω	PROPN
ap-1829	141	6	=	=	SYM
ap-1829	141	7	∫	∫	PROPN
ap-1829	142	1	γn	γn	NUM
ap-1829	142	2	m	m	PROPN
ap-1829	142	3	hn+1,n	hn+1,n	PROPN
ap-1829	142	4	m	m	PROPN
ap-1829	142	5	ϕi1dγnm	ϕi1dγnm	NOUN
ap-1829	143	1	(	(	PUNCT
ap-1829	143	2	11	11	NUM
ap-1829	143	3	)	)	PUNCT
ap-1829	143	4	for	for	ADP
ap-1829	143	5	all	all	DET
ap-1829	143	6	i	i	PRON
ap-1829	143	7	=	=	NOUN
ap-1829	143	8	1	1	NUM
ap-1829	143	9	;	;	PUNCT
ap-1829	143	10	2	2	NUM
ap-1829	143	11	;	;	PUNCT
ap-1829	143	12	.	.	PUNCT
ap-1829	143	13	.	.	PUNCT
ap-1829	143	14	.	.	PUNCT
ap-1829	144	1	;	;	PUNCT
ap-1829	144	2	dm	dm	PROPN
ap-1829	144	3	,	,	PUNCT
ap-1829	144	4	and∫	and∫	PROPN
ap-1829	144	5	ω	ω	NUM
ap-1829	144	6	cf	cf	NOUN
ap-1829	144	7	(	(	PUNCT
ap-1829	144	8	hn+1	hn+1	NOUN
ap-1829	144	9	f	f	PROPN
ap-1829	144	10	,	,	PUNCT
ap-1829	144	11	k	k	PROPN
ap-1829	144	12	)	)	PUNCT
ap-1829	144	13	hn+1	hn+1	PROPN
ap-1829	145	1	f	f	PROPN
ap-1829	145	2	,	,	PUNCT
ap-1829	145	3	k+1	k+1	X
ap-1829	145	4	−	−	PROPN
ap-1829	145	5	hnf	hnf	NOUN
ap-1829	145	6	∆t	∆t	PROPN
ap-1829	145	7	ϕi2dω	ϕi2dω	PROPN
ap-1829	145	8	+	+	CCONJ
ap-1829	145	9	∫	∫	PROPN
ap-1829	145	10	ω	ω	PROPN
ap-1829	145	11	(	(	PUNCT
ap-1829	145	12	kf	kf	PROPN
ap-1829	145	13	(	(	PUNCT
ap-1829	145	14	hn+1	hn+1	PROPN
ap-1829	145	15	f	f	PROPN
ap-1829	145	16	,	,	PUNCT
ap-1829	145	17	k	k	PROPN
ap-1829	145	18	)	)	PUNCT
ap-1829	145	19	∇hn+1	∇hn+1	PROPN
ap-1829	146	1	f	f	PROPN
ap-1829	146	2	,	,	PUNCT
ap-1829	146	3	k+1	k+1	X
ap-1829	146	4	)	)	PUNCT
ap-1829	146	5	∇ϕi2dω	∇ϕi2dω	PROPN
ap-1829	146	6	−	−	PROPN
ap-1829	147	1	∫	∫	PROPN
ap-1829	147	2	ω	ω	PROPN
ap-1829	147	3	k	k	PROPN
ap-1829	147	4	′f	′f	PROPN
ap-1829	147	5	(	(	PUNCT
ap-1829	147	6	hn+1	hn+1	NOUN
ap-1829	147	7	f	f	PROPN
ap-1829	147	8	,	,	PUNCT
ap-1829	147	9	k	k	PROPN
ap-1829	147	10	)	)	PUNCT
ap-1829	147	11	∂hn+1	∂hn+1	PROPN
ap-1829	148	1	f	f	X
ap-1829	148	2	,	,	PUNCT
ap-1829	148	3	k+1	k+1	PROPN
ap-1829	148	4	∂z	∂z	PROPN
ap-1829	148	5	ϕi2dω	ϕi2dω	PROPN
ap-1829	149	1	−	−	PROPN
ap-1829	149	2	∫	∫	PROPN
ap-1829	150	1	ω	ω	NUM
ap-1829	150	2	γw	γw	PROPN
ap-1829	150	3	ωf	ωf	PROPN
ap-1829	150	4	ϕi2dω	ϕi2dω	PROPN
ap-1829	150	5	=	=	SYM
ap-1829	150	6	∫	∫	PROPN
ap-1829	150	7	γn	γn	ADP
ap-1829	151	1	f	f	PROPN
ap-1829	151	2	hn+1,n	hn+1,n	PROPN
ap-1829	151	3	f	f	PROPN
ap-1829	151	4	ϕi2dγnf	ϕi2dγnf	PROPN
ap-1829	151	5	(	(	PUNCT
ap-1829	151	6	12	12	NUM
ap-1829	151	7	)	)	PUNCT
ap-1829	151	8	for	for	ADP
ap-1829	151	9	all	all	DET
ap-1829	151	10	i	i	PRON
ap-1829	151	11	=	=	NOUN
ap-1829	151	12	1	1	NUM
ap-1829	151	13	;	;	PUNCT
ap-1829	151	14	2	2	NUM
ap-1829	151	15	;	;	PUNCT
ap-1829	151	16	.	.	PUNCT
ap-1829	151	17	.	.	PUNCT
ap-1829	151	18	.	.	PUNCT
ap-1829	152	1	;	;	PUNCT
ap-1829	152	2	df	df	PROPN
ap-1829	152	3	.	.	PUNCT
ap-1829	153	1	here	here	ADV
ap-1829	153	2	the	the	DET
ap-1829	153	3	subscript	subscript	NOUN
ap-1829	153	4	k	k	PROPN
ap-1829	153	5	denotes	denote	VERB
ap-1829	153	6	the	the	DET
ap-1829	153	7	iteration	iteration	NOUN
ap-1829	153	8	level	level	NOUN
ap-1829	153	9	.	.	PUNCT
ap-1829	154	1	the	the	DET
ap-1829	154	2	stopping	stop	VERB
ap-1829	154	3	criterion	criterion	NOUN
ap-1829	154	4	was	be	AUX
ap-1829	154	5	obtained	obtain	VERB
ap-1829	154	6	by	by	ADP
ap-1829	154	7	looking	look	VERB
ap-1829	154	8	at	at	ADP
ap-1829	154	9	the	the	DET
ap-1829	154	10	distance	distance	NOUN
ap-1829	154	11	of	of	ADP
ap-1829	154	12	two	two	NUM
ap-1829	154	13	consecutive	consecutive	ADJ
ap-1829	154	14	349	349	NUM
ap-1829	154	15	michal	michal	PROPN
ap-1829	154	16	kuráž	kuráž	PROPN
ap-1829	154	17	,	,	PUNCT
ap-1829	154	18	petr	petr	PROPN
ap-1829	154	19	mayer	mayer	PROPN
ap-1829	154	20	acta	acta	PROPN
ap-1829	154	21	polytechnica	polytechnica	PROPN
ap-1829	154	22	figure	figure	NOUN
ap-1829	154	23	2	2	NUM
ap-1829	154	24	.	.	PUNCT
ap-1829	155	1	the	the	DET
ap-1829	155	2	critical	critical	ADJ
ap-1829	155	3	point	point	NOUN
ap-1829	155	4	of	of	ADP
ap-1829	155	5	solution	solution	NOUN
ap-1829	155	6	h	h	NOUN
ap-1829	155	7	was	be	AUX
ap-1829	155	8	assumed	assume	VERB
ap-1829	155	9	from	from	ADP
ap-1829	155	10	nodal	nodal	ADJ
ap-1829	155	11	values	value	NOUN
ap-1829	155	12	of	of	ADP
ap-1829	155	13	the	the	DET
ap-1829	155	14	discretization	discretization	NOUN
ap-1829	155	15	mesh	mesh	NOUN
ap-1829	155	16	.	.	PUNCT
ap-1829	156	1	then	then	ADV
ap-1829	156	2	the	the	DET
ap-1829	156	3	only	only	ADJ
ap-1829	156	4	acceptable	acceptable	ADJ
ap-1829	156	5	solution	solution	NOUN
ap-1829	156	6	in	in	ADP
ap-1829	156	7	the	the	DET
ap-1829	156	8	next	next	ADJ
ap-1829	156	9	time	time	NOUN
ap-1829	156	10	level	level	NOUN
ap-1829	156	11	is	be	AUX
ap-1829	156	12	a	a	DET
ap-1829	156	13	solution	solution	NOUN
ap-1829	156	14	that	that	PRON
ap-1829	156	15	does	do	AUX
ap-1829	156	16	not	not	PART
ap-1829	156	17	exceed	exceed	VERB
ap-1829	156	18	the	the	DET
ap-1829	156	19	ranges	range	NOUN
ap-1829	156	20	defined	define	VERB
ap-1829	156	21	by	by	ADP
ap-1829	156	22	some	some	DET
ap-1829	156	23	critical	critical	ADJ
ap-1829	156	24	error	error	NOUN
ap-1829	156	25	of	of	ADP
ap-1829	156	26	the	the	DET
ap-1829	156	27	first	first	ADJ
ap-1829	156	28	order	order	NOUN
ap-1829	156	29	taylor	taylor	PROPN
ap-1829	156	30	series	series	PROPN
ap-1829	156	31	approximation	approximation	NOUN
ap-1829	156	32	of	of	ADP
ap-1829	156	33	solution	solution	NOUN
ap-1829	156	34	h	h	NOUN
ap-1829	156	35	at	at	ADP
ap-1829	156	36	the	the	DET
ap-1829	156	37	previous	previous	ADJ
ap-1829	156	38	time	time	NOUN
ap-1829	156	39	level	level	NOUN
ap-1829	156	40	.	.	PUNCT
ap-1829	157	1	picard	picard	NOUN
ap-1829	157	2	approximations	approximation	NOUN
ap-1829	157	3	of	of	ADP
ap-1829	157	4	the	the	DET
ap-1829	157	5	solutions	solution	NOUN
ap-1829	157	6	in	in	ADP
ap-1829	157	7	the	the	DET
ap-1829	157	8	both	both	DET
ap-1829	157	9	domains	domain	NOUN
ap-1829	157	10	–	–	PUNCT
ap-1829	157	11	‖hn+1	‖hn+1	X
ap-1829	157	12	m	m	NOUN
ap-1829	157	13	,	,	PUNCT
ap-1829	157	14	k+1	k+1	X
ap-1829	157	15	−	−	PROPN
ap-1829	157	16	h	h	NOUN
ap-1829	157	17	n+1	n+1	PROPN
ap-1829	157	18	m	m	PROPN
ap-1829	157	19	,	,	PUNCT
ap-1829	157	20	k	k	PROPN
ap-1829	157	21	‖2	‖2	NOUN
ap-1829	157	22	+	+	CCONJ
ap-1829	157	23	‖hn+1	‖hn+1	X
ap-1829	157	24	f	f	X
ap-1829	157	25	,	,	PUNCT
ap-1829	157	26	k+1	k+1	X
ap-1829	157	27	−	−	PROPN
ap-1829	157	28	h	h	NOUN
ap-1829	157	29	n+1	n+1	PROPN
ap-1829	157	30	f	f	PROPN
ap-1829	157	31	,	,	PUNCT
ap-1829	157	32	k	k	X
ap-1829	157	33	‖2	‖2	NOUN
ap-1829	157	34	<	<	X
ap-1829	157	35	ε	ε	PROPN
ap-1829	157	36	,	,	PUNCT
ap-1829	157	37	(	(	PUNCT
ap-1829	157	38	13	13	NUM
ap-1829	157	39	)	)	PUNCT
ap-1829	157	40	where	where	SCONJ
ap-1829	157	41	ε	ε	PROPN
ap-1829	157	42	is	be	AUX
ap-1829	157	43	the	the	DET
ap-1829	157	44	desired	desire	VERB
ap-1829	157	45	accuracy	accuracy	NOUN
ap-1829	157	46	of	of	ADP
ap-1829	157	47	the	the	DET
ap-1829	157	48	method	method	NOUN
ap-1829	157	49	.	.	PUNCT
ap-1829	158	1	equations	equation	NOUN
ap-1829	158	2	(	(	PUNCT
ap-1829	158	3	11)–(12	11)–(12	NUM
ap-1829	158	4	)	)	PUNCT
ap-1829	158	5	constitute	constitute	VERB
ap-1829	158	6	the	the	DET
ap-1829	158	7	system	system	NOUN
ap-1829	158	8	of	of	ADP
ap-1829	158	9	linear	linear	PROPN
ap-1829	158	10	algebraic	algebraic	ADJ
ap-1829	158	11	equations	equation	NOUN
ap-1829	158	12	to	to	PART
ap-1829	158	13	be	be	AUX
ap-1829	158	14	solved	solve	VERB
ap-1829	158	15	in	in	ADP
ap-1829	158	16	each	each	DET
ap-1829	158	17	iteration	iteration	NOUN
ap-1829	158	18	.	.	PUNCT
ap-1829	159	1	the	the	DET
ap-1829	159	2	solution	solution	NOUN
ap-1829	159	3	of	of	ADP
ap-1829	159	4	this	this	DET
ap-1829	159	5	problem	problem	NOUN
ap-1829	159	6	is	be	AUX
ap-1829	159	7	scattered	scatter	VERB
ap-1829	159	8	into	into	ADP
ap-1829	159	9	hm	hm	INTJ
ap-1829	159	10	,	,	PUNCT
ap-1829	159	11	and	and	CCONJ
ap-1829	159	12	hf	hf	INTJ
ap-1829	159	13	.	.	PUNCT
ap-1829	160	1	however	however	ADV
ap-1829	160	2	the	the	DET
ap-1829	160	3	scattered	scatter	VERB
ap-1829	160	4	outputs	output	NOUN
ap-1829	160	5	hm	hm	INTJ
ap-1829	160	6	,	,	PUNCT
ap-1829	160	7	hf	hf	PROPN
ap-1829	160	8	are	be	AUX
ap-1829	160	9	not	not	PART
ap-1829	160	10	as	as	ADV
ap-1829	160	11	interesting	interesting	ADJ
ap-1829	160	12	as	as	ADP
ap-1829	160	13	the	the	DET
ap-1829	160	14	behavior	behavior	NOUN
ap-1829	160	15	of	of	ADP
ap-1829	160	16	the	the	DET
ap-1829	160	17	capillary	capillary	ADJ
ap-1829	160	18	pressure	pressure	NOUN
ap-1829	160	19	head	head	NOUN
ap-1829	160	20	h	h	NOUN
ap-1829	160	21	,	,	PUNCT
ap-1829	160	22	which	which	PRON
ap-1829	160	23	is	be	AUX
ap-1829	160	24	obtained	obtain	VERB
ap-1829	160	25	by	by	ADP
ap-1829	160	26	averaging	average	VERB
ap-1829	160	27	the	the	DET
ap-1829	160	28	matrix	matrix	NOUN
ap-1829	160	29	domain	domain	NOUN
ap-1829	160	30	m	m	NOUN
ap-1829	160	31	and	and	CCONJ
ap-1829	160	32	the	the	DET
ap-1829	160	33	fast	fast	ADJ
ap-1829	160	34	domain	domain	NOUN
ap-1829	160	35	f	f	NOUN
ap-1829	161	1	:	:	PUNCT
ap-1829	161	2	h	h	NOUN
ap-1829	161	3	=	=	PUNCT
ap-1829	161	4	(	(	PUNCT
ap-1829	161	5	1−	1−	NUM
ap-1829	161	6	ωf	ωf	ADV
ap-1829	161	7	)	)	PUNCT
ap-1829	161	8	hm	hm	PROPN
ap-1829	161	9	+	+	NUM
ap-1829	161	10	ωfhf	ωfhf	NOUN
ap-1829	161	11	.	.	PUNCT
ap-1829	162	1	(	(	PUNCT
ap-1829	162	2	14	14	NUM
ap-1829	162	3	)	)	PUNCT
ap-1829	162	4	one	one	PRON
ap-1829	162	5	could	could	AUX
ap-1829	162	6	also	also	ADV
ap-1829	162	7	hardly	hardly	ADV
ap-1829	162	8	find	find	VERB
ap-1829	162	9	any	any	DET
ap-1829	162	10	real	real	ADJ
ap-1829	162	11	problem	problem	NOUN
ap-1829	162	12	,	,	PUNCT
ap-1829	162	13	where	where	SCONJ
ap-1829	162	14	such	such	ADJ
ap-1829	162	15	scattering	scattering	NOUN
ap-1829	162	16	could	could	AUX
ap-1829	162	17	be	be	AUX
ap-1829	162	18	required	require	VERB
ap-1829	162	19	in	in	ADP
ap-1829	162	20	the	the	DET
ap-1829	162	21	boundary	boundary	ADJ
ap-1829	162	22	and	and	CCONJ
ap-1829	162	23	initial	initial	ADJ
ap-1829	162	24	condition	condition	NOUN
ap-1829	162	25	setup	setup	NOUN
ap-1829	162	26	.	.	PUNCT
ap-1829	163	1	thus	thus	ADV
ap-1829	163	2	the	the	DET
ap-1829	163	3	initial	initial	ADJ
ap-1829	163	4	condition	condition	NOUN
ap-1829	163	5	and	and	CCONJ
ap-1829	163	6	the	the	DET
ap-1829	163	7	dirichlet	dirichlet	PROPN
ap-1829	163	8	boundary	boundary	PROPN
ap-1829	163	9	condition	condition	NOUN
ap-1829	163	10	are	be	AUX
ap-1829	163	11	always	always	ADV
ap-1829	163	12	considered	consider	VERB
ap-1829	163	13	identical	identical	ADJ
ap-1829	163	14	for	for	ADP
ap-1829	163	15	the	the	DET
ap-1829	163	16	both	both	DET
ap-1829	163	17	domains	domain	NOUN
ap-1829	163	18	,	,	PUNCT
ap-1829	163	19	and	and	CCONJ
ap-1829	163	20	the	the	DET
ap-1829	163	21	neumann	neumann	PROPN
ap-1829	163	22	boundary	boundary	ADJ
ap-1829	163	23	condition	condition	NOUN
ap-1829	163	24	(	(	PUNCT
ap-1829	163	25	volume	volume	NOUN
ap-1829	163	26	flux	flux	NOUN
ap-1829	163	27	)	)	PUNCT
ap-1829	163	28	is	be	AUX
ap-1829	163	29	always	always	ADV
ap-1829	163	30	proportionally	proportionally	ADV
ap-1829	163	31	scattered	scatter	VERB
ap-1829	163	32	into	into	ADP
ap-1829	163	33	the	the	DET
ap-1829	163	34	both	both	DET
ap-1829	163	35	domains	domain	NOUN
ap-1829	163	36	.	.	PUNCT
ap-1829	164	1	3	3	NUM
ap-1829	164	2	.	.	NOUN
ap-1829	164	3	time	time	NOUN
ap-1829	164	4	step	step	NOUN
ap-1829	164	5	adaptivity	adaptivity	NOUN
ap-1829	164	6	it	it	PRON
ap-1829	164	7	is	be	AUX
ap-1829	164	8	well	well	ADV
ap-1829	164	9	known	know	VERB
ap-1829	164	10	that	that	SCONJ
ap-1829	164	11	incorrect	incorrect	ADJ
ap-1829	164	12	discretization	discretization	NOUN
ap-1829	164	13	of	of	ADP
ap-1829	164	14	the	the	DET
ap-1829	164	15	mass	mass	ADJ
ap-1829	164	16	term	term	NOUN
ap-1829	164	17	(	(	PUNCT
ap-1829	164	18	time	time	NOUN
ap-1829	164	19	derivative	derivative	ADJ
ap-1829	164	20	term	term	NOUN
ap-1829	164	21	)	)	PUNCT
ap-1829	164	22	yields	yield	VERB
ap-1829	164	23	mass	mass	ADJ
ap-1829	164	24	balance	balance	NOUN
ap-1829	164	25	errors	error	NOUN
ap-1829	164	26	.	.	PUNCT
ap-1829	165	1	this	this	DET
ap-1829	165	2	topic	topic	NOUN
ap-1829	165	3	,	,	PUNCT
ap-1829	165	4	particularly	particularly	ADV
ap-1829	165	5	for	for	ADP
ap-1829	165	6	the	the	DET
ap-1829	165	7	richards	richard	NOUN
ap-1829	165	8	equation	equation	NOUN
ap-1829	165	9	,	,	PUNCT
ap-1829	165	10	was	be	AUX
ap-1829	165	11	already	already	ADV
ap-1829	165	12	documented	document	VERB
ap-1829	165	13	by	by	ADP
ap-1829	165	14	celia	celia	PROPN
ap-1829	165	15	,	,	PUNCT
ap-1829	165	16	et	et	PROPN
ap-1829	165	17	.	.	PUNCT
ap-1829	166	1	al	al	PROPN
ap-1829	166	2	.	.	PUNCT
ap-1829	167	1	[	[	X
ap-1829	167	2	5	5	NUM
ap-1829	167	3	]	]	PUNCT
ap-1829	167	4	in	in	ADP
ap-1829	167	5	the	the	DET
ap-1829	167	6	1990s	1990s	NUM
ap-1829	167	7	.	.	PUNCT
ap-1829	168	1	the	the	DET
ap-1829	168	2	primary	primary	ADJ
ap-1829	168	3	solution	solution	NOUN
ap-1829	168	4	of	of	ADP
ap-1829	168	5	the	the	DET
ap-1829	168	6	richards	richard	NOUN
ap-1829	168	7	equation	equation	NOUN
ap-1829	168	8	in	in	ADP
ap-1829	168	9	h	h	NOUN
ap-1829	168	10	-	-	PUNCT
ap-1829	168	11	based	base	VERB
ap-1829	168	12	form	form	NOUN
ap-1829	168	13	is	be	AUX
ap-1829	168	14	the	the	DET
ap-1829	168	15	capillary	capillary	ADJ
ap-1829	168	16	pressure	pressure	NOUN
ap-1829	168	17	head	head	NOUN
ap-1829	168	18	h.	h.	PROPN
ap-1829	169	1	the	the	DET
ap-1829	169	2	richards	richards	PROPN
ap-1829	169	3	equation	equation	NOUN
ap-1829	169	4	law	law	NOUN
ap-1829	169	5	originates	originate	NOUN
ap-1829	169	6	from	from	ADP
ap-1829	169	7	the	the	DET
ap-1829	169	8	law	law	NOUN
ap-1829	169	9	of	of	ADP
ap-1829	169	10	mass	mass	NOUN
ap-1829	169	11	balance	balance	NOUN
ap-1829	169	12	,	,	PUNCT
ap-1829	169	13	and	and	CCONJ
ap-1829	169	14	thus	thus	ADV
ap-1829	169	15	the	the	DET
ap-1829	169	16	time	time	NOUN
ap-1829	169	17	derivative	derivative	ADJ
ap-1829	169	18	term	term	NOUN
ap-1829	169	19	can	can	AUX
ap-1829	169	20	be	be	AUX
ap-1829	169	21	referred	refer	VERB
ap-1829	169	22	to	to	ADP
ap-1829	169	23	as	as	ADP
ap-1829	169	24	a	a	DET
ap-1829	169	25	mass	mass	ADJ
ap-1829	169	26	term	term	NOUN
ap-1829	169	27	.	.	PUNCT
ap-1829	170	1	the	the	DET
ap-1829	170	2	original	original	ADJ
ap-1829	170	3	form	form	NOUN
ap-1829	170	4	of	of	ADP
ap-1829	170	5	the	the	DET
ap-1829	170	6	richards	richard	NOUN
ap-1829	170	7	equation	equation	NOUN
ap-1829	170	8	published	publish	VERB
ap-1829	170	9	by	by	ADP
ap-1829	170	10	richards	richard	NOUN
ap-1829	170	11	[	[	X
ap-1829	170	12	2	2	NUM
ap-1829	170	13	]	]	PUNCT
ap-1829	170	14	considers	consider	VERB
ap-1829	170	15	the	the	DET
ap-1829	170	16	mass	mass	ADJ
ap-1829	170	17	term	term	NOUN
ap-1829	170	18	to	to	PART
ap-1829	170	19	be	be	AUX
ap-1829	170	20	of	of	ADP
ap-1829	170	21	the	the	DET
ap-1829	170	22	form	form	NOUN
ap-1829	170	23	∂θ(h	∂θ(h	PROPN
ap-1829	170	24	)	)	PUNCT
ap-1829	170	25	∂t	∂t	PROPN
ap-1829	170	26	,	,	PUNCT
ap-1829	170	27	where	where	SCONJ
ap-1829	170	28	θ(h	θ(h	PROPN
ap-1829	170	29	)	)	PUNCT
ap-1829	170	30	is	be	AUX
ap-1829	170	31	the	the	DET
ap-1829	170	32	water	water	NOUN
ap-1829	170	33	content	content	NOUN
ap-1829	170	34	function	function	NOUN
ap-1829	170	35	(	(	PUNCT
ap-1829	170	36	mass	mass	NOUN
ap-1829	170	37	function	function	NOUN
ap-1829	170	38	)	)	PUNCT
ap-1829	170	39	.	.	PUNCT
ap-1829	171	1	the	the	DET
ap-1829	171	2	so	so	ADV
ap-1829	171	3	-	-	PUNCT
ap-1829	171	4	called	call	VERB
ap-1829	171	5	h	h	NOUN
ap-1829	171	6	-	-	PUNCT
ap-1829	171	7	based	base	VERB
ap-1829	171	8	form	form	NOUN
ap-1829	171	9	of	of	ADP
ap-1829	171	10	the	the	DET
ap-1829	171	11	richards	richard	NOUN
ap-1829	171	12	equation	equation	NOUN
ap-1829	171	13	considers	consider	VERB
ap-1829	171	14	the	the	DET
ap-1829	171	15	mass	mass	ADJ
ap-1829	171	16	term	term	NOUN
ap-1829	171	17	in	in	ADP
ap-1829	171	18	the	the	DET
ap-1829	171	19	form	form	NOUN
ap-1829	171	20	c(h)∂h∂t	c(h)∂h∂t	PROPN
ap-1829	171	21	,	,	PUNCT
ap-1829	171	22	where	where	SCONJ
ap-1829	171	23	c(h	c(h	VERB
ap-1829	171	24	)	)	PUNCT
ap-1829	171	25	=	=	SYM
ap-1829	171	26	θ(h)′	θ(h)′	PROPN
ap-1829	171	27	(	(	PUNCT
ap-1829	171	28	if	if	SCONJ
ap-1829	171	29	zero	zero	NUM
ap-1829	171	30	specific	specific	ADJ
ap-1829	171	31	storage	storage	NOUN
ap-1829	171	32	is	be	AUX
ap-1829	171	33	assumed	assume	VERB
ap-1829	171	34	)	)	PUNCT
ap-1829	171	35	.	.	PUNCT
ap-1829	172	1	due	due	ADP
ap-1829	172	2	to	to	ADP
ap-1829	172	3	the	the	DET
ap-1829	172	4	non	non	NOUN
ap-1829	172	5	-	-	NOUN
ap-1829	172	6	linearities	linearity	NOUN
ap-1829	172	7	involved	involve	VERB
ap-1829	172	8	in	in	ADP
ap-1829	172	9	the	the	DET
ap-1829	172	10	constitutive	constitutive	ADJ
ap-1829	172	11	mass	mass	NOUN
ap-1829	172	12	function	function	NOUN
ap-1829	172	13	,	,	PUNCT
ap-1829	172	14	see	see	VERB
ap-1829	172	15	figure	figure	NOUN
ap-1829	172	16	1	1	NUM
ap-1829	172	17	,	,	PUNCT
ap-1829	172	18	an	an	DET
ap-1829	172	19	efficient	efficient	ADJ
ap-1829	172	20	and	and	CCONJ
ap-1829	172	21	accurate	accurate	ADJ
ap-1829	172	22	time	time	NOUN
ap-1829	172	23	integration	integration	NOUN
ap-1829	172	24	algorithm	algorithm	NOUN
ap-1829	172	25	based	base	VERB
ap-1829	172	26	on	on	ADP
ap-1829	172	27	the	the	DET
ap-1829	172	28	euler	euler	NOUN
ap-1829	172	29	method	method	NOUN
ap-1829	172	30	should	should	AUX
ap-1829	172	31	handle	handle	VERB
ap-1829	172	32	the	the	DET
ap-1829	172	33	selection	selection	NOUN
ap-1829	172	34	of	of	ADP
ap-1829	172	35	an	an	DET
ap-1829	172	36	adaptive	adaptive	ADJ
ap-1829	172	37	time	time	NOUN
ap-1829	172	38	step	step	NOUN
ap-1829	172	39	.	.	PUNCT
ap-1829	173	1	time	time	NOUN
ap-1829	173	2	step	step	NOUN
ap-1829	173	3	adaptivity	adaptivity	NOUN
ap-1829	173	4	has	have	AUX
ap-1829	173	5	been	be	AUX
ap-1829	173	6	the	the	DET
ap-1829	173	7	subject	subject	NOUN
ap-1829	173	8	of	of	ADP
ap-1829	173	9	several	several	ADJ
ap-1829	173	10	works	work	NOUN
ap-1829	173	11	.	.	PUNCT
ap-1829	174	1	most	most	ADJ
ap-1829	174	2	of	of	ADP
ap-1829	174	3	them	they	PRON
ap-1829	174	4	focus	focus	VERB
ap-1829	174	5	on	on	ADP
ap-1829	174	6	limiting	limit	VERB
ap-1829	174	7	the	the	DET
ap-1829	174	8	truncation	truncation	NOUN
ap-1829	174	9	error	error	NOUN
ap-1829	174	10	in	in	ADP
ap-1829	174	11	the	the	DET
ap-1829	174	12	mass	mass	ADJ
ap-1829	174	13	term	term	NOUN
ap-1829	174	14	.	.	PUNCT
ap-1829	175	1	the	the	DET
ap-1829	175	2	original	original	ADJ
ap-1829	175	3	work	work	NOUN
ap-1829	175	4	presenting	present	VERB
ap-1829	175	5	an	an	DET
ap-1829	175	6	implementation	implementation	NOUN
ap-1829	175	7	of	of	ADP
ap-1829	175	8	the	the	DET
ap-1829	175	9	method	method	NOUN
ap-1829	175	10	of	of	ADP
ap-1829	175	11	lines	line	NOUN
ap-1829	175	12	for	for	ADP
ap-1829	175	13	limiting	limit	VERB
ap-1829	175	14	the	the	DET
ap-1829	175	15	truncation	truncation	NOUN
ap-1829	175	16	error	error	NOUN
ap-1829	175	17	of	of	ADP
ap-1829	175	18	the	the	DET
ap-1829	175	19	mixed	mixed	ADJ
ap-1829	175	20	form	form	NOUN
ap-1829	175	21	of	of	ADP
ap-1829	175	22	the	the	DET
ap-1829	175	23	richards	richard	NOUN
ap-1829	175	24	’	'	PUNCT
ap-1829	175	25	equation	equation	NOUN
ap-1829	175	26	was	be	AUX
ap-1829	175	27	published	publish	VERB
ap-1829	175	28	by	by	ADP
ap-1829	175	29	kavetski	kavetski	PROPN
ap-1829	175	30	et	et	PROPN
ap-1829	175	31	al	al	PROPN
ap-1829	175	32	.	.	PUNCT
ap-1829	176	1	[	[	X
ap-1829	176	2	14	14	NUM
ap-1829	176	3	]	]	PUNCT
ap-1829	176	4	.	.	PUNCT
ap-1829	177	1	based	base	VERB
ap-1829	177	2	on	on	ADP
ap-1829	177	3	celia	celia	PROPN
ap-1829	177	4	’s	’s	PART
ap-1829	177	5	work	work	NOUN
ap-1829	177	6	[	[	X
ap-1829	177	7	5	5	X
ap-1829	177	8	]	]	PUNCT
ap-1829	177	9	the	the	DET
ap-1829	177	10	h	h	NOUN
ap-1829	177	11	-	-	PUNCT
ap-1829	177	12	based	base	VERB
ap-1829	177	13	form	form	NOUN
ap-1829	177	14	of	of	ADP
ap-1829	177	15	the	the	DET
ap-1829	177	16	richards	richard	NOUN
ap-1829	177	17	’	'	PUNCT
ap-1829	177	18	equation	equation	NOUN
ap-1829	177	19	,	,	PUNCT
ap-1829	177	20	if	if	SCONJ
ap-1829	177	21	numerically	numerically	ADV
ap-1829	177	22	approximated	approximate	VERB
ap-1829	177	23	by	by	ADP
ap-1829	177	24	the	the	DET
ap-1829	177	25	implicit	implicit	ADJ
ap-1829	177	26	euler	euler	NOUN
ap-1829	177	27	method	method	NOUN
ap-1829	177	28	,	,	PUNCT
ap-1829	177	29	is	be	AUX
ap-1829	177	30	inappropriate	inappropriate	ADJ
ap-1829	177	31	due	due	ADP
ap-1829	177	32	to	to	ADP
ap-1829	177	33	the	the	DET
ap-1829	177	34	huge	huge	ADJ
ap-1829	177	35	inaccuracies	inaccuracy	NOUN
ap-1829	177	36	in	in	ADP
ap-1829	177	37	the	the	DET
ap-1829	177	38	mass	mass	NOUN
ap-1829	177	39	balance	balance	NOUN
ap-1829	177	40	.	.	PUNCT
ap-1829	178	1	however	however	ADV
ap-1829	178	2	,	,	PUNCT
ap-1829	178	3	it	it	PRON
ap-1829	178	4	was	be	AUX
ap-1829	178	5	later	later	ADV
ap-1829	178	6	presented	present	VERB
ap-1829	178	7	by	by	ADP
ap-1829	178	8	tocci	tocci	NOUN
ap-1829	178	9	et	et	PROPN
ap-1829	178	10	al	al	PROPN
ap-1829	178	11	.	.	PUNCT
ap-1829	179	1	[	[	X
ap-1829	179	2	15	15	NUM
ap-1829	179	3	]	]	X
ap-1829	179	4	,	,	PUNCT
ap-1829	179	5	that	that	SCONJ
ap-1829	179	6	limiting	limit	VERB
ap-1829	179	7	the	the	DET
ap-1829	179	8	truncation	truncation	NOUN
ap-1829	179	9	error	error	NOUN
ap-1829	179	10	in	in	ADP
ap-1829	179	11	function	function	NOUN
ap-1829	179	12	h	h	NOUN
ap-1829	179	13	by	by	ADP
ap-1829	179	14	adaptive	adaptive	ADJ
ap-1829	179	15	time	time	NOUN
ap-1829	179	16	step	step	NOUN
ap-1829	179	17	selection	selection	NOUN
ap-1829	179	18	preserves	preserve	VERB
ap-1829	179	19	the	the	DET
ap-1829	179	20	mass	mass	NOUN
ap-1829	179	21	balance	balance	NOUN
ap-1829	179	22	and	and	CCONJ
ap-1829	179	23	the	the	DET
ap-1829	179	24	h	h	NOUN
ap-1829	179	25	-	-	PUNCT
ap-1829	179	26	based	base	VERB
ap-1829	179	27	form	form	NOUN
ap-1829	179	28	of	of	ADP
ap-1829	179	29	the	the	DET
ap-1829	179	30	richards	richard	NOUN
ap-1829	179	31	equation	equation	NOUN
ap-1829	179	32	becomes	become	VERB
ap-1829	179	33	a	a	DET
ap-1829	179	34	suitable	suitable	ADJ
ap-1829	179	35	governing	govern	VERB
ap-1829	179	36	equation	equation	NOUN
ap-1829	179	37	for	for	ADP
ap-1829	179	38	subsurface	subsurface	NOUN
ap-1829	179	39	transport	transport	NOUN
ap-1829	179	40	processes	process	NOUN
ap-1829	179	41	.	.	PUNCT
ap-1829	180	1	in	in	ADP
ap-1829	180	2	the	the	DET
ap-1829	180	3	works	work	NOUN
ap-1829	180	4	of	of	ADP
ap-1829	180	5	both	both	DET
ap-1829	180	6	kavetski	kavetski	PROPN
ap-1829	180	7	et	et	PROPN
ap-1829	180	8	al	al	PROPN
ap-1829	180	9	.	.	PROPN
ap-1829	181	1	and	and	CCONJ
ap-1829	181	2	tocci	tocci	VERB
ap-1829	181	3	et	et	PROPN
ap-1829	181	4	al	al	PROPN
ap-1829	181	5	.	.	PROPN
ap-1829	181	6	,	,	PUNCT
ap-1829	181	7	the	the	DET
ap-1829	181	8	truncation	truncation	NOUN
ap-1829	181	9	error	error	NOUN
ap-1829	181	10	was	be	AUX
ap-1829	181	11	limited	limit	VERB
ap-1829	181	12	by	by	ADP
ap-1829	181	13	applying	apply	VERB
ap-1829	181	14	the	the	DET
ap-1829	181	15	method	method	NOUN
ap-1829	181	16	of	of	ADP
ap-1829	181	17	lines	line	NOUN
ap-1829	181	18	with	with	ADP
ap-1829	181	19	a	a	DET
ap-1829	181	20	fixed	fix	VERB
ap-1829	181	21	order	order	NOUN
ap-1829	181	22	of	of	ADP
ap-1829	181	23	approximation	approximation	NOUN
ap-1829	181	24	.	.	PUNCT
ap-1829	182	1	even	even	ADV
ap-1829	182	2	more	more	ADV
ap-1829	182	3	sophisticated	sophisticated	ADJ
ap-1829	182	4	work	work	NOUN
ap-1829	182	5	was	be	AUX
ap-1829	182	6	later	later	ADV
ap-1829	182	7	published	publish	VERB
ap-1829	182	8	by	by	ADP
ap-1829	182	9	miller	miller	PROPN
ap-1829	182	10	et	et	PROPN
ap-1829	182	11	al	al	PROPN
ap-1829	182	12	.	.	PUNCT
ap-1829	183	1	[	[	X
ap-1829	183	2	16	16	NUM
ap-1829	183	3	]	]	X
ap-1829	183	4	,	,	PUNCT
ap-1829	183	5	where	where	SCONJ
ap-1829	183	6	temporal	temporal	ADJ
ap-1829	183	7	adaption	adaption	NOUN
ap-1829	183	8	was	be	AUX
ap-1829	183	9	accomplished	accomplish	VERB
ap-1829	183	10	by	by	ADP
ap-1829	183	11	variable	variable	ADJ
ap-1829	183	12	order	order	NOUN
ap-1829	183	13	and	and	CCONJ
ap-1829	183	14	variable	variable	ADJ
ap-1829	183	15	step	step	NOUN
ap-1829	183	16	size	size	NOUN
ap-1829	183	17	approximations	approximation	NOUN
ap-1829	183	18	.	.	PUNCT
ap-1829	184	1	the	the	DET
ap-1829	184	2	proposed	propose	VERB
ap-1829	184	3	time	time	NOUN
ap-1829	184	4	integration	integration	NOUN
ap-1829	184	5	method	method	NOUN
ap-1829	184	6	does	do	AUX
ap-1829	184	7	not	not	PART
ap-1829	184	8	limit	limit	VERB
ap-1829	184	9	the	the	DET
ap-1829	184	10	truncation	truncation	NOUN
ap-1829	184	11	error	error	NOUN
ap-1829	184	12	of	of	ADP
ap-1829	184	13	the	the	DET
ap-1829	184	14	time	time	NOUN
ap-1829	184	15	derivative	derivative	ADJ
ap-1829	184	16	term	term	NOUN
ap-1829	184	17	,	,	PUNCT
ap-1829	184	18	as	as	SCONJ
ap-1829	184	19	mentioned	mention	VERB
ap-1829	184	20	in	in	ADP
ap-1829	184	21	the	the	DET
ap-1829	184	22	previous	previous	ADJ
ap-1829	184	23	paragraph	paragraph	NOUN
ap-1829	184	24	.	.	PUNCT
ap-1829	185	1	it	it	PRON
ap-1829	185	2	limits	limit	VERB
ap-1829	185	3	the	the	DET
ap-1829	185	4	error	error	NOUN
ap-1829	185	5	of	of	ADP
ap-1829	185	6	the	the	DET
ap-1829	185	7	h	h	NOUN
ap-1829	185	8	-	-	PUNCT
ap-1829	185	9	based	base	VERB
ap-1829	185	10	approximation	approximation	NOUN
ap-1829	185	11	in	in	ADP
ap-1829	185	12	a	a	DET
ap-1829	185	13	discrete	discrete	ADJ
ap-1829	185	14	analogue	analogue	NOUN
ap-1829	185	15	of	of	ADP
ap-1829	185	16	the	the	DET
ap-1829	185	17	mass	mass	ADJ
ap-1829	185	18	term	term	NOUN
ap-1829	185	19	(	(	PUNCT
ap-1829	185	20	∂θ(h	∂θ(h	NOUN
ap-1829	185	21	)	)	PUNCT
ap-1829	185	22	∂t	∂t	PROPN
ap-1829	185	23	≈	≈	PROPN
ap-1829	185	24	∆θ(h	∆θ(h	PROPN
ap-1829	185	25	)	)	PUNCT
ap-1829	185	26	∆t	∆t	PROPN
ap-1829	186	1	≈	≈	PROPN
ap-1829	186	2	c(h)∆h	c(h)∆h	PROPN
ap-1829	186	3	∆t	∆t	PROPN
ap-1829	186	4	)	)	PUNCT
ap-1829	186	5	.	.	PUNCT
ap-1829	187	1	this	this	DET
ap-1829	187	2	error	error	NOUN
ap-1829	187	3	can	can	AUX
ap-1829	187	4	be	be	AUX
ap-1829	187	5	controlled	control	VERB
ap-1829	187	6	by	by	ADP
ap-1829	187	7	defining	define	VERB
ap-1829	187	8	the	the	DET
ap-1829	187	9	ranges	range	NOUN
ap-1829	187	10	for	for	ADP
ap-1829	187	11	the	the	DET
ap-1829	187	12	shift	shift	NOUN
ap-1829	187	13	of	of	ADP
ap-1829	187	14	the	the	DET
ap-1829	187	15	solution	solution	NOUN
ap-1829	187	16	h	h	NOUN
ap-1829	187	17	in	in	ADP
ap-1829	187	18	two	two	NUM
ap-1829	187	19	sequential	sequential	ADJ
ap-1829	187	20	time	time	NOUN
ap-1829	187	21	steps	step	NOUN
ap-1829	187	22	.	.	PUNCT
ap-1829	188	1	the	the	DET
ap-1829	188	2	method	method	NOUN
ap-1829	188	3	is	be	AUX
ap-1829	188	4	depicted	depict	VERB
ap-1829	188	5	in	in	ADP
ap-1829	188	6	figure	figure	NOUN
ap-1829	188	7	2	2	NUM
ap-1829	188	8	.	.	PUNCT
ap-1829	189	1	the	the	DET
ap-1829	189	2	range	range	NOUN
ap-1829	189	3	of	of	ADP
ap-1829	189	4	the	the	DET
ap-1829	189	5	accepted	accept	VERB
ap-1829	189	6	shift	shift	NOUN
ap-1829	189	7	of	of	ADP
ap-1829	189	8	the	the	DET
ap-1829	189	9	solution	solution	NOUN
ap-1829	189	10	h	h	NOUN
ap-1829	189	11	in	in	ADP
ap-1829	189	12	two	two	NUM
ap-1829	189	13	sequential	sequential	ADJ
ap-1829	189	14	time	time	NOUN
ap-1829	189	15	steps	step	NOUN
ap-1829	189	16	is	be	AUX
ap-1829	189	17	a	a	DET
ap-1829	189	18	function	function	NOUN
ap-1829	189	19	of	of	ADP
ap-1829	189	20	h.	h.	PROPN
ap-1829	189	21	it	it	PRON
ap-1829	189	22	will	will	AUX
ap-1829	189	23	be	be	AUX
ap-1829	189	24	referred	refer	VERB
ap-1829	189	25	to	to	ADP
ap-1829	189	26	as	as	ADP
ap-1829	189	27	hhigh	hhigh	NOUN
ap-1829	189	28	and	and	CCONJ
ap-1829	189	29	hlow	hlow	NOUN
ap-1829	189	30	,	,	PUNCT
ap-1829	189	31	and	and	CCONJ
ap-1829	189	32	thus	thus	ADV
ap-1829	189	33	the	the	DET
ap-1829	189	34	following	follow	VERB
ap-1829	189	35	implicit	implicit	ADJ
ap-1829	189	36	functions	function	NOUN
ap-1829	189	37	are	be	AUX
ap-1829	189	38	formed	form	VERB
ap-1829	189	39	:	:	PUNCT
ap-1829	189	40	|θ(h)−	|θ(h)−	NOUN
ap-1829	189	41	c(h)(h−	c(h)(h−	PROPN
ap-1829	190	1	hlow)−	hlow)−	PROPN
ap-1829	190	2	θ(hlow)|	θ(hlow)|	VERB
ap-1829	190	3	−	−	PROPN
ap-1829	190	4	ε	ε	PROPN
ap-1829	190	5	=	=	SYM
ap-1829	190	6	0	0	NUM
ap-1829	190	7	,	,	PUNCT
ap-1829	190	8	|θ(h	|θ(h	NOUN
ap-1829	190	9	)	)	PUNCT
ap-1829	190	10	+	+	NUM
ap-1829	190	11	c(h)(hhigh	c(h)(hhigh	NOUN
ap-1829	190	12	−	−	PROPN
ap-1829	190	13	h)−	h)−	PROPN
ap-1829	190	14	θ(hhigh)|	θ(hhigh)|	PROPN
ap-1829	190	15	−	−	NOUN
ap-1829	190	16	ε	ε	PROPN
ap-1829	190	17	=	=	SYM
ap-1829	190	18	0	0	PROPN
ap-1829	190	19	,	,	PUNCT
ap-1829	190	20	(	(	PUNCT
ap-1829	190	21	15	15	NUM
ap-1829	190	22	)	)	PUNCT
ap-1829	190	23	where	where	SCONJ
ap-1829	190	24	ε	ε	PROPN
ap-1829	190	25	is	be	AUX
ap-1829	190	26	the	the	DET
ap-1829	190	27	error	error	NOUN
ap-1829	190	28	constant	constant	ADJ
ap-1829	190	29	–	–	PUNCT
ap-1829	190	30	an	an	DET
ap-1829	190	31	error	error	NOUN
ap-1829	190	32	of	of	ADP
ap-1829	190	33	the	the	DET
ap-1829	190	34	first	first	ADJ
ap-1829	190	35	order	order	NOUN
ap-1829	190	36	taylor	taylor	PROPN
ap-1829	190	37	series	series	PROPN
ap-1829	190	38	approximation	approximation	NOUN
ap-1829	190	39	of	of	ADP
ap-1829	190	40	the	the	DET
ap-1829	190	41	constitutive	constitutive	ADJ
ap-1829	190	42	mass	mass	NOUN
ap-1829	190	43	function	function	NOUN
ap-1829	190	44	,	,	PUNCT
ap-1829	190	45	see	see	VERB
ap-1829	190	46	figure	figure	NOUN
ap-1829	190	47	2	2	NUM
ap-1829	190	48	.	.	PUNCT
ap-1829	191	1	this	this	DET
ap-1829	191	2	implicit	implicit	ADJ
ap-1829	191	3	equation	equation	NOUN
ap-1829	191	4	was	be	AUX
ap-1829	191	5	solved	solve	VERB
ap-1829	191	6	by	by	ADP
ap-1829	191	7	the	the	DET
ap-1829	191	8	bisection	bisection	NOUN
ap-1829	191	9	method	method	NOUN
ap-1829	191	10	.	.	PUNCT
ap-1829	192	1	because	because	SCONJ
ap-1829	192	2	it	it	PRON
ap-1829	192	3	is	be	AUX
ap-1829	192	4	a	a	DET
ap-1829	192	5	resource	resource	NOUN
ap-1829	192	6	-	-	PUNCT
ap-1829	192	7	consuming	consume	VERB
ap-1829	192	8	computer	computer	NOUN
ap-1829	192	9	operation	operation	NOUN
ap-1829	192	10	,	,	PUNCT
ap-1829	192	11	the	the	DET
ap-1829	192	12	equation	equation	NOUN
ap-1829	192	13	is	be	AUX
ap-1829	192	14	tabelized	tabelize	VERB
ap-1829	192	15	by	by	ADP
ap-1829	192	16	the	the	DET
ap-1829	192	17	initialization	initialization	NOUN
ap-1829	192	18	procedures	procedure	NOUN
ap-1829	192	19	.	.	PUNCT
ap-1829	193	1	starting	start	VERB
ap-1829	193	2	with	with	ADP
ap-1829	193	3	some	some	DET
ap-1829	193	4	initial	initial	ADJ
ap-1829	193	5	time	time	NOUN
ap-1829	193	6	step	step	NOUN
ap-1829	193	7	guess	guess	NOUN
ap-1829	193	8	,	,	PUNCT
ap-1829	193	9	the	the	DET
ap-1829	193	10	solution	solution	NOUN
ap-1829	193	11	is	be	AUX
ap-1829	193	12	checked	check	VERB
ap-1829	193	13	always	always	ADV
ap-1829	193	14	at	at	ADP
ap-1829	193	15	the	the	DET
ap-1829	193	16	first	first	ADJ
ap-1829	193	17	and	and	CCONJ
ap-1829	193	18	last	last	ADJ
ap-1829	193	19	picard	picard	NOUN
ap-1829	193	20	iteration	iteration	NOUN
ap-1829	193	21	level	level	NOUN
ap-1829	193	22	(	(	PUNCT
ap-1829	193	23	the	the	DET
ap-1829	193	24	last	last	ADJ
ap-1829	193	25	iteration	iteration	NOUN
ap-1829	193	26	level	level	NOUN
ap-1829	193	27	of	of	ADP
ap-1829	193	28	the	the	DET
ap-1829	193	29	picard	picard	NOUN
ap-1829	193	30	method	method	NOUN
ap-1829	193	31	is	be	AUX
ap-1829	193	32	the	the	DET
ap-1829	193	33	level	level	NOUN
ap-1829	193	34	,	,	PUNCT
ap-1829	193	35	where	where	SCONJ
ap-1829	193	36	the	the	DET
ap-1829	193	37	distance	distance	NOUN
ap-1829	193	38	between	between	ADP
ap-1829	193	39	two	two	NUM
ap-1829	193	40	consecutive	consecutive	ADJ
ap-1829	193	41	picard	picard	NOUN
ap-1829	193	42	’s	’s	PART
ap-1829	193	43	approximations	approximation	NOUN
ap-1829	193	44	is	be	AUX
ap-1829	193	45	lower	low	ADJ
ap-1829	193	46	than	than	ADP
ap-1829	193	47	a	a	DET
ap-1829	193	48	certain	certain	ADJ
ap-1829	193	49	value	value	NOUN
ap-1829	193	50	(	(	PUNCT
ap-1829	193	51	‖hn+1	‖hn+1	PUNCT
ap-1829	193	52	k+1	k+1	X
ap-1829	193	53	−	−	PROPN
ap-1829	193	54	h	h	NOUN
ap-1829	193	55	n+1	n+1	PROPN
ap-1829	193	56	k	k	X
ap-1829	193	57	‖2	‖2	NOUN
ap-1829	193	58	<	<	X
ap-1829	193	59	ε	ε	PROPN
ap-1829	193	60	–	–	PUNCT
ap-1829	193	61	see	see	VERB
ap-1829	193	62	section	section	NOUN
ap-1829	193	63	2.1	2.1	NUM
ap-1829	193	64	)	)	PUNCT
ap-1829	193	65	.	.	PUNCT
ap-1829	194	1	the	the	DET
ap-1829	194	2	range	range	NOUN
ap-1829	194	3	〈	〈	PROPN
ap-1829	194	4	hlow	hlow	NOUN
ap-1829	194	5	,	,	PUNCT
ap-1829	194	6	hhigh	hhigh	PROPN
ap-1829	194	7	〉	〉	PROPN
ap-1829	194	8	is	be	AUX
ap-1829	194	9	evaluated	evaluate	VERB
ap-1829	194	10	for	for	ADP
ap-1829	194	11	all	all	DET
ap-1829	194	12	mesh	mesh	NOUN
ap-1829	194	13	nodal	nodal	NOUN
ap-1829	194	14	values	value	NOUN
ap-1829	194	15	by	by	ADP
ap-1829	194	16	solving	solve	VERB
ap-1829	194	17	equation	equation	NOUN
ap-1829	194	18	(	(	PUNCT
ap-1829	194	19	15	15	NUM
ap-1829	194	20	)	)	PUNCT
ap-1829	194	21	,	,	PUNCT
ap-1829	194	22	where	where	SCONJ
ap-1829	194	23	value	value	NOUN
ap-1829	194	24	h	h	NOUN
ap-1829	194	25	is	be	AUX
ap-1829	194	26	supplied	supply	VERB
ap-1829	194	27	by	by	ADP
ap-1829	194	28	the	the	DET
ap-1829	194	29	previous	previous	ADJ
ap-1829	194	30	time	time	NOUN
ap-1829	194	31	step	step	NOUN
ap-1829	194	32	function	function	NOUN
ap-1829	194	33	.	.	PUNCT
ap-1829	195	1	it	it	PRON
ap-1829	195	2	is	be	AUX
ap-1829	195	3	apparent	apparent	ADJ
ap-1829	195	4	that	that	SCONJ
ap-1829	195	5	evaluating	evaluate	VERB
ap-1829	195	6	this	this	DET
ap-1829	195	7	implicit	implicit	ADJ
ap-1829	195	8	function	function	NOUN
ap-1829	195	9	directly	directly	ADV
ap-1829	195	10	at	at	ADP
ap-1829	195	11	each	each	DET
ap-1829	195	12	time	time	NOUN
ap-1829	195	13	350	350	NUM
ap-1829	195	14	vol	vol	NOUN
ap-1829	195	15	.	.	PUNCT
ap-1829	196	1	53	53	NUM
ap-1829	196	2	no	no	NOUN
ap-1829	196	3	.	.	PUNCT
ap-1829	197	1	4/2013	4/2013	NOUN
ap-1829	197	2	algorithms	algorithm	NOUN
ap-1829	197	3	for	for	ADP
ap-1829	197	4	solving	solve	VERB
ap-1829	197	5	darcian	darcian	NOUN
ap-1829	197	6	flow	flow	NOUN
ap-1829	197	7	in	in	ADP
ap-1829	197	8	structured	structured	ADJ
ap-1829	197	9	porous	porous	ADJ
ap-1829	197	10	media	medium	NOUN
ap-1829	197	11	figure	figure	NOUN
ap-1829	197	12	3	3	NUM
ap-1829	197	13	.	.	PUNCT
ap-1829	197	14	scheme	scheme	NOUN
ap-1829	197	15	of	of	ADP
ap-1829	197	16	the	the	DET
ap-1829	197	17	one	one	NUM
ap-1829	197	18	-	-	PUNCT
ap-1829	197	19	dimensional	dimensional	ADJ
ap-1829	197	20	vertical	vertical	ADJ
ap-1829	197	21	infiltration	infiltration	NOUN
ap-1829	197	22	experiment	experiment	NOUN
ap-1829	197	23	.	.	PUNCT
ap-1829	198	1	step	step	NOUN
ap-1829	198	2	for	for	ADP
ap-1829	198	3	each	each	DET
ap-1829	198	4	nodal	nodal	NOUN
ap-1829	198	5	value	value	NOUN
ap-1829	198	6	would	would	AUX
ap-1829	198	7	markedly	markedly	ADV
ap-1829	198	8	influence	influence	VERB
ap-1829	198	9	the	the	DET
ap-1829	198	10	performance	performance	NOUN
ap-1829	198	11	of	of	ADP
ap-1829	198	12	the	the	DET
ap-1829	198	13	code	code	NOUN
ap-1829	198	14	,	,	PUNCT
ap-1829	198	15	and	and	CCONJ
ap-1829	198	16	therefore	therefore	ADV
ap-1829	198	17	an	an	DET
ap-1829	198	18	efficient	efficient	ADJ
ap-1829	198	19	and	and	CCONJ
ap-1829	198	20	simple	simple	ADJ
ap-1829	198	21	algorithm	algorithm	NOUN
ap-1829	198	22	that	that	PRON
ap-1829	198	23	searches	search	VERB
ap-1829	198	24	the	the	DET
ap-1829	198	25	values	value	NOUN
ap-1829	198	26	in	in	ADP
ap-1829	198	27	a	a	DET
ap-1829	198	28	table	table	NOUN
ap-1829	198	29	was	be	AUX
ap-1829	198	30	constructed	construct	VERB
ap-1829	198	31	.	.	PUNCT
ap-1829	199	1	the	the	DET
ap-1829	199	2	solutions	solution	NOUN
ap-1829	199	3	of	of	ADP
ap-1829	199	4	(	(	PUNCT
ap-1829	199	5	15	15	NUM
ap-1829	199	6	)	)	PUNCT
ap-1829	199	7	(	(	PUNCT
ap-1829	199	8	hlow	hlow	NOUN
ap-1829	199	9	and	and	CCONJ
ap-1829	199	10	hhigh	hhigh	NOUN
ap-1829	199	11	)	)	PUNCT
ap-1829	199	12	are	be	AUX
ap-1829	199	13	precalculated	precalculate	VERB
ap-1829	199	14	for	for	ADP
ap-1829	199	15	several	several	ADJ
ap-1829	199	16	discrete	discrete	ADJ
ap-1829	199	17	values	value	NOUN
ap-1829	199	18	of	of	ADP
ap-1829	199	19	the	the	DET
ap-1829	199	20	h	h	NOUN
ap-1829	199	21	function	function	NOUN
ap-1829	199	22	within	within	ADP
ap-1829	199	23	some	some	DET
ap-1829	199	24	user	user	NOUN
ap-1829	199	25	defined	define	VERB
ap-1829	199	26	ranges	range	NOUN
ap-1829	199	27	and	and	CCONJ
ap-1829	199	28	density	density	NOUN
ap-1829	199	29	.	.	PUNCT
ap-1829	200	1	then	then	ADV
ap-1829	200	2	the	the	DET
ap-1829	200	3	solution	solution	NOUN
ap-1829	200	4	of	of	ADP
ap-1829	200	5	(	(	PUNCT
ap-1829	200	6	15	15	NUM
ap-1829	200	7	)	)	PUNCT
ap-1829	200	8	for	for	ADP
ap-1829	200	9	any	any	DET
ap-1829	200	10	arbitrary	arbitrary	ADJ
ap-1829	200	11	h	h	NOUN
ap-1829	200	12	value	value	NOUN
ap-1829	200	13	is	be	AUX
ap-1829	200	14	obtained	obtain	VERB
ap-1829	200	15	by	by	ADP
ap-1829	200	16	the	the	DET
ap-1829	200	17	following	following	ADJ
ap-1829	200	18	algorithm	algorithm	NOUN
ap-1829	200	19	:	:	PUNCT
ap-1829	200	20	•	•	ADP
ap-1829	200	21	the	the	DET
ap-1829	200	22	h	h	NOUN
ap-1829	200	23	value	value	NOUN
ap-1829	200	24	is	be	AUX
ap-1829	200	25	converted	convert	VERB
ap-1829	200	26	into	into	ADP
ap-1829	200	27	an	an	DET
ap-1829	200	28	integer	integer	NOUN
ap-1829	200	29	value	value	NOUN
ap-1829	200	30	that	that	PRON
ap-1829	200	31	points	point	VERB
ap-1829	200	32	the	the	DET
ap-1829	200	33	position	position	NOUN
ap-1829	200	34	of	of	ADP
ap-1829	200	35	the	the	DET
ap-1829	200	36	nearest	near	ADJ
ap-1829	200	37	smallest	small	ADJ
ap-1829	200	38	discrete	discrete	ADJ
ap-1829	200	39	value	value	NOUN
ap-1829	200	40	of	of	ADP
ap-1829	200	41	the	the	DET
ap-1829	200	42	tabelized	tabelize	VERB
ap-1829	200	43	function	function	NOUN
ap-1829	200	44	(	(	PUNCT
ap-1829	200	45	15	15	NUM
ap-1829	200	46	)	)	PUNCT
ap-1829	200	47	,	,	PUNCT
ap-1829	200	48	•	•	X
ap-1829	200	49	then	then	ADV
ap-1829	200	50	the	the	DET
ap-1829	200	51	values	value	NOUN
ap-1829	200	52	of	of	ADP
ap-1829	200	53	solutions	solution	NOUN
ap-1829	200	54	hlow	hlow	NOUN
ap-1829	200	55	and	and	CCONJ
ap-1829	200	56	hhigh	hhigh	NOUN
ap-1829	200	57	are	be	AUX
ap-1829	200	58	obtained	obtain	VERB
ap-1829	200	59	by	by	ADP
ap-1829	200	60	a	a	DET
ap-1829	200	61	linear	linear	ADJ
ap-1829	200	62	interpolation	interpolation	NOUN
ap-1829	200	63	between	between	ADP
ap-1829	200	64	the	the	DET
ap-1829	200	65	nearest	near	ADJ
ap-1829	200	66	discrete	discrete	ADJ
ap-1829	200	67	values	value	NOUN
ap-1829	200	68	of	of	ADP
ap-1829	200	69	the	the	DET
ap-1829	200	70	tabelized	tabelize	VERB
ap-1829	200	71	function	function	NOUN
ap-1829	200	72	(	(	PUNCT
ap-1829	200	73	15	15	NUM
ap-1829	200	74	)	)	PUNCT
ap-1829	200	75	.	.	PUNCT
ap-1829	201	1	in	in	ADP
ap-1829	201	2	order	order	NOUN
ap-1829	201	3	to	to	PART
ap-1829	201	4	speed	speed	VERB
ap-1829	201	5	up	up	ADP
ap-1829	201	6	the	the	DET
ap-1829	201	7	code	code	NOUN
ap-1829	201	8	performance	performance	NOUN
ap-1829	201	9	this	this	DET
ap-1829	201	10	technique	technique	NOUN
ap-1829	201	11	is	be	AUX
ap-1829	201	12	also	also	ADV
ap-1829	201	13	offered	offer	VERB
ap-1829	201	14	to	to	PART
ap-1829	201	15	evaluate	evaluate	VERB
ap-1829	201	16	values	value	NOUN
ap-1829	201	17	for	for	ADP
ap-1829	201	18	all	all	DET
ap-1829	201	19	material	material	NOUN
ap-1829	201	20	functions	function	NOUN
ap-1829	201	21	with	with	ADP
ap-1829	201	22	real	real	ADJ
ap-1829	201	23	exponents	exponent	NOUN
ap-1829	201	24	.	.	PUNCT
ap-1829	202	1	the	the	DET
ap-1829	202	2	user	user	NOUN
ap-1829	202	3	can	can	AUX
ap-1829	202	4	switch	switch	VERB
ap-1829	202	5	between	between	ADP
ap-1829	202	6	this	this	DET
ap-1829	202	7	approximate	approximate	ADJ
ap-1829	202	8	and	and	CCONJ
ap-1829	202	9	direct	direct	ADJ
ap-1829	202	10	material	material	NOUN
ap-1829	202	11	function	function	NOUN
ap-1829	202	12	evaluation	evaluation	NOUN
ap-1829	202	13	method	method	NOUN
ap-1829	202	14	.	.	PUNCT
ap-1829	203	1	this	this	DET
ap-1829	203	2	method	method	NOUN
ap-1829	203	3	was	be	AUX
ap-1829	203	4	tested	test	VERB
ap-1829	203	5	on	on	ADP
ap-1829	203	6	a	a	DET
ap-1829	203	7	standard	standard	ADJ
ap-1829	203	8	laptop	laptop	NOUN
ap-1829	203	9	(	(	PUNCT
ap-1829	203	10	intel	intel	PROPN
ap-1829	203	11	cpu	cpu	PROPN
ap-1829	203	12	1.6ghz	1.6ghz	NUM
ap-1829	203	13	)	)	PUNCT
ap-1829	203	14	for	for	ADP
ap-1829	203	15	a	a	DET
ap-1829	203	16	mesh	mesh	NOUN
ap-1829	203	17	of	of	ADP
ap-1829	203	18	106	106	NUM
ap-1829	203	19	elements	element	NOUN
ap-1829	203	20	with	with	ADP
ap-1829	203	21	the	the	DET
ap-1829	203	22	nine	nine	NUM
ap-1829	203	23	points	point	NOUN
ap-1829	203	24	integration	integration	NOUN
ap-1829	203	25	method	method	NOUN
ap-1829	203	26	.	.	PUNCT
ap-1829	204	1	if	if	SCONJ
ap-1829	204	2	constitutive	constitutive	ADJ
ap-1829	204	3	functions	function	NOUN
ap-1829	204	4	were	be	AUX
ap-1829	204	5	evaluated	evaluate	VERB
ap-1829	204	6	directly	directly	ADV
ap-1829	204	7	,	,	PUNCT
ap-1829	204	8	the	the	DET
ap-1829	204	9	finite	finite	PROPN
ap-1829	204	10	element	element	NOUN
ap-1829	204	11	method	method	NOUN
ap-1829	204	12	matrix	matrix	NOUN
ap-1829	204	13	was	be	AUX
ap-1829	204	14	built	build	VERB
ap-1829	204	15	in	in	ADP
ap-1829	204	16	approximately	approximately	ADV
ap-1829	204	17	20	20	NUM
ap-1829	204	18	min	min	NOUN
ap-1829	204	19	.	.	PUNCT
ap-1829	204	20	;	;	PUNCT
ap-1829	204	21	if	if	SCONJ
ap-1829	204	22	constitutive	constitutive	ADJ
ap-1829	204	23	functions	function	NOUN
ap-1829	204	24	were	be	AUX
ap-1829	204	25	tabelized	tabelize	VERB
ap-1829	204	26	as	as	ADP
ap-1829	204	27	described	describe	VERB
ap-1829	204	28	,	,	PUNCT
ap-1829	204	29	the	the	DET
ap-1829	204	30	solution	solution	NOUN
ap-1829	204	31	matrix	matrix	NOUN
ap-1829	204	32	was	be	AUX
ap-1829	204	33	created	create	VERB
ap-1829	204	34	in	in	ADP
ap-1829	204	35	approximately	approximately	ADV
ap-1829	204	36	one	one	NUM
ap-1829	204	37	minute	minute	NOUN
ap-1829	204	38	.	.	PUNCT
ap-1829	205	1	the	the	DET
ap-1829	205	2	array	array	PROPN
ap-1829	205	3	initialization	initialization	NOUN
ap-1829	205	4	took	take	VERB
ap-1829	205	5	not	not	PART
ap-1829	205	6	more	more	ADJ
ap-1829	205	7	than	than	ADP
ap-1829	205	8	a	a	DET
ap-1829	205	9	few	few	ADJ
ap-1829	205	10	seconds	second	NOUN
ap-1829	205	11	.	.	PUNCT
ap-1829	206	1	this	this	DET
ap-1829	206	2	experiment	experiment	NOUN
ap-1829	206	3	involved	involve	VERB
ap-1829	206	4	only	only	ADV
ap-1829	206	5	the	the	DET
ap-1829	206	6	van	van	PROPN
ap-1829	206	7	genuchten	genuchten	NOUN
ap-1829	206	8	’s	’s	PART
ap-1829	206	9	constitutive	constitutive	ADJ
ap-1829	206	10	functions	function	NOUN
ap-1829	206	11	without	without	ADP
ap-1829	206	12	evaluating	evaluate	VERB
ap-1829	206	13	the	the	DET
ap-1829	206	14	function	function	NOUN
ap-1829	206	15	(	(	PUNCT
ap-1829	206	16	15	15	NUM
ap-1829	206	17	)	)	PUNCT
ap-1829	207	1	[	[	X
ap-1829	207	2	24	24	NUM
ap-1829	207	3	]	]	PUNCT
ap-1829	207	4	.	.	PUNCT
ap-1829	208	1	if	if	SCONJ
ap-1829	208	2	some	some	DET
ap-1829	208	3	nodal	nodal	NOUN
ap-1829	208	4	value	value	NOUN
ap-1829	208	5	in	in	ADP
ap-1829	208	6	a	a	DET
ap-1829	208	7	newly	newly	ADV
ap-1829	208	8	evaluated	evaluate	VERB
ap-1829	208	9	solution	solution	NOUN
ap-1829	208	10	falls	fall	VERB
ap-1829	208	11	beyond	beyond	ADP
ap-1829	208	12	the	the	DET
ap-1829	208	13	range	range	NOUN
ap-1829	208	14	〈	〈	PROPN
ap-1829	208	15	hlow	hlow	NOUN
ap-1829	208	16	,	,	PUNCT
ap-1829	208	17	hhigh	hhigh	PROPN
ap-1829	208	18	〉	〉	PROPN
ap-1829	208	19	,	,	PUNCT
ap-1829	208	20	the	the	DET
ap-1829	208	21	new	new	ADJ
ap-1829	208	22	time	time	NOUN
ap-1829	208	23	step	step	NOUN
ap-1829	208	24	solution	solution	NOUN
ap-1829	208	25	is	be	AUX
ap-1829	208	26	rejected	reject	VERB
ap-1829	208	27	,	,	PUNCT
ap-1829	208	28	the	the	DET
ap-1829	208	29	time	time	NOUN
ap-1829	208	30	step	step	NOUN
ap-1829	208	31	is	be	AUX
ap-1829	208	32	decreased	decrease	VERB
ap-1829	208	33	,	,	PUNCT
ap-1829	208	34	and	and	CCONJ
ap-1829	208	35	the	the	DET
ap-1829	208	36	new	new	ADJ
ap-1829	208	37	solution	solution	NOUN
ap-1829	208	38	is	be	AUX
ap-1829	208	39	tested	test	VERB
ap-1829	208	40	again	again	ADV
ap-1829	208	41	–	–	PUNCT
ap-1829	208	42	until	until	SCONJ
ap-1829	208	43	the	the	DET
ap-1829	208	44	criterion	criterion	NOUN
ap-1829	208	45	is	be	AUX
ap-1829	208	46	fulfilled	fulfil	VERB
ap-1829	208	47	.	.	PUNCT
ap-1829	209	1	it	it	PRON
ap-1829	209	2	can	can	AUX
ap-1829	209	3	be	be	AUX
ap-1829	209	4	assumed	assume	VERB
ap-1829	209	5	that	that	SCONJ
ap-1829	209	6	the	the	DET
ap-1829	209	7	constant	constant	ADJ
ap-1829	209	8	ε	ε	PROPN
ap-1829	209	9	controls	control	VERB
ap-1829	209	10	the	the	DET
ap-1829	209	11	error	error	NOUN
ap-1829	209	12	caused	cause	VERB
ap-1829	209	13	by	by	ADP
ap-1829	209	14	discretization	discretization	NOUN
ap-1829	209	15	of	of	ADP
ap-1829	209	16	the	the	DET
ap-1829	209	17	mass	mass	ADJ
ap-1829	209	18	term	term	NOUN
ap-1829	209	19	in	in	ADP
ap-1829	209	20	the	the	DET
ap-1829	209	21	h	h	NOUN
ap-1829	209	22	-	-	PUNCT
ap-1829	209	23	based	base	VERB
ap-1829	209	24	form	form	NOUN
ap-1829	209	25	of	of	ADP
ap-1829	209	26	the	the	DET
ap-1829	209	27	richards	richard	NOUN
ap-1829	209	28	equation.the	equation.the	DET
ap-1829	209	29	method	method	NOUN
ap-1829	209	30	will	will	AUX
ap-1829	209	31	be	be	AUX
ap-1829	209	32	further	far	ADV
ap-1829	209	33	referred	refer	VERB
ap-1829	209	34	as	as	ADP
ap-1829	209	35	to	to	ADP
ap-1829	209	36	the	the	DET
ap-1829	209	37	mass	mass	ADJ
ap-1829	209	38	curve	curve	NOUN
ap-1829	209	39	zone	zone	NOUN
ap-1829	209	40	approach	approach	NOUN
ap-1829	209	41	.	.	PUNCT
ap-1829	210	1	it	it	PRON
ap-1829	210	2	should	should	AUX
ap-1829	210	3	be	be	AUX
ap-1829	210	4	emphasized	emphasize	VERB
ap-1829	210	5	that	that	SCONJ
ap-1829	210	6	equation	equation	NOUN
ap-1829	210	7	(	(	PUNCT
ap-1829	210	8	15	15	NUM
ap-1829	210	9	)	)	PUNCT
ap-1829	210	10	has	have	VERB
ap-1829	210	11	a	a	DET
ap-1829	210	12	unique	unique	ADJ
ap-1829	210	13	solution	solution	NOUN
ap-1829	210	14	only	only	ADV
ap-1829	210	15	for	for	ADP
ap-1829	210	16	monotone	monotone	ADJ
ap-1829	210	17	convex	convex	NOUN
ap-1829	210	18	retention	retention	NOUN
ap-1829	210	19	curves	curve	NOUN
ap-1829	210	20	,	,	PUNCT
ap-1829	210	21	e.g.	e.g.	ADV
ap-1829	210	22	the	the	DET
ap-1829	210	23	gardner	gardner	NOUN
ap-1829	210	24	’s	’s	PART
ap-1829	210	25	model	model	NOUN
ap-1829	210	26	[	[	X
ap-1829	210	27	17	17	NUM
ap-1829	210	28	]	]	PUNCT
ap-1829	210	29	.	.	PUNCT
ap-1829	211	1	for	for	ADP
ap-1829	211	2	the	the	DET
ap-1829	211	3	van	van	PROPN
ap-1829	211	4	genuchten	genuchten	ADJ
ap-1829	211	5	function	function	NOUN
ap-1829	211	6	this	this	DET
ap-1829	211	7	algorithm	algorithm	NOUN
ap-1829	211	8	uses	use	VERB
ap-1829	211	9	only	only	ADV
ap-1829	211	10	the	the	DET
ap-1829	211	11	solution	solution	NOUN
ap-1829	211	12	hlow	hlow	NOUN
ap-1829	211	13	,	,	PUNCT
ap-1829	211	14	resp	resp	NOUN
ap-1829	211	15	.	.	PUNCT
ap-1829	212	1	hhigh	hhigh	PROPN
ap-1829	212	2	,	,	PUNCT
ap-1829	212	3	which	which	PRON
ap-1829	212	4	is	be	AUX
ap-1829	212	5	closer	close	ADJ
ap-1829	212	6	to	to	ADP
ap-1829	212	7	the	the	DET
ap-1829	212	8	particular	particular	ADJ
ap-1829	212	9	evaluated	evaluate	VERB
ap-1829	212	10	h	h	NOUN
ap-1829	212	11	value	value	NOUN
ap-1829	212	12	.	.	PUNCT
ap-1829	213	1	3.1	3.1	NUM
ap-1829	213	2	.	.	PUNCT
ap-1829	213	3	case	case	NOUN
ap-1829	213	4	study	study	VERB
ap-1829	213	5	a	a	DET
ap-1829	213	6	simulation	simulation	NOUN
ap-1829	213	7	of	of	ADP
ap-1829	213	8	a	a	DET
ap-1829	213	9	vertical	vertical	ADJ
ap-1829	213	10	one	one	NUM
ap-1829	213	11	-	-	PUNCT
ap-1829	213	12	dimensional	dimensional	ADJ
ap-1829	213	13	infiltration	infiltration	NOUN
ap-1829	213	14	experiment	experiment	NOUN
ap-1829	213	15	was	be	AUX
ap-1829	213	16	conducted	conduct	VERB
ap-1829	213	17	,	,	PUNCT
ap-1829	213	18	see	see	VERB
ap-1829	213	19	figure	figure	NOUN
ap-1829	213	20	3	3	NUM
ap-1829	213	21	.	.	PUNCT
ap-1829	214	1	for	for	ADP
ap-1829	214	2	this	this	DET
ap-1829	214	3	numerical	numerical	ADJ
ap-1829	214	4	example	example	NOUN
ap-1829	214	5	,	,	PUNCT
ap-1829	214	6	the	the	DET
ap-1829	214	7	dual	dual	ADJ
ap-1829	214	8	porosity	porosity	NOUN
ap-1829	214	9	approach	approach	NOUN
ap-1829	214	10	was	be	AUX
ap-1829	214	11	found	find	VERB
ap-1829	214	12	to	to	PART
ap-1829	214	13	be	be	AUX
ap-1829	214	14	useless	useless	ADJ
ap-1829	214	15	for	for	ADP
ap-1829	214	16	demonstration	demonstration	NOUN
ap-1829	214	17	purposes	purpose	NOUN
ap-1829	214	18	.	.	PUNCT
ap-1829	215	1	the	the	DET
ap-1829	215	2	problem	problem	NOUN
ap-1829	215	3	was	be	AUX
ap-1829	215	4	therefore	therefore	ADV
ap-1829	215	5	evaluated	evaluate	VERB
ap-1829	215	6	on	on	ADP
ap-1829	215	7	the	the	DET
ap-1829	215	8	classical	classical	ADJ
ap-1829	215	9	richards	richard	NOUN
ap-1829	215	10	equation	equation	NOUN
ap-1829	215	11	only	only	ADV
ap-1829	215	12	.	.	PUNCT
ap-1829	216	1	the	the	DET
ap-1829	216	2	selected	select	VERB
ap-1829	216	3	flow	flow	NOUN
ap-1829	216	4	domain	domain	NOUN
ap-1829	216	5	ω	ω	NOUN
ap-1829	216	6	was	be	AUX
ap-1829	216	7	a	a	DET
ap-1829	216	8	porous	porous	ADJ
ap-1829	216	9	material	material	NOUN
ap-1829	216	10	block	block	NOUN
ap-1829	216	11	5	5	NUM
ap-1829	216	12	m	m	NOUN
ap-1829	216	13	in	in	ADP
ap-1829	216	14	length	length	NOUN
ap-1829	216	15	and	and	CCONJ
ap-1829	216	16	of	of	ADP
ap-1829	216	17	infinite	infinite	ADJ
ap-1829	216	18	width	width	NOUN
ap-1829	216	19	.	.	PUNCT
ap-1829	217	1	thus	thus	ADV
ap-1829	217	2	only	only	ADV
ap-1829	217	3	vertical	vertical	ADJ
ap-1829	217	4	one	one	NUM
ap-1829	217	5	-	-	PUNCT
ap-1829	217	6	dimensional	dimensional	ADJ
ap-1829	217	7	flow	flow	NOUN
ap-1829	217	8	was	be	AUX
ap-1829	217	9	taking	take	VERB
ap-1829	217	10	place	place	NOUN
ap-1829	217	11	.	.	PUNCT
ap-1829	218	1	porous	porous	ADJ
ap-1829	218	2	material	material	NOUN
ap-1829	218	3	properties	property	NOUN
ap-1829	218	4	(	(	PUNCT
ap-1829	218	5	parameters	parameter	NOUN
ap-1829	218	6	of	of	ADP
ap-1829	218	7	the	the	DET
ap-1829	218	8	van	van	PROPN
ap-1829	218	9	genuchten	genuchten	NOUN
ap-1829	218	10	and	and	CCONJ
ap-1829	218	11	mualem	mualem	NOUN
ap-1829	218	12	constitutive	constitutive	ADJ
ap-1829	218	13	functions	function	NOUN
ap-1829	218	14	)	)	PUNCT
ap-1829	218	15	were	be	AUX
ap-1829	218	16	assumed	assume	VERB
ap-1829	218	17	for	for	ADP
ap-1829	218	18	highly	highly	ADV
ap-1829	218	19	permeable	permeable	ADJ
ap-1829	218	20	sandstone	sandstone	NOUN
ap-1829	218	21	(	(	PUNCT
ap-1829	218	22	α	α	NOUN
ap-1829	218	23	=	=	SYM
ap-1829	218	24	0.075	0.075	NUM
ap-1829	218	25	cm−1	cm−1	NOUN
ap-1829	218	26	,	,	PUNCT
ap-1829	218	27	n	n	NOUN
ap-1829	218	28	=	=	NOUN
ap-1829	218	29	1.89	1.89	NUM
ap-1829	218	30	,	,	PUNCT
ap-1829	218	31	m	m	VERB
ap-1829	218	32	=	=	NOUN
ap-1829	218	33	0.47	0.47	NUM
ap-1829	218	34	,	,	PUNCT
ap-1829	218	35	ks	ks	NOUN
ap-1829	218	36	=	=	PUNCT
ap-1829	218	37	4.42	4.42	NUM
ap-1829	218	38	cmh−1	cmh−1	NOUN
ap-1829	218	39	)	)	PUNCT
ap-1829	218	40	.	.	PUNCT
ap-1829	219	1	the	the	DET
ap-1829	219	2	domain	domain	NOUN
ap-1829	219	3	was	be	AUX
ap-1829	219	4	discretized	discretize	VERB
ap-1829	219	5	by	by	ADP
ap-1829	219	6	a	a	DET
ap-1829	219	7	uniform	uniform	ADJ
ap-1829	219	8	mesh	mesh	NOUN
ap-1829	219	9	of	of	ADP
ap-1829	219	10	grid	grid	NOUN
ap-1829	219	11	size	size	NOUN
ap-1829	219	12	5	5	NUM
ap-1829	219	13	cm	cm	NOUN
ap-1829	219	14	.	.	PUNCT
ap-1829	220	1	the	the	DET
ap-1829	220	2	non	non	ADJ
ap-1829	220	3	-	-	ADJ
ap-1829	220	4	linear	linear	ADJ
ap-1829	220	5	richards	richard	NOUN
ap-1829	220	6	equation	equation	NOUN
ap-1829	220	7	operator	operator	NOUN
ap-1829	220	8	was	be	AUX
ap-1829	220	9	linearized	linearize	VERB
ap-1829	220	10	by	by	ADP
ap-1829	220	11	the	the	DET
ap-1829	220	12	picard	picard	NOUN
ap-1829	220	13	method	method	NOUN
ap-1829	220	14	,	,	PUNCT
ap-1829	220	15	the	the	DET
ap-1829	220	16	stopping	stop	VERB
ap-1829	220	17	criterion	criterion	NOUN
ap-1829	220	18	was	be	AUX
ap-1829	220	19	defined	define	VERB
ap-1829	220	20	as	as	ADP
ap-1829	220	21	‖hk+1	‖hk+1	PUNCT
ap-1829	220	22	−	−	PROPN
ap-1829	220	23	hk‖2	hk‖2	ADJ
ap-1829	220	24	≤	≤	NOUN
ap-1829	220	25	10−3	10−3	NUM
ap-1829	220	26	,	,	PUNCT
ap-1829	220	27	(	(	PUNCT
ap-1829	220	28	16	16	NUM
ap-1829	220	29	)	)	PUNCT
ap-1829	220	30	where	where	SCONJ
ap-1829	220	31	subscript	subscript	NOUN
ap-1829	220	32	k	k	PROPN
ap-1829	220	33	is	be	AUX
ap-1829	220	34	an	an	DET
ap-1829	220	35	iteration	iteration	NOUN
ap-1829	220	36	level	level	NOUN
ap-1829	220	37	.	.	PUNCT
ap-1829	221	1	in	in	ADP
ap-1829	221	2	order	order	NOUN
ap-1829	221	3	to	to	PART
ap-1829	221	4	evaluate	evaluate	VERB
ap-1829	221	5	the	the	DET
ap-1829	221	6	method	method	NOUN
ap-1829	221	7	presented	present	VERB
ap-1829	221	8	here	here	ADV
ap-1829	221	9	,	,	PUNCT
ap-1829	221	10	the	the	DET
ap-1829	221	11	simulation	simulation	NOUN
ap-1829	221	12	was	be	AUX
ap-1829	221	13	performed	perform	VERB
ap-1829	221	14	three	three	NUM
ap-1829	221	15	times	time	NOUN
ap-1829	221	16	,	,	PUNCT
ap-1829	221	17	each	each	DET
ap-1829	221	18	time	time	NOUN
ap-1829	221	19	with	with	ADP
ap-1829	221	20	a	a	DET
ap-1829	221	21	different	different	ADJ
ap-1829	221	22	temporal	temporal	ADJ
ap-1829	221	23	adaptivity	adaptivity	NOUN
ap-1829	221	24	mechanism	mechanism	NOUN
ap-1829	221	25	.	.	PUNCT
ap-1829	222	1	all	all	DET
ap-1829	222	2	selected	select	VERB
ap-1829	222	3	adaptivity	adaptivity	NOUN
ap-1829	222	4	methods	method	NOUN
ap-1829	222	5	were	be	AUX
ap-1829	222	6	purely	purely	ADV
ap-1829	222	7	empirical	empirical	ADJ
ap-1829	222	8	.	.	PUNCT
ap-1829	223	1	(	(	PUNCT
ap-1829	223	2	1	1	NUM
ap-1829	223	3	.	.	PUNCT
ap-1829	223	4	)	)	PUNCT
ap-1829	223	5	number	number	NOUN
ap-1829	223	6	of	of	ADP
ap-1829	223	7	iterations	iteration	NOUN
ap-1829	223	8	of	of	ADP
ap-1829	223	9	the	the	DET
ap-1829	223	10	picard	picard	NOUN
ap-1829	223	11	method	method	NOUN
ap-1829	223	12	(	(	PUNCT
ap-1829	223	13	max	max	PROPN
ap-1829	223	14	.	.	PROPN
ap-1829	223	15	10	10	NUM
ap-1829	223	16	iterations	iteration	NOUN
ap-1829	223	17	with	with	ADP
ap-1829	223	18	a	a	DET
ap-1829	223	19	defined	define	VERB
ap-1829	223	20	stopping	stopping	NOUN
ap-1829	223	21	criterion	criterion	NOUN
ap-1829	223	22	)	)	PUNCT
ap-1829	223	23	—	—	PUNCT
ap-1829	223	24	h	h	NOUN
ap-1829	223	25	-	-	PUNCT
ap-1829	223	26	based	base	VERB
ap-1829	223	27	form	form	NOUN
ap-1829	223	28	of	of	ADP
ap-1829	223	29	the	the	DET
ap-1829	223	30	richards	richard	NOUN
ap-1829	223	31	equation	equation	NOUN
ap-1829	223	32	.	.	PUNCT
ap-1829	224	1	(	(	PUNCT
ap-1829	224	2	2	2	NUM
ap-1829	224	3	.	.	PUNCT
ap-1829	224	4	)	)	PUNCT
ap-1829	224	5	number	number	NOUN
ap-1829	224	6	of	of	ADP
ap-1829	224	7	iterations	iteration	NOUN
ap-1829	224	8	of	of	ADP
ap-1829	224	9	the	the	DET
ap-1829	224	10	picard	picard	NOUN
ap-1829	224	11	method	method	NOUN
ap-1829	224	12	(	(	PUNCT
ap-1829	224	13	max	max	PROPN
ap-1829	224	14	.	.	PROPN
ap-1829	224	15	10	10	NUM
ap-1829	224	16	iterations	iteration	NOUN
ap-1829	224	17	with	with	ADP
ap-1829	224	18	the	the	DET
ap-1829	224	19	defined	define	VERB
ap-1829	224	20	stopping	stopping	NOUN
ap-1829	224	21	criterion	criterion	NOUN
ap-1829	224	22	)	)	PUNCT
ap-1829	224	23	—	—	PUNCT
ap-1829	224	24	mixed	mixed	ADJ
ap-1829	224	25	form	form	NOUN
ap-1829	224	26	of	of	ADP
ap-1829	224	27	the	the	DET
ap-1829	224	28	richards	richard	NOUN
ap-1829	224	29	equation	equation	NOUN
ap-1829	224	30	(	(	PUNCT
ap-1829	224	31	the	the	DET
ap-1829	224	32	discrete	discrete	ADJ
ap-1829	224	33	analogue	analogue	NOUN
ap-1829	224	34	of	of	ADP
ap-1829	224	35	the	the	DET
ap-1829	224	36	mass	mass	ADJ
ap-1829	224	37	term	term	NOUN
ap-1829	224	38	was	be	AUX
ap-1829	224	39	considered	consider	VERB
ap-1829	224	40	as	as	ADP
ap-1829	224	41	∆θ(h	∆θ(h	NOUN
ap-1829	224	42	)	)	PUNCT
ap-1829	224	43	∆t	∆t	PROPN
ap-1829	224	44	)	)	PUNCT
ap-1829	224	45	.	.	PUNCT
ap-1829	225	1	(	(	PUNCT
ap-1829	225	2	3	3	X
ap-1829	225	3	.	.	PUNCT
ap-1829	225	4	)	)	PUNCT
ap-1829	225	5	mass	mass	ADJ
ap-1829	225	6	curve	curve	NOUN
ap-1829	225	7	zone	zone	NOUN
ap-1829	225	8	approach	approach	NOUN
ap-1829	225	9	(	(	PUNCT
ap-1829	225	10	the	the	DET
ap-1829	225	11	maximal	maximal	ADJ
ap-1829	225	12	error	error	NOUN
ap-1829	225	13	of	of	ADP
ap-1829	225	14	a	a	DET
ap-1829	225	15	first	first	ADJ
ap-1829	225	16	-	-	PUNCT
ap-1829	225	17	order	order	NOUN
ap-1829	225	18	taylor	taylor	PROPN
ap-1829	225	19	series	series	PROPN
ap-1829	225	20	,	,	PUNCT
ap-1829	225	21	see	see	VERB
ap-1829	225	22	figure	figure	NOUN
ap-1829	225	23	2	2	NUM
ap-1829	225	24	,	,	PUNCT
ap-1829	225	25	was	be	AUX
ap-1829	225	26	5	5	NUM
ap-1829	225	27	·	·	SYM
ap-1829	225	28	10−6	10−6	NUM
ap-1829	225	29	)	)	PUNCT
ap-1829	225	30	.	.	PUNCT
ap-1829	226	1	the	the	DET
ap-1829	226	2	initial	initial	ADJ
ap-1829	226	3	condition	condition	NOUN
ap-1829	226	4	was	be	AUX
ap-1829	226	5	defined	define	VERB
ap-1829	226	6	as	as	ADP
ap-1829	226	7	h(x	h(x	PROPN
ap-1829	226	8	,	,	PUNCT
ap-1829	226	9	0	0	NUM
ap-1829	226	10	)	)	PUNCT
ap-1829	226	11	=	=	PUNCT
ap-1829	227	1	−8700.0	−8700.0	ADJ
ap-1829	227	2	cm	cm	NOUN
ap-1829	227	3	∀x	∀x	X
ap-1829	227	4	∈	∈	PROPN
ap-1829	227	5	ω	ω	NOUN
ap-1829	227	6	.	.	PUNCT
ap-1829	227	7	(	(	PUNCT
ap-1829	227	8	17	17	NUM
ap-1829	227	9	)	)	PUNCT
ap-1829	227	10	the	the	DET
ap-1829	227	11	top	top	ADJ
ap-1829	227	12	boundary	boundary	ADJ
ap-1829	227	13	condition	condition	NOUN
ap-1829	227	14	was	be	AUX
ap-1829	227	15	defined	define	VERB
ap-1829	227	16	as	as	ADP
ap-1829	227	17	h(x	h(x	PROPN
ap-1829	227	18	,	,	PUNCT
ap-1829	227	19	t	t	PROPN
ap-1829	227	20	)	)	PUNCT
ap-1829	227	21	=	=	SYM
ap-1829	227	22	5.0	5.0	NUM
ap-1829	227	23	cm	cm	NUM
ap-1829	227	24	∀(x	∀(x	NUM
ap-1829	227	25	,	,	PUNCT
ap-1829	227	26	t	t	NOUN
ap-1829	227	27	)	)	PUNCT
ap-1829	227	28	∈	∈	PROPN
ap-1829	227	29	γtop	γtop	NOUN
ap-1829	227	30	×	×	PROPN
ap-1829	227	31	(	(	PUNCT
ap-1829	227	32	0	0	NUM
ap-1829	227	33	,	,	PUNCT
ap-1829	227	34	t	t	X
ap-1829	227	35	]	]	PUNCT
ap-1829	227	36	.	.	PUNCT
ap-1829	228	1	(	(	PUNCT
ap-1829	228	2	18	18	NUM
ap-1829	228	3	)	)	PUNCT
ap-1829	228	4	and	and	CCONJ
ap-1829	228	5	the	the	DET
ap-1829	228	6	bottom	bottom	ADJ
ap-1829	228	7	boundary	boundary	NOUN
ap-1829	228	8	was	be	AUX
ap-1829	228	9	the	the	DET
ap-1829	228	10	homogeneous	homogeneous	ADJ
ap-1829	228	11	neumann	neumann	PROPN
ap-1829	228	12	boundary	boundary	ADJ
ap-1829	228	13	condition	condition	NOUN
ap-1829	228	14	(	(	PUNCT
ap-1829	228	15	in	in	ADP
ap-1829	228	16	technical	technical	ADJ
ap-1829	228	17	practice	practice	NOUN
ap-1829	228	18	this	this	DET
ap-1829	228	19	type	type	NOUN
ap-1829	228	20	of	of	ADP
ap-1829	228	21	the	the	DET
ap-1829	228	22	bottom	bottom	ADJ
ap-1829	228	23	boundary	boundary	ADJ
ap-1829	228	24	setup	setup	NOUN
ap-1829	228	25	is	be	AUX
ap-1829	228	26	referred	refer	VERB
ap-1829	228	27	to	to	ADP
ap-1829	228	28	as	as	ADP
ap-1829	228	29	free	free	ADJ
ap-1829	228	30	drainage	drainage	NOUN
ap-1829	228	31	)	)	PUNCT
ap-1829	228	32	.	.	PUNCT
ap-1829	229	1	351	351	NUM
ap-1829	229	2	michal	michal	PROPN
ap-1829	229	3	kuráž	kuráž	PROPN
ap-1829	229	4	,	,	PUNCT
ap-1829	229	5	petr	petr	PROPN
ap-1829	229	6	mayer	mayer	PROPN
ap-1829	229	7	acta	acta	PROPN
ap-1829	229	8	polytechnica	polytechnica	PROPN
ap-1829	229	9	method	method	PROPN
ap-1829	229	10	mass	mass	NOUN
ap-1829	229	11	error	error	NOUN
ap-1829	229	12	number	number	NOUN
ap-1829	229	13	[	[	X
ap-1829	229	14	%	%	X
ap-1829	229	15	]	]	PUNCT
ap-1829	229	16	of	of	ADP
ap-1829	229	17	iterations	iteration	NOUN
ap-1829	229	18	1st	1st	ADJ
ap-1829	229	19	5.842	5.842	NUM
ap-1829	229	20	130	130	NUM
ap-1829	229	21	2nd	2nd	NOUN
ap-1829	229	22	0.201	0.201	NUM
ap-1829	229	23	44382	44382	NUM
ap-1829	229	24	3rd	3rd	ADJ
ap-1829	229	25	0.193	0.193	NUM
ap-1829	229	26	1746	1746	NUM
ap-1829	229	27	table	table	NOUN
ap-1829	229	28	1	1	NUM
ap-1829	229	29	.	.	PUNCT
ap-1829	229	30	summary	summary	NOUN
ap-1829	229	31	of	of	ADP
ap-1829	229	32	code	code	NOUN
ap-1829	229	33	execution	execution	NOUN
ap-1829	229	34	after	after	ADP
ap-1829	229	35	the	the	DET
ap-1829	229	36	numerical	numerical	PROPN
ap-1829	229	37	infiltration	infiltration	NOUN
ap-1829	229	38	experiment	experiment	NOUN
ap-1829	229	39	.	.	PUNCT
ap-1829	230	1	3.2	3.2	NUM
ap-1829	230	2	.	.	PUNCT
ap-1829	230	3	results	result	NOUN
ap-1829	230	4	and	and	CCONJ
ap-1829	230	5	conclusions	conclusion	NOUN
ap-1829	230	6	as	as	SCONJ
ap-1829	230	7	stated	state	VERB
ap-1829	230	8	in	in	ADP
ap-1829	230	9	[	[	X
ap-1829	230	10	5	5	NUM
ap-1829	230	11	]	]	PUNCT
ap-1829	230	12	the	the	DET
ap-1829	230	13	successful	successful	ADJ
ap-1829	230	14	iteration	iteration	NOUN
ap-1829	230	15	criterion	criterion	NOUN
ap-1829	230	16	for	for	ADP
ap-1829	230	17	adaptive	adaptive	ADJ
ap-1829	230	18	time	time	NOUN
ap-1829	230	19	-	-	PUNCT
ap-1829	230	20	step	step	NOUN
ap-1829	230	21	selection	selection	NOUN
ap-1829	230	22	of	of	ADP
ap-1829	230	23	the	the	DET
ap-1829	230	24	h	h	NOUN
ap-1829	230	25	-	-	PUNCT
ap-1829	230	26	based	base	VERB
ap-1829	230	27	richards	richard	NOUN
ap-1829	230	28	equation	equation	NOUN
ap-1829	230	29	is	be	AUX
ap-1829	230	30	not	not	PART
ap-1829	230	31	a	a	DET
ap-1829	230	32	sufficient	sufficient	ADJ
ap-1829	230	33	condition	condition	NOUN
ap-1829	230	34	to	to	PART
ap-1829	230	35	ensure	ensure	VERB
ap-1829	230	36	accuracy	accuracy	NOUN
ap-1829	230	37	.	.	PUNCT
ap-1829	231	1	the	the	DET
ap-1829	231	2	mixed	mixed	ADJ
ap-1829	231	3	form	form	NOUN
ap-1829	231	4	of	of	ADP
ap-1829	231	5	the	the	DET
ap-1829	231	6	richards	richard	NOUN
ap-1829	231	7	equation	equation	NOUN
ap-1829	231	8	provides	provide	VERB
ap-1829	231	9	very	very	ADV
ap-1829	231	10	accurate	accurate	ADJ
ap-1829	231	11	results	result	NOUN
ap-1829	231	12	,	,	PUNCT
ap-1829	231	13	but	but	CCONJ
ap-1829	231	14	the	the	DET
ap-1829	231	15	computational	computational	ADJ
ap-1829	231	16	effort	effort	NOUN
ap-1829	231	17	is	be	AUX
ap-1829	231	18	excessive	excessive	ADJ
ap-1829	231	19	in	in	ADP
ap-1829	231	20	the	the	DET
ap-1829	231	21	case	case	NOUN
ap-1829	231	22	evaluated	evaluate	VERB
ap-1829	231	23	here	here	ADV
ap-1829	231	24	.	.	PUNCT
ap-1829	232	1	the	the	DET
ap-1829	232	2	mass	mass	ADJ
ap-1829	232	3	curve	curve	NOUN
ap-1829	232	4	zone	zone	NOUN
ap-1829	232	5	approach	approach	NOUN
ap-1829	232	6	provides	provide	VERB
ap-1829	232	7	results	result	NOUN
ap-1829	232	8	of	of	ADP
ap-1829	232	9	similar	similar	ADJ
ap-1829	232	10	quality	quality	NOUN
ap-1829	232	11	,	,	PUNCT
ap-1829	232	12	but	but	CCONJ
ap-1829	232	13	the	the	DET
ap-1829	232	14	total	total	ADJ
ap-1829	232	15	number	number	NOUN
ap-1829	232	16	of	of	ADP
ap-1829	232	17	iterations	iteration	NOUN
ap-1829	232	18	(	(	PUNCT
ap-1829	232	19	number	number	NOUN
ap-1829	232	20	of	of	ADP
ap-1829	232	21	calls	call	NOUN
ap-1829	232	22	of	of	ADP
ap-1829	232	23	the	the	DET
ap-1829	232	24	linear	linear	ADJ
ap-1829	232	25	equation	equation	NOUN
ap-1829	232	26	solver	solver	ADV
ap-1829	232	27	)	)	PUNCT
ap-1829	232	28	is	be	AUX
ap-1829	232	29	only	only	ADV
ap-1829	232	30	approximately	approximately	ADV
ap-1829	232	31	4	4	NUM
ap-1829	232	32	%	%	NOUN
ap-1829	232	33	of	of	ADP
ap-1829	232	34	the	the	DET
ap-1829	232	35	amount	amount	NOUN
ap-1829	232	36	required	require	VERB
ap-1829	232	37	for	for	ADP
ap-1829	232	38	solving	solve	VERB
ap-1829	232	39	the	the	DET
ap-1829	232	40	mixed	mix	VERB
ap-1829	232	41	-	-	PUNCT
ap-1829	232	42	form	form	NOUN
ap-1829	232	43	richards	richard	NOUN
ap-1829	232	44	equation	equation	NOUN
ap-1829	232	45	.	.	PUNCT
ap-1829	233	1	this	this	DET
ap-1829	233	2	method	method	NOUN
ap-1829	233	3	offers	offer	VERB
ap-1829	233	4	an	an	DET
ap-1829	233	5	efficient	efficient	ADJ
ap-1829	233	6	condition	condition	NOUN
ap-1829	233	7	for	for	ADP
ap-1829	233	8	a	a	DET
ap-1829	233	9	numerical	numerical	ADJ
ap-1829	233	10	solution	solution	NOUN
ap-1829	233	11	of	of	ADP
ap-1829	233	12	the	the	DET
ap-1829	233	13	h	h	NOUN
ap-1829	233	14	-	-	PUNCT
ap-1829	233	15	based	base	VERB
ap-1829	233	16	equation	equation	NOUN
ap-1829	233	17	based	base	VERB
ap-1829	233	18	on	on	ADP
ap-1829	233	19	the	the	DET
ap-1829	233	20	implicit	implicit	ADJ
ap-1829	233	21	backward	backward	ADJ
ap-1829	233	22	euler	euler	NOUN
ap-1829	233	23	scheme	scheme	NOUN
ap-1829	233	24	,	,	PUNCT
ap-1829	233	25	exactly	exactly	ADV
ap-1829	233	26	reflecting	reflect	VERB
ap-1829	233	27	the	the	DET
ap-1829	233	28	problem	problem	NOUN
ap-1829	233	29	of	of	ADP
ap-1829	233	30	the	the	DET
ap-1829	233	31	h	h	NOUN
ap-1829	233	32	-	-	PUNCT
ap-1829	233	33	based	base	VERB
ap-1829	233	34	approximation	approximation	NOUN
ap-1829	233	35	.	.	PUNCT
ap-1829	234	1	compared	compare	VERB
ap-1829	234	2	to	to	ADP
ap-1829	234	3	the	the	DET
ap-1829	234	4	tocci	tocci	NOUN
ap-1829	234	5	approach	approach	NOUN
ap-1829	234	6	[	[	X
ap-1829	234	7	15	15	NUM
ap-1829	234	8	]	]	PUNCT
ap-1829	234	9	,	,	PUNCT
ap-1829	234	10	our	our	PRON
ap-1829	234	11	algorithm	algorithm	NOUN
ap-1829	234	12	does	do	AUX
ap-1829	234	13	not	not	PART
ap-1829	234	14	limit	limit	VERB
ap-1829	234	15	the	the	DET
ap-1829	234	16	truncation	truncation	NOUN
ap-1829	234	17	error	error	NOUN
ap-1829	234	18	of	of	ADP
ap-1829	234	19	the	the	DET
ap-1829	234	20	time	time	NOUN
ap-1829	234	21	derivative	derivative	ADJ
ap-1829	234	22	term	term	NOUN
ap-1829	234	23	,	,	PUNCT
ap-1829	234	24	it	it	PRON
ap-1829	234	25	only	only	ADV
ap-1829	234	26	limits	limit	VERB
ap-1829	234	27	the	the	DET
ap-1829	234	28	error	error	NOUN
ap-1829	234	29	of	of	ADP
ap-1829	234	30	the	the	DET
ap-1829	234	31	discrete	discrete	ADJ
ap-1829	234	32	analogue	analogue	NOUN
ap-1829	234	33	of	of	ADP
ap-1829	234	34	the	the	DET
ap-1829	234	35	mass	mass	ADJ
ap-1829	234	36	term	term	NOUN
ap-1829	234	37	if	if	SCONJ
ap-1829	234	38	the	the	DET
ap-1829	234	39	h	h	NOUN
ap-1829	234	40	-	-	PUNCT
ap-1829	234	41	based	base	VERB
ap-1829	234	42	form	form	NOUN
ap-1829	234	43	of	of	ADP
ap-1829	234	44	the	the	DET
ap-1829	234	45	richards	richard	NOUN
ap-1829	234	46	’	'	PUNCT
ap-1829	234	47	equation	equation	NOUN
ap-1829	234	48	is	be	AUX
ap-1829	234	49	considered	consider	VERB
ap-1829	234	50	.	.	PUNCT
ap-1829	235	1	however	however	ADV
ap-1829	235	2	,	,	PUNCT
ap-1829	235	3	our	our	PRON
ap-1829	235	4	algorithm	algorithm	NOUN
ap-1829	235	5	behaves	behave	VERB
ap-1829	235	6	in	in	ADP
ap-1829	235	7	a	a	DET
ap-1829	235	8	different	different	ADJ
ap-1829	235	9	way	way	NOUN
ap-1829	235	10	.	.	PUNCT
ap-1829	236	1	it	it	PRON
ap-1829	236	2	should	should	AUX
ap-1829	236	3	be	be	AUX
ap-1829	236	4	evaluated	evaluate	VERB
ap-1829	236	5	whether	whether	SCONJ
ap-1829	236	6	there	there	PRON
ap-1829	236	7	is	be	VERB
ap-1829	236	8	any	any	DET
ap-1829	236	9	relation	relation	NOUN
ap-1829	236	10	between	between	ADP
ap-1829	236	11	these	these	DET
ap-1829	236	12	two	two	NUM
ap-1829	236	13	errors	error	NOUN
ap-1829	236	14	,	,	PUNCT
ap-1829	236	15	or	or	CCONJ
ap-1829	236	16	at	at	ADP
ap-1829	236	17	least	least	ADJ
ap-1829	236	18	which	which	DET
ap-1829	236	19	criterion	criterion	NOUN
ap-1829	236	20	is	be	AUX
ap-1829	236	21	more	more	ADV
ap-1829	236	22	appropriate	appropriate	ADJ
ap-1829	236	23	for	for	ADP
ap-1829	236	24	achieving	achieve	VERB
ap-1829	236	25	mass	mass	NOUN
ap-1829	236	26	consistency	consistency	NOUN
ap-1829	236	27	.	.	PUNCT
ap-1829	237	1	for	for	ADP
ap-1829	237	2	particular	particular	ADJ
ap-1829	237	3	results	result	NOUN
ap-1829	237	4	see	see	VERB
ap-1829	237	5	table	table	NOUN
ap-1829	237	6	1	1	NUM
ap-1829	237	7	.	.	NOUN
ap-1829	237	8	4	4	NUM
ap-1829	237	9	.	.	NOUN
ap-1829	237	10	preconditioner	preconditioner	PROPN
ap-1829	237	11	finite	finite	PROPN
ap-1829	237	12	element	element	NOUN
ap-1829	237	13	approximation	approximation	NOUN
ap-1829	237	14	of	of	ADP
ap-1829	237	15	the	the	DET
ap-1829	237	16	richards	richard	NOUN
ap-1829	237	17	equation	equation	NOUN
ap-1829	237	18	problem	problem	NOUN
ap-1829	237	19	combined	combine	VERB
ap-1829	237	20	with	with	ADP
ap-1829	237	21	the	the	DET
ap-1829	237	22	fully	fully	ADV
ap-1829	237	23	implicit	implicit	ADJ
ap-1829	237	24	roth	roth	NOUN
ap-1829	237	25	method	method	NOUN
ap-1829	237	26	typically	typically	ADV
ap-1829	237	27	forms	form	VERB
ap-1829	237	28	very	very	ADV
ap-1829	237	29	badly	badly	ADV
ap-1829	237	30	-	-	PUNCT
ap-1829	237	31	conditioned	condition	VERB
ap-1829	237	32	matrices	matrix	NOUN
ap-1829	237	33	,	,	PUNCT
ap-1829	237	34	especially	especially	ADV
ap-1829	237	35	if	if	SCONJ
ap-1829	237	36	coarse	coarse	ADJ
ap-1829	237	37	-	-	PUNCT
ap-1829	237	38	grain	grain	NOUN
ap-1829	237	39	material	material	NOUN
ap-1829	237	40	is	be	AUX
ap-1829	237	41	involved	involve	VERB
ap-1829	237	42	.	.	PUNCT
ap-1829	238	1	the	the	DET
ap-1829	238	2	plot	plot	NOUN
ap-1829	238	3	of	of	ADP
ap-1829	238	4	the	the	DET
ap-1829	238	5	unsaturated	unsaturated	ADJ
ap-1829	238	6	hydraulic	hydraulic	ADJ
ap-1829	238	7	conductivity	conductivity	NOUN
ap-1829	238	8	,	,	PUNCT
ap-1829	238	9	figure	figure	NOUN
ap-1829	238	10	1	1	NUM
ap-1829	238	11	right	right	ADJ
ap-1829	238	12	,	,	PUNCT
ap-1829	238	13	covers	cover	VERB
ap-1829	238	14	a	a	DET
ap-1829	238	15	typical	typical	ADJ
ap-1829	238	16	capillary	capillary	ADJ
ap-1829	238	17	pressure	pressure	NOUN
ap-1829	238	18	head	head	NOUN
ap-1829	238	19	range	range	VERB
ap-1829	238	20	for	for	ADP
ap-1829	238	21	a	a	DET
ap-1829	238	22	certain	certain	ADJ
ap-1829	238	23	richards	richard	NOUN
ap-1829	238	24	equation	equation	NOUN
ap-1829	238	25	problem	problem	NOUN
ap-1829	238	26	,	,	PUNCT
ap-1829	238	27	and	and	CCONJ
ap-1829	238	28	thus	thus	ADV
ap-1829	238	29	it	it	PRON
ap-1829	238	30	is	be	AUX
ap-1829	238	31	not	not	PART
ap-1829	238	32	uncommon	uncommon	ADJ
ap-1829	238	33	to	to	PART
ap-1829	238	34	solve	solve	VERB
ap-1829	238	35	problems	problem	NOUN
ap-1829	238	36	where	where	SCONJ
ap-1829	238	37	the	the	DET
ap-1829	238	38	non	non	ADJ
ap-1829	238	39	-	-	ADJ
ap-1829	238	40	linear	linear	ADJ
ap-1829	238	41	model	model	NOUN
ap-1829	238	42	parameters	parameter	NOUN
ap-1829	238	43	can	can	AUX
ap-1829	238	44	vary	vary	VERB
ap-1829	238	45	between	between	ADP
ap-1829	238	46	eight	eight	NUM
ap-1829	238	47	or	or	CCONJ
ap-1829	238	48	even	even	ADV
ap-1829	238	49	ten	ten	NUM
ap-1829	238	50	orders	order	NOUN
ap-1829	238	51	of	of	ADP
ap-1829	238	52	magnitude	magnitude	NOUN
ap-1829	238	53	.	.	PUNCT
ap-1829	239	1	the	the	DET
ap-1829	239	2	poor	poor	ADJ
ap-1829	239	3	conditioning	conditioning	NOUN
ap-1829	239	4	of	of	ADP
ap-1829	239	5	the	the	DET
ap-1829	239	6	richards	richard	NOUN
ap-1829	239	7	equation	equation	NOUN
ap-1829	239	8	is	be	AUX
ap-1829	239	9	caused	cause	VERB
ap-1829	239	10	by	by	ADP
ap-1829	239	11	the	the	DET
ap-1829	239	12	huge	huge	ADJ
ap-1829	239	13	range	range	NOUN
ap-1829	239	14	of	of	ADP
ap-1829	239	15	values	value	NOUN
ap-1829	239	16	of	of	ADP
ap-1829	239	17	the	the	DET
ap-1829	239	18	constitutive	constitutive	ADJ
ap-1829	239	19	functions	function	NOUN
ap-1829	239	20	.	.	PUNCT
ap-1829	240	1	another	another	DET
ap-1829	240	2	property	property	NOUN
ap-1829	240	3	of	of	ADP
ap-1829	240	4	the	the	DET
ap-1829	240	5	richards	richard	NOUN
ap-1829	240	6	equation	equation	NOUN
ap-1829	240	7	also	also	ADV
ap-1829	240	8	applies	apply	VERB
ap-1829	240	9	.	.	PUNCT
ap-1829	241	1	due	due	ADP
ap-1829	241	2	to	to	ADP
ap-1829	241	3	the	the	DET
ap-1829	241	4	small	small	ADJ
ap-1829	241	5	time	time	NOUN
ap-1829	241	6	steps	step	NOUN
ap-1829	241	7	that	that	PRON
ap-1829	241	8	are	be	AUX
ap-1829	241	9	typically	typically	ADV
ap-1829	241	10	required	require	VERB
ap-1829	241	11	for	for	ADP
ap-1829	241	12	an	an	DET
ap-1829	241	13	accurate	accurate	ADJ
ap-1829	241	14	solution	solution	NOUN
ap-1829	241	15	of	of	ADP
ap-1829	241	16	this	this	DET
ap-1829	241	17	problem	problem	NOUN
ap-1829	241	18	,	,	PUNCT
ap-1829	241	19	and	and	CCONJ
ap-1829	241	20	due	due	ADP
ap-1829	241	21	to	to	ADP
ap-1829	241	22	lumping	lump	VERB
ap-1829	241	23	of	of	ADP
ap-1829	241	24	the	the	DET
ap-1829	241	25	capacity	capacity	NOUN
ap-1829	241	26	matrices	matrix	NOUN
ap-1829	241	27	in	in	ADP
ap-1829	241	28	order	order	NOUN
ap-1829	241	29	to	to	PART
ap-1829	241	30	preserve	preserve	VERB
ap-1829	241	31	the	the	DET
ap-1829	241	32	discrete	discrete	ADJ
ap-1829	241	33	maximum	maximum	ADJ
ap-1829	241	34	principle	principle	NOUN
ap-1829	241	35	,	,	PUNCT
ap-1829	241	36	the	the	DET
ap-1829	241	37	matrices	matrix	NOUN
ap-1829	241	38	of	of	ADP
ap-1829	241	39	its	its	PRON
ap-1829	241	40	numerical	numerical	ADJ
ap-1829	241	41	approximation	approximation	NOUN
ap-1829	241	42	are	be	AUX
ap-1829	241	43	diagonally	diagonally	ADV
ap-1829	241	44	dominant	dominant	ADJ
ap-1829	241	45	.	.	PUNCT
ap-1829	242	1	then	then	ADV
ap-1829	242	2	it	it	PRON
ap-1829	242	3	was	be	AUX
ap-1829	242	4	observed	observe	VERB
ap-1829	242	5	that	that	SCONJ
ap-1829	242	6	badly	badly	ADV
ap-1829	242	7	conditioned	condition	VERB
ap-1829	242	8	matrices	matrix	NOUN
ap-1829	242	9	of	of	ADP
ap-1829	242	10	this	this	DET
ap-1829	242	11	type	type	NOUN
ap-1829	242	12	are	be	AUX
ap-1829	242	13	formed	form	VERB
ap-1829	242	14	out	out	ADP
ap-1829	242	15	of	of	ADP
ap-1829	242	16	clusters	cluster	NOUN
ap-1829	242	17	with	with	ADP
ap-1829	242	18	a	a	DET
ap-1829	242	19	lower	low	ADJ
ap-1829	242	20	condition	condition	NOUN
ap-1829	242	21	number	number	NOUN
ap-1829	242	22	.	.	PUNCT
ap-1829	243	1	for	for	ADP
ap-1829	243	2	simple	simple	ADJ
ap-1829	243	3	infiltration	infiltration	NOUN
ap-1829	243	4	problems	problem	NOUN
ap-1829	243	5	,	,	PUNCT
ap-1829	243	6	the	the	DET
ap-1829	243	7	clusters	cluster	NOUN
ap-1829	243	8	are	be	AUX
ap-1829	243	9	formed	form	VERB
ap-1829	243	10	at	at	ADP
ap-1829	243	11	(	(	PUNCT
ap-1829	243	12	1	1	NUM
ap-1829	243	13	.	.	PUNCT
ap-1829	243	14	)	)	PUNCT
ap-1829	243	15	fracture	fracture	NOUN
ap-1829	243	16	and	and	CCONJ
ap-1829	243	17	matrix	matrix	NOUN
ap-1829	243	18	flow	flow	NOUN
ap-1829	243	19	domains	domain	NOUN
ap-1829	243	20	,	,	PUNCT
ap-1829	243	21	(	(	PUNCT
ap-1829	243	22	2	2	NUM
ap-1829	243	23	.	.	NUM
ap-1829	243	24	)	)	PUNCT
ap-1829	243	25	regions	region	NOUN
ap-1829	243	26	separated	separate	VERB
ap-1829	243	27	by	by	ADP
ap-1829	243	28	the	the	DET
ap-1829	243	29	wetting	wetting	NOUN
ap-1829	243	30	front	front	NOUN
ap-1829	243	31	.	.	PUNCT
ap-1829	244	1	and	and	CCONJ
ap-1829	244	2	thus	thus	ADV
ap-1829	244	3	it	it	PRON
ap-1829	244	4	can	can	AUX
ap-1829	244	5	be	be	AUX
ap-1829	244	6	summarized	summarize	VERB
ap-1829	244	7	that	that	SCONJ
ap-1829	244	8	,	,	PUNCT
ap-1829	244	9	•	•	ADP
ap-1829	244	10	due	due	ADP
ap-1829	244	11	to	to	ADP
ap-1829	244	12	the	the	DET
ap-1829	244	13	small	small	ADJ
ap-1829	244	14	time	time	NOUN
ap-1829	244	15	steps	step	NOUN
ap-1829	244	16	,	,	PUNCT
ap-1829	244	17	matrices	matrix	NOUN
ap-1829	244	18	are	be	AUX
ap-1829	244	19	diagonally	diagonally	ADV
ap-1829	244	20	dominant	dominant	ADJ
ap-1829	244	21	,	,	PUNCT
ap-1829	244	22	•	•	ADP
ap-1829	244	23	due	due	ADP
ap-1829	244	24	to	to	ADP
ap-1829	244	25	the	the	DET
ap-1829	244	26	small	small	ADJ
ap-1829	244	27	time	time	NOUN
ap-1829	244	28	steps	step	NOUN
ap-1829	244	29	and	and	CCONJ
ap-1829	244	30	the	the	DET
ap-1829	244	31	continuity	continuity	NOUN
ap-1829	244	32	of	of	ADP
ap-1829	244	33	the	the	DET
ap-1829	244	34	solution	solution	NOUN
ap-1829	244	35	(	(	PUNCT
ap-1829	244	36	it	it	PRON
ap-1829	244	37	is	be	AUX
ap-1829	244	38	in	in	ADP
ap-1829	244	39	fact	fact	NOUN
ap-1829	244	40	just	just	ADV
ap-1829	244	41	a	a	DET
ap-1829	244	42	non	non	ADJ
ap-1829	244	43	-	-	ADJ
ap-1829	244	44	linear	linear	ADJ
ap-1829	244	45	diffusion	diffusion	NOUN
ap-1829	244	46	with	with	ADP
ap-1829	244	47	convection	convection	NOUN
ap-1829	244	48	)	)	PUNCT
ap-1829	244	49	,	,	PUNCT
ap-1829	244	50	the	the	DET
ap-1829	244	51	matrices	matrix	NOUN
ap-1829	244	52	are	be	AUX
ap-1829	244	53	"	"	PUNCT
ap-1829	244	54	similar	similar	ADJ
ap-1829	244	55	"	"	PUNCT
ap-1829	244	56	in	in	ADP
ap-1829	244	57	two	two	NUM
ap-1829	244	58	sequential	sequential	ADJ
ap-1829	244	59	time	time	NOUN
ap-1829	244	60	steps	step	NOUN
ap-1829	244	61	,	,	PUNCT
ap-1829	244	62	•	•	SCONJ
ap-1829	244	63	the	the	DET
ap-1829	244	64	domain	domain	NOUN
ap-1829	244	65	can	can	AUX
ap-1829	244	66	be	be	AUX
ap-1829	244	67	clustered	cluster	VERB
ap-1829	244	68	into	into	ADP
ap-1829	244	69	subdomains	subdomain	NOUN
ap-1829	244	70	with	with	ADP
ap-1829	244	71	similar	similar	ADJ
ap-1829	244	72	values	value	NOUN
ap-1829	244	73	of	of	ADP
ap-1829	244	74	the	the	DET
ap-1829	244	75	constitutive	constitutive	ADJ
ap-1829	244	76	functions	function	NOUN
ap-1829	244	77	,	,	PUNCT
ap-1829	244	78	and	and	CCONJ
ap-1829	244	79	thus	thus	ADV
ap-1829	244	80	the	the	DET
ap-1829	244	81	matrix	matrix	NOUN
ap-1829	244	82	can	can	AUX
ap-1829	244	83	be	be	AUX
ap-1829	244	84	clustered	cluster	VERB
ap-1829	244	85	into	into	ADP
ap-1829	244	86	"	"	PUNCT
ap-1829	244	87	submatrices	submatrice	NOUN
ap-1829	244	88	"	"	PUNCT
ap-1829	244	89	with	with	ADP
ap-1829	244	90	a	a	DET
ap-1829	244	91	lower	low	ADJ
ap-1829	244	92	condition	condition	NOUN
ap-1829	244	93	number	number	NOUN
ap-1829	244	94	(	(	PUNCT
ap-1829	244	95	as	as	SCONJ
ap-1829	244	96	the	the	DET
ap-1829	244	97	problem	problem	NOUN
ap-1829	244	98	is	be	AUX
ap-1829	244	99	nonlinear	nonlinear	ADJ
ap-1829	244	100	and	and	CCONJ
ap-1829	244	101	often	often	ADV
ap-1829	244	102	unsteady	unsteady	ADJ
ap-1829	244	103	,	,	PUNCT
ap-1829	244	104	the	the	DET
ap-1829	244	105	position	position	NOUN
ap-1829	244	106	of	of	ADP
ap-1829	244	107	these	these	DET
ap-1829	244	108	subdomains	subdomain	NOUN
ap-1829	244	109	is	be	AUX
ap-1829	244	110	not	not	PART
ap-1829	244	111	constant	constant	ADJ
ap-1829	244	112	in	in	ADP
ap-1829	244	113	time	time	NOUN
ap-1829	244	114	)	)	PUNCT
ap-1829	244	115	.	.	PUNCT
ap-1829	245	1	based	base	VERB
ap-1829	245	2	on	on	ADP
ap-1829	245	3	these	these	DET
ap-1829	245	4	assumptions	assumption	NOUN
ap-1829	245	5	,	,	PUNCT
ap-1829	245	6	the	the	DET
ap-1829	245	7	perfect	perfect	ADJ
ap-1829	245	8	preconditioner	preconditioner	NOUN
ap-1829	245	9	should	should	AUX
ap-1829	245	10	adjust	adjust	VERB
ap-1829	245	11	the	the	DET
ap-1829	245	12	material	material	NOUN
ap-1829	245	13	properties	property	NOUN
ap-1829	245	14	in	in	ADP
ap-1829	245	15	the	the	DET
ap-1829	245	16	computational	computational	ADJ
ap-1829	245	17	domain	domain	NOUN
ap-1829	245	18	into	into	ADP
ap-1829	245	19	such	such	DET
ap-1829	245	20	a	a	DET
ap-1829	245	21	state	state	NOUN
ap-1829	245	22	,	,	PUNCT
ap-1829	245	23	that	that	SCONJ
ap-1829	245	24	the	the	DET
ap-1829	245	25	material	material	NOUN
ap-1829	245	26	parameters	parameter	NOUN
ap-1829	245	27	(	(	PUNCT
ap-1829	245	28	values	value	NOUN
ap-1829	245	29	of	of	ADP
ap-1829	245	30	the	the	DET
ap-1829	245	31	constitutive	constitutive	ADJ
ap-1829	245	32	functions	function	NOUN
ap-1829	245	33	k(h	k(h	PROPN
ap-1829	245	34	,	,	PUNCT
ap-1829	245	35	x	x	NOUN
ap-1829	245	36	)	)	PUNCT
ap-1829	245	37	and	and	CCONJ
ap-1829	245	38	c(h	c(h	PROPN
ap-1829	245	39	,	,	PUNCT
ap-1829	245	40	x))are	x))are	VERB
ap-1829	245	41	transformed	transform	VERB
ap-1829	245	42	into	into	ADP
ap-1829	245	43	certain	certain	ADJ
ap-1829	245	44	homogeneous	homogeneous	ADJ
ap-1829	245	45	values	value	NOUN
ap-1829	245	46	.	.	PUNCT
ap-1829	246	1	behavior	behavior	NOUN
ap-1829	246	2	of	of	ADP
ap-1829	246	3	this	this	DET
ap-1829	246	4	kind	kind	NOUN
ap-1829	246	5	is	be	AUX
ap-1829	246	6	actually	actually	ADV
ap-1829	246	7	achieved	achieve	VERB
ap-1829	246	8	by	by	ADP
ap-1829	246	9	the	the	DET
ap-1829	246	10	standard	standard	ADJ
ap-1829	246	11	jacobi	jacobi	PROPN
ap-1829	246	12	preconditioner	preconditioner	NOUN
ap-1829	246	13	(	(	PUNCT
ap-1829	246	14	diagonal	diagonal	ADJ
ap-1829	246	15	scaling	scaling	NOUN
ap-1829	246	16	)	)	PUNCT
ap-1829	246	17	assumed	assume	VERB
ap-1829	246	18	from	from	ADP
ap-1829	246	19	the	the	DET
ap-1829	246	20	right	right	ADJ
ap-1829	246	21	hand	hand	NOUN
ap-1829	246	22	side	side	NOUN
ap-1829	246	23	.	.	PUNCT
ap-1829	247	1	the	the	DET
ap-1829	247	2	jacobi	jacobi	PROPN
ap-1829	247	3	preconditioner	preconditioner	NOUN
ap-1829	247	4	is	be	AUX
ap-1829	247	5	one	one	NUM
ap-1829	247	6	of	of	ADP
ap-1829	247	7	the	the	DET
ap-1829	247	8	simplest	simple	ADJ
ap-1829	247	9	forms	form	NOUN
ap-1829	247	10	of	of	ADP
ap-1829	247	11	preconditioning	precondition	VERB
ap-1829	247	12	,	,	PUNCT
ap-1829	247	13	in	in	ADP
ap-1829	247	14	which	which	PRON
ap-1829	247	15	the	the	DET
ap-1829	247	16	preconditioner	preconditioner	NOUN
ap-1829	247	17	matrix	matrix	NOUN
ap-1829	247	18	is	be	AUX
ap-1829	247	19	the	the	DET
ap-1829	247	20	diagonal	diagonal	ADJ
ap-1829	247	21	of	of	ADP
ap-1829	247	22	the	the	DET
ap-1829	247	23	original	original	ADJ
ap-1829	247	24	matrix	matrix	NOUN
ap-1829	247	25	a.	a.	NOUN
ap-1829	247	26	the	the	DET
ap-1829	247	27	method	method	NOUN
ap-1829	247	28	can	can	AUX
ap-1829	247	29	be	be	AUX
ap-1829	247	30	described	describe	VERB
ap-1829	247	31	by	by	ADP
ap-1829	247	32	the	the	DET
ap-1829	247	33	following	follow	VERB
ap-1829	247	34	scheme	scheme	NOUN
ap-1829	247	35			PROPN
ap-1829	247	36	a11	a11	PROPN
ap-1829	247	37	a12	a12	PROPN
ap-1829	247	38	.	.	PUNCT
ap-1829	247	39	.	.	PUNCT
ap-1829	247	40	.	.	PUNCT
ap-1829	248	1	a1n	a1n	PRON
ap-1829	248	2	a21	a21	PROPN
ap-1829	248	3	a22	a22	PROPN
ap-1829	248	4	.	.	PUNCT
ap-1829	248	5	.	.	PUNCT
ap-1829	248	6	.	.	PUNCT
ap-1829	249	1	a2n	a2n	PROPN
ap-1829	249	2	...	...	PUNCT
ap-1829	249	3	...	...	PUNCT
ap-1829	249	4	.	.	PUNCT
ap-1829	249	5	.	.	PUNCT
ap-1829	249	6	.	.	PUNCT
ap-1829	249	7	...	...	PUNCT
ap-1829	250	1	an1	an1	PROPN
ap-1829	250	2	an2	an2	PROPN
ap-1829	250	3	.	.	PUNCT
ap-1829	250	4	.	.	PUNCT
ap-1829	250	5	.	.	PUNCT
ap-1829	251	1	ann	ann	PROPN
ap-1829	251	2			PROPN
ap-1829	251	3	→	→	SYM
ap-1829	251	4			PROPN
ap-1829	251	5	1.0	1.0	NUM
ap-1829	251	6	a12	a12	NOUN
ap-1829	251	7	a22	a22	PROPN
ap-1829	251	8	.	.	PUNCT
ap-1829	251	9	.	.	PUNCT
ap-1829	251	10	.	.	PUNCT
ap-1829	252	1	a1n	a1n	PRON
ap-1829	252	2	ann	ann	PROPN
ap-1829	252	3	a21	a21	PROPN
ap-1829	252	4	a11	a11	PROPN
ap-1829	252	5	1.0	1.0	NUM
ap-1829	252	6	.	.	PUNCT
ap-1829	252	7	.	.	PUNCT
ap-1829	252	8	.	.	PUNCT
ap-1829	253	1	a2n	a2n	PROPN
ap-1829	254	1	ann	ann	PROPN
ap-1829	254	2	...	...	PUNCT
ap-1829	254	3	...	...	PUNCT
ap-1829	254	4	.	.	PUNCT
ap-1829	254	5	.	.	PUNCT
ap-1829	254	6	.	.	PUNCT
ap-1829	254	7	...	...	PUNCT
ap-1829	255	1	an1	an1	PROPN
ap-1829	255	2	a11	a11	PROPN
ap-1829	255	3	an2	an2	PROPN
ap-1829	255	4	a22	a22	PROPN
ap-1829	255	5	.	.	PUNCT
ap-1829	255	6	.	.	PUNCT
ap-1829	255	7	.	.	PUNCT
ap-1829	256	1	1.0	1.0	NUM
ap-1829	256	2			NUM
ap-1829	256	3	,	,	PUNCT
ap-1829	256	4	(	(	PUNCT
ap-1829	256	5	19	19	NUM
ap-1829	256	6	)	)	PUNCT
ap-1829	256	7	and	and	CCONJ
ap-1829	256	8	thus	thus	ADV
ap-1829	256	9	this	this	DET
ap-1829	256	10	method	method	NOUN
ap-1829	256	11	can	can	AUX
ap-1829	256	12	be	be	AUX
ap-1829	256	13	referred	refer	VERB
ap-1829	256	14	to	to	ADP
ap-1829	256	15	as	as	ADP
ap-1829	256	16	a	a	DET
ap-1829	256	17	right	right	ADJ
ap-1829	256	18	hand	hand	NOUN
ap-1829	256	19	side	side	NOUN
ap-1829	256	20	diagonal	diagonal	ADJ
ap-1829	256	21	preconditioner	preconditioner	NOUN
ap-1829	256	22	aprcd	aprcd	PROPN
ap-1829	256	23	=	=	PUNCT
ap-1829	256	24	a×d	a×d	PROPN
ap-1829	256	25	,	,	PUNCT
ap-1829	256	26	(	(	PUNCT
ap-1829	256	27	20	20	NUM
ap-1829	256	28	)	)	PUNCT
ap-1829	256	29	where	where	SCONJ
ap-1829	256	30	d	d	NOUN
ap-1829	256	31	=	=	SYM
ap-1829	256	32			PROPN
ap-1829	256	33	1	1	NUM
ap-1829	256	34	a11	a11	NOUN
ap-1829	256	35	0	0	NUM
ap-1829	256	36	.	.	PUNCT
ap-1829	256	37	.	.	PUNCT
ap-1829	257	1	.	.	PUNCT
ap-1829	258	1	0	0	NUM
ap-1829	258	2	0	0	NUM
ap-1829	258	3	1	1	NUM
ap-1829	258	4	a22	a22	NOUN
ap-1829	258	5	.	.	PUNCT
ap-1829	258	6	.	.	PUNCT
ap-1829	259	1	.	.	PUNCT
ap-1829	260	1	0	0	NUM
ap-1829	260	2	...	...	PUNCT
ap-1829	260	3	...	...	PUNCT
ap-1829	260	4	.	.	PUNCT
ap-1829	260	5	.	.	PUNCT
ap-1829	260	6	.	.	PUNCT
ap-1829	261	1	...	...	PUNCT
ap-1829	262	1	0	0	NUM
ap-1829	262	2	0	0	NUM
ap-1829	262	3	.	.	PUNCT
ap-1829	262	4	.	.	PUNCT
ap-1829	262	5	.	.	PUNCT
ap-1829	263	1	1	1	NUM
ap-1829	263	2	ann	ann	PROPN
ap-1829	263	3			PROPN
ap-1829	263	4	.	.	PUNCT
ap-1829	264	1	(	(	PUNCT
ap-1829	264	2	21	21	NUM
ap-1829	264	3	)	)	PUNCT
ap-1829	264	4	this	this	DET
ap-1829	264	5	method	method	NOUN
ap-1829	264	6	suffers	suffer	VERB
ap-1829	264	7	from	from	ADP
ap-1829	264	8	one	one	NUM
ap-1829	264	9	notable	notable	ADJ
ap-1829	264	10	disadvantage	disadvantage	NOUN
ap-1829	264	11	–	–	PUNCT
ap-1829	264	12	it	it	PRON
ap-1829	264	13	creates	create	VERB
ap-1829	264	14	non	non	ADJ
ap-1829	264	15	-	-	ADJ
ap-1829	264	16	symmetric	symmetric	ADJ
ap-1829	264	17	matrices	matrix	NOUN
ap-1829	264	18	even	even	ADV
ap-1829	264	19	out	out	ADP
ap-1829	264	20	of	of	ADP
ap-1829	264	21	symmetric	symmetric	ADJ
ap-1829	264	22	matrices	matrix	NOUN
ap-1829	264	23	.	.	PUNCT
ap-1829	265	1	however	however	ADV
ap-1829	265	2	,	,	PUNCT
ap-1829	265	3	transport	transport	NOUN
ap-1829	265	4	processes	process	NOUN
ap-1829	265	5	are	be	AUX
ap-1829	265	6	in	in	ADP
ap-1829	265	7	352	352	NUM
ap-1829	265	8	vol	vol	NOUN
ap-1829	265	9	.	.	PUNCT
ap-1829	266	1	53	53	NUM
ap-1829	266	2	no	no	NOUN
ap-1829	266	3	.	.	PUNCT
ap-1829	267	1	4/2013	4/2013	NOUN
ap-1829	267	2	algorithms	algorithm	NOUN
ap-1829	267	3	for	for	ADP
ap-1829	267	4	solving	solve	VERB
ap-1829	267	5	darcian	darcian	NOUN
ap-1829	267	6	flow	flow	NOUN
ap-1829	267	7	in	in	ADP
ap-1829	267	8	structured	structured	ADJ
ap-1829	267	9	porous	porous	ADJ
ap-1829	267	10	media	medium	NOUN
ap-1829	267	11	general	general	NOUN
ap-1829	267	12	a	a	DET
ap-1829	267	13	convection	convection	NOUN
ap-1829	267	14	-	-	PUNCT
ap-1829	267	15	diffusion	diffusion	NOUN
ap-1829	267	16	process	process	NOUN
ap-1829	267	17	,	,	PUNCT
ap-1829	267	18	and	and	CCONJ
ap-1829	267	19	thus	thus	ADV
ap-1829	267	20	they	they	PRON
ap-1829	267	21	are	be	AUX
ap-1829	267	22	non	non	ADJ
ap-1829	267	23	-	-	ADJ
ap-1829	267	24	symmetric	symmetric	ADJ
ap-1829	267	25	.	.	PUNCT
ap-1829	268	1	in	in	ADP
ap-1829	268	2	the	the	DET
ap-1829	268	3	context	context	NOUN
ap-1829	268	4	of	of	ADP
ap-1829	268	5	the	the	DET
ap-1829	268	6	conjugate	conjugate	ADJ
ap-1829	268	7	gradient	gradient	NOUN
ap-1829	268	8	method	method	NOUN
ap-1829	268	9	for	for	ADP
ap-1829	268	10	normal	normal	ADJ
ap-1829	268	11	equations	equation	NOUN
ap-1829	268	12	,	,	PUNCT
ap-1829	268	13	this	this	DET
ap-1829	268	14	method	method	NOUN
ap-1829	268	15	of	of	ADP
ap-1829	268	16	preconditioning	precondition	VERB
ap-1829	268	17	can	can	AUX
ap-1829	268	18	be	be	AUX
ap-1829	268	19	formulated	formulate	VERB
ap-1829	268	20	as	as	ADP
ap-1829	268	21	dtatad	dtatad	NOUN
ap-1829	268	22	,	,	PUNCT
ap-1829	268	23	which	which	PRON
ap-1829	268	24	is	be	AUX
ap-1829	268	25	actually	actually	ADV
ap-1829	268	26	a	a	DET
ap-1829	268	27	standard	standard	ADJ
ap-1829	268	28	approach	approach	NOUN
ap-1829	268	29	.	.	PUNCT
ap-1829	269	1	4.1	4.1	NUM
ap-1829	269	2	.	.	PUNCT
ap-1829	270	1	on	on	ADP
ap-1829	270	2	selecting	select	VERB
ap-1829	270	3	an	an	DET
ap-1829	270	4	algorithm	algorithm	NOUN
ap-1829	270	5	for	for	ADP
ap-1829	270	6	solving	solve	VERB
ap-1829	270	7	the	the	DET
ap-1829	270	8	systems	system	NOUN
ap-1829	270	9	of	of	ADP
ap-1829	270	10	linear	linear	PROPN
ap-1829	270	11	equations	equation	NOUN
ap-1829	270	12	transport	transport	NOUN
ap-1829	270	13	processes	process	NOUN
ap-1829	270	14	in	in	ADP
ap-1829	270	15	porous	porous	ADJ
ap-1829	270	16	media	medium	NOUN
ap-1829	270	17	are	be	AUX
ap-1829	270	18	in	in	ADP
ap-1829	270	19	general	general	ADJ
ap-1829	270	20	of	of	ADP
ap-1829	270	21	a	a	DET
ap-1829	270	22	convection	convection	NOUN
ap-1829	270	23	-	-	PUNCT
ap-1829	270	24	diffusion	diffusion	NOUN
ap-1829	270	25	-	-	PUNCT
ap-1829	270	26	reaction	reaction	NOUN
ap-1829	270	27	form	form	NOUN
ap-1829	270	28	.	.	PUNCT
ap-1829	271	1	in	in	ADP
ap-1829	271	2	the	the	DET
ap-1829	271	3	case	case	NOUN
ap-1829	271	4	of	of	ADP
ap-1829	271	5	the	the	DET
ap-1829	271	6	standard	standard	ADJ
ap-1829	271	7	richards	richard	NOUN
ap-1829	271	8	equation	equation	NOUN
ap-1829	271	9	the	the	DET
ap-1829	271	10	convection	convection	NOUN
ap-1829	271	11	is	be	AUX
ap-1829	271	12	caused	cause	VERB
ap-1829	271	13	by	by	ADP
ap-1829	271	14	gravitational	gravitational	ADJ
ap-1829	271	15	forces	force	NOUN
ap-1829	271	16	,	,	PUNCT
ap-1829	271	17	and	and	CCONJ
ap-1829	271	18	then	then	ADV
ap-1829	271	19	the	the	DET
ap-1829	271	20	problem	problem	NOUN
ap-1829	271	21	can	can	AUX
ap-1829	271	22	be	be	AUX
ap-1829	271	23	formulated	formulate	VERB
ap-1829	271	24	symmetrically	symmetrically	ADV
ap-1829	271	25	with	with	ADP
ap-1829	271	26	respect	respect	NOUN
ap-1829	271	27	to	to	ADP
ap-1829	271	28	the	the	DET
ap-1829	271	29	total	total	ADJ
ap-1829	271	30	hydraulic	hydraulic	ADJ
ap-1829	271	31	head	head	NOUN
ap-1829	271	32	h	h	NOUN
ap-1829	271	33	instead	instead	ADV
ap-1829	271	34	of	of	ADP
ap-1829	272	1	the	the	DET
ap-1829	272	2	pressure	pressure	NOUN
ap-1829	272	3	head	head	NOUN
ap-1829	272	4	h.	h.	PROPN
ap-1829	272	5	this	this	DET
ap-1829	272	6	approach	approach	NOUN
ap-1829	272	7	would	would	AUX
ap-1829	272	8	be	be	AUX
ap-1829	272	9	efficient	efficient	ADJ
ap-1829	272	10	for	for	ADP
ap-1829	272	11	the	the	DET
ap-1829	272	12	case	case	NOUN
ap-1829	272	13	studies	study	NOUN
ap-1829	272	14	evaluated	evaluate	VERB
ap-1829	272	15	here	here	ADV
ap-1829	272	16	,	,	PUNCT
ap-1829	272	17	but	but	CCONJ
ap-1829	272	18	the	the	DET
ap-1829	272	19	transport	transport	NOUN
ap-1829	272	20	processes	process	NOUN
ap-1829	272	21	in	in	ADP
ap-1829	272	22	porous	porous	ADJ
ap-1829	272	23	media	medium	NOUN
ap-1829	272	24	are	be	AUX
ap-1829	272	25	more	more	ADV
ap-1829	272	26	accurately	accurately	ADV
ap-1829	272	27	described	describe	VERB
ap-1829	272	28	by	by	ADP
ap-1829	272	29	a	a	DET
ap-1829	272	30	coupled	couple	VERB
ap-1829	272	31	process	process	NOUN
ap-1829	272	32	of	of	ADP
ap-1829	272	33	moisture	moisture	NOUN
ap-1829	272	34	,	,	PUNCT
ap-1829	272	35	heat	heat	NOUN
ap-1829	272	36	and	and	CCONJ
ap-1829	272	37	solute	solute	NOUN
ap-1829	272	38	transport	transport	NOUN
ap-1829	272	39	,	,	PUNCT
ap-1829	272	40	as	as	SCONJ
ap-1829	272	41	described	describe	VERB
ap-1829	272	42	by	by	ADP
ap-1829	272	43	noborio	noborio	PROPN
ap-1829	272	44	et	et	PROPN
ap-1829	272	45	al	al	PROPN
ap-1829	272	46	.	.	PUNCT
ap-1829	273	1	[	[	X
ap-1829	273	2	18	18	NUM
ap-1829	273	3	]	]	PUNCT
ap-1829	273	4	.	.	PUNCT
ap-1829	274	1	thus	thus	ADV
ap-1829	274	2	the	the	DET
ap-1829	274	3	search	search	NOUN
ap-1829	274	4	for	for	ADP
ap-1829	274	5	an	an	DET
ap-1829	274	6	efficient	efficient	ADJ
ap-1829	274	7	solver	solver	NOUN
ap-1829	274	8	should	should	AUX
ap-1829	274	9	not	not	PART
ap-1829	274	10	be	be	AUX
ap-1829	274	11	limited	limit	VERB
ap-1829	274	12	to	to	ADP
ap-1829	274	13	symmetric	symmetric	ADJ
ap-1829	274	14	problems	problem	NOUN
ap-1829	274	15	only	only	ADV
ap-1829	274	16	.	.	PUNCT
ap-1829	275	1	moreover	moreover	ADV
ap-1829	275	2	,	,	PUNCT
ap-1829	275	3	preserving	preserve	VERB
ap-1829	275	4	the	the	DET
ap-1829	275	5	formulation	formulation	NOUN
ap-1829	275	6	of	of	ADP
ap-1829	275	7	the	the	DET
ap-1829	275	8	richards	richard	NOUN
ap-1829	275	9	equation	equation	NOUN
ap-1829	275	10	in	in	ADP
ap-1829	275	11	the	the	DET
ap-1829	275	12	pressure	pressure	NOUN
ap-1829	275	13	head	head	NOUN
ap-1829	275	14	form	form	NOUN
ap-1829	275	15	h	h	NOUN
ap-1829	275	16	enables	enable	VERB
ap-1829	275	17	density	density	NOUN
ap-1829	275	18	dependent	dependent	ADJ
ap-1829	275	19	transport	transport	NOUN
ap-1829	275	20	problems	problem	NOUN
ap-1829	275	21	to	to	PART
ap-1829	275	22	be	be	AUX
ap-1829	275	23	solved	solve	VERB
ap-1829	275	24	,	,	PUNCT
ap-1829	275	25	e.g.	e.g.	ADV
ap-1829	275	26	sea	sea	NOUN
ap-1829	275	27	water	water	NOUN
ap-1829	275	28	intrusion	intrusion	NOUN
ap-1829	275	29	.	.	PUNCT
ap-1829	276	1	this	this	DET
ap-1829	276	2	form	form	NOUN
ap-1829	276	3	was	be	AUX
ap-1829	276	4	therefore	therefore	ADV
ap-1829	276	5	preferred	prefer	VERB
ap-1829	276	6	in	in	ADP
ap-1829	276	7	implementing	implement	VERB
ap-1829	276	8	the	the	DET
ap-1829	276	9	drutes	drute	NOUN
ap-1829	276	10	code	code	NOUN
ap-1829	276	11	.	.	PUNCT
ap-1829	277	1	secondly	secondly	ADV
ap-1829	277	2	,	,	PUNCT
ap-1829	277	3	the	the	DET
ap-1829	277	4	diagonal	diagonal	ADJ
ap-1829	277	5	scaling	scaling	NOUN
ap-1829	277	6	method	method	NOUN
ap-1829	277	7	that	that	PRON
ap-1829	277	8	is	be	AUX
ap-1829	277	9	applied	apply	VERB
ap-1829	277	10	forms	form	NOUN
ap-1829	277	11	non	non	ADJ
ap-1829	277	12	-	-	ADJ
ap-1829	277	13	symmetric	symmetric	ADJ
ap-1829	277	14	matrices	matrix	NOUN
ap-1829	277	15	out	out	ADP
ap-1829	277	16	of	of	ADP
ap-1829	277	17	symmetric	symmetric	ADJ
ap-1829	277	18	matrices	matrix	NOUN
ap-1829	277	19	.	.	PUNCT
ap-1829	278	1	this	this	DET
ap-1829	278	2	property	property	NOUN
ap-1829	278	3	is	be	AUX
ap-1829	278	4	obviously	obviously	ADV
ap-1829	278	5	inconvenient	inconvenient	ADJ
ap-1829	278	6	,	,	PUNCT
ap-1829	278	7	but	but	CCONJ
ap-1829	278	8	based	base	VERB
ap-1829	278	9	on	on	ADP
ap-1829	278	10	the	the	DET
ap-1829	278	11	following	follow	VERB
ap-1829	278	12	assumption	assumption	NOUN
ap-1829	278	13	the	the	DET
ap-1829	278	14	cost	cost	NOUN
ap-1829	278	15	for	for	ADP
ap-1829	278	16	losing	lose	VERB
ap-1829	278	17	the	the	DET
ap-1829	278	18	symmetricity	symmetricity	NOUN
ap-1829	278	19	,	,	PUNCT
ap-1829	278	20	either	either	CCONJ
ap-1829	278	21	due	due	ADP
ap-1829	278	22	to	to	ADP
ap-1829	278	23	a	a	DET
ap-1829	278	24	less	less	ADV
ap-1829	278	25	appropriate	appropriate	ADJ
ap-1829	278	26	formulation	formulation	NOUN
ap-1829	278	27	of	of	ADP
ap-1829	278	28	the	the	DET
ap-1829	278	29	richards	richard	NOUN
ap-1829	278	30	equation	equation	NOUN
ap-1829	278	31	or	or	CCONJ
ap-1829	278	32	due	due	ADP
ap-1829	278	33	to	to	ADP
ap-1829	278	34	the	the	DET
ap-1829	278	35	application	application	NOUN
ap-1829	278	36	of	of	ADP
ap-1829	278	37	right	right	ADJ
ap-1829	278	38	hand	hand	NOUN
ap-1829	278	39	side	side	NOUN
ap-1829	278	40	diagonal	diagonal	ADJ
ap-1829	278	41	scaling	scaling	NOUN
ap-1829	278	42	,	,	PUNCT
ap-1829	278	43	is	be	AUX
ap-1829	278	44	insignificant	insignificant	ADJ
ap-1829	278	45	.	.	PUNCT
ap-1829	279	1	let	let	VERB
ap-1829	279	2	a	a	DET
ap-1829	279	3	be	be	AUX
ap-1829	279	4	the	the	DET
ap-1829	279	5	matrix	matrix	NOUN
ap-1829	279	6	obtained	obtain	VERB
ap-1829	279	7	by	by	ADP
ap-1829	279	8	a	a	DET
ap-1829	279	9	numerical	numerical	ADJ
ap-1829	279	10	approximation	approximation	NOUN
ap-1829	279	11	of	of	ADP
ap-1829	279	12	the	the	DET
ap-1829	279	13	richards	richard	NOUN
ap-1829	279	14	equation	equation	NOUN
ap-1829	279	15	problem	problem	NOUN
ap-1829	279	16	into	into	ADP
ap-1829	279	17	the	the	DET
ap-1829	279	18	system	system	NOUN
ap-1829	279	19	of	of	ADP
ap-1829	279	20	linear	linear	ADJ
ap-1829	279	21	equations	equation	NOUN
ap-1829	279	22	ax	ax	NOUN
ap-1829	279	23	=	=	SYM
ap-1829	279	24	b	b	PROPN
ap-1829	279	25	,	,	PUNCT
ap-1829	279	26	as	as	SCONJ
ap-1829	279	27	described	describe	VERB
ap-1829	279	28	in	in	ADP
ap-1829	279	29	section	section	NOUN
ap-1829	279	30	2.1	2.1	NUM
ap-1829	279	31	.	.	PUNCT
ap-1829	280	1	for	for	ADP
ap-1829	280	2	each	each	DET
ap-1829	280	3	iteration	iteration	NOUN
ap-1829	280	4	of	of	ADP
ap-1829	280	5	the	the	DET
ap-1829	280	6	picard	picard	NOUN
ap-1829	280	7	method	method	NOUN
ap-1829	280	8	,	,	PUNCT
ap-1829	280	9	matrix	matrix	VERB
ap-1829	280	10	a	a	PRON
ap-1829	280	11	and	and	CCONJ
ap-1829	280	12	vector	vector	PROPN
ap-1829	280	13	b	b	PROPN
ap-1829	280	14	is	be	AUX
ap-1829	280	15	assembled	assemble	VERB
ap-1829	280	16	from	from	ADP
ap-1829	280	17	equations	equation	NOUN
ap-1829	280	18	(	(	PUNCT
ap-1829	280	19	11	11	NUM
ap-1829	280	20	)	)	PUNCT
ap-1829	280	21	–	–	PUNCT
ap-1829	280	22	(	(	PUNCT
ap-1829	280	23	12	12	NUM
ap-1829	280	24	)	)	PUNCT
ap-1829	280	25	and	and	CCONJ
ap-1829	280	26	from	from	ADP
ap-1829	280	27	the	the	DET
ap-1829	280	28	boundary	boundary	ADJ
ap-1829	280	29	condition	condition	NOUN
ap-1829	280	30	setup	setup	NOUN
ap-1829	280	31	(	(	PUNCT
ap-1829	280	32	4	4	NUM
ap-1829	280	33	)	)	PUNCT
ap-1829	280	34	.	.	PUNCT
ap-1829	281	1	due	due	ADP
ap-1829	281	2	to	to	ADP
ap-1829	281	3	nonlinearities	nonlinearitie	NOUN
ap-1829	281	4	in	in	ADP
ap-1829	281	5	the	the	DET
ap-1829	281	6	richards	richard	NOUN
ap-1829	281	7	equation	equation	NOUN
ap-1829	281	8	,	,	PUNCT
ap-1829	281	9	and	and	CCONJ
ap-1829	281	10	due	due	ADP
ap-1829	281	11	to	to	ADP
ap-1829	281	12	preserving	preserve	VERB
ap-1829	281	13	the	the	DET
ap-1829	281	14	mass	mass	NOUN
ap-1829	281	15	balance	balance	NOUN
ap-1829	281	16	,	,	PUNCT
ap-1829	281	17	the	the	DET
ap-1829	281	18	problem	problem	NOUN
ap-1829	281	19	is	be	AUX
ap-1829	281	20	temporally	temporally	ADV
ap-1829	281	21	discretized	discretize	VERB
ap-1829	281	22	into	into	ADP
ap-1829	281	23	small	small	ADJ
ap-1829	281	24	time	time	NOUN
ap-1829	281	25	steps	step	NOUN
ap-1829	281	26	.	.	PUNCT
ap-1829	282	1	together	together	ADV
ap-1829	282	2	with	with	ADP
ap-1829	282	3	lumping	lump	VERB
ap-1829	282	4	the	the	DET
ap-1829	282	5	capacity	capacity	NOUN
ap-1829	282	6	matrix	matrix	NOUN
ap-1829	282	7	as	as	SCONJ
ap-1829	282	8	recommended	recommend	VERB
ap-1829	282	9	by	by	ADP
ap-1829	282	10	rank	rank	PROPN
ap-1829	282	11	et	et	PROPN
ap-1829	282	12	al	al	PROPN
ap-1829	282	13	.	.	PUNCT
ap-1829	283	1	[	[	X
ap-1829	283	2	19	19	NUM
ap-1829	283	3	]	]	PUNCT
ap-1829	283	4	,	,	PUNCT
ap-1829	283	5	in	in	ADP
ap-1829	283	6	order	order	NOUN
ap-1829	283	7	to	to	PART
ap-1829	283	8	preserve	preserve	VERB
ap-1829	283	9	the	the	DET
ap-1829	283	10	discrete	discrete	ADJ
ap-1829	283	11	maximum	maximum	ADJ
ap-1829	283	12	principle	principle	NOUN
ap-1829	283	13	,	,	PUNCT
ap-1829	283	14	we	we	PRON
ap-1829	283	15	could	could	AUX
ap-1829	283	16	start	start	VERB
ap-1829	283	17	with	with	ADP
ap-1829	283	18	the	the	DET
ap-1829	283	19	hypothesis	hypothesis	NOUN
ap-1829	283	20	of	of	ADP
ap-1829	283	21	a	a	DET
ap-1829	283	22	strong	strong	ADJ
ap-1829	283	23	diagonal	diagonal	ADJ
ap-1829	283	24	dominance	dominance	NOUN
ap-1829	283	25	of	of	ADP
ap-1829	283	26	matrix	matrix	NOUN
ap-1829	283	27	a.	a.	NOUN
ap-1829	283	28	then	then	ADV
ap-1829	283	29	matrix	matrix	VERB
ap-1829	283	30	a	a	PRON
ap-1829	283	31	can	can	AUX
ap-1829	283	32	be	be	AUX
ap-1829	283	33	decomposed	decompose	VERB
ap-1829	283	34	into	into	ADP
ap-1829	283	35	the	the	DET
ap-1829	283	36	sum	sum	NOUN
ap-1829	283	37	of	of	ADP
ap-1829	283	38	its	its	PRON
ap-1829	283	39	diagonal	diagonal	ADJ
ap-1829	283	40	and	and	CCONJ
ap-1829	283	41	nondiagonal	nondiagonal	ADJ
ap-1829	283	42	part	part	NOUN
ap-1829	283	43	a	a	PRON
ap-1829	283	44	=	=	SYM
ap-1829	283	45	d	d	PROPN
ap-1829	283	46	+	+	NUM
ap-1829	283	47	b	b	PROPN
ap-1829	283	48	,	,	PUNCT
ap-1829	283	49	(	(	PUNCT
ap-1829	283	50	22	22	NUM
ap-1829	283	51	)	)	PUNCT
ap-1829	283	52	where	where	SCONJ
ap-1829	283	53	d	d	NOUN
ap-1829	283	54	=	=	SYM
ap-1829	283	55	diag(a	diag(a	PROPN
ap-1829	283	56	)	)	PUNCT
ap-1829	283	57	,	,	PUNCT
ap-1829	283	58	and	and	CCONJ
ap-1829	283	59	obviously	obviously	ADV
ap-1829	283	60	b	b	X
ap-1829	283	61	=	=	PUNCT
ap-1829	283	62	a−d	a−d	PROPN
ap-1829	283	63	.	.	PUNCT
ap-1829	284	1	the	the	DET
ap-1829	284	2	right	right	ADJ
ap-1829	284	3	hand	hand	NOUN
ap-1829	284	4	side	side	NOUN
ap-1829	284	5	diagonal	diagonal	ADJ
ap-1829	284	6	scaling	scaling	NOUN
ap-1829	284	7	rearranges	rearrange	VERB
ap-1829	284	8	the	the	DET
ap-1829	284	9	original	original	ADJ
ap-1829	284	10	problem	problem	NOUN
ap-1829	284	11	ax	ax	NOUN
ap-1829	284	12	=	=	NOUN
ap-1829	284	13	b	b	NOUN
ap-1829	284	14	into	into	ADP
ap-1829	284	15	ad−1y	ad−1y	PROPN
ap-1829	284	16	=	=	SYM
ap-1829	284	17	b	b	NOUN
ap-1829	284	18	,	,	PUNCT
ap-1829	284	19	(	(	PUNCT
ap-1829	284	20	23	23	NUM
ap-1829	284	21	)	)	PUNCT
ap-1829	284	22	where	where	SCONJ
ap-1829	284	23	x	x	SYM
ap-1829	284	24	=	=	SYM
ap-1829	284	25	d−1y	d−1y	PROPN
ap-1829	284	26	.	.	PUNCT
ap-1829	285	1	then	then	ADV
ap-1829	285	2	the	the	DET
ap-1829	285	3	matrix	matrix	NOUN
ap-1829	285	4	ad−1	ad−1	NOUN
ap-1829	285	5	can	can	AUX
ap-1829	285	6	be	be	AUX
ap-1829	285	7	considered	consider	VERB
ap-1829	285	8	as	as	ADP
ap-1829	285	9	ad−1	ad−1	PROPN
ap-1829	285	10	=	=	PUNCT
ap-1829	285	11	i	i	PROPN
ap-1829	285	12	+	+	CCONJ
ap-1829	285	13	bd−1	bd−1	PROPN
ap-1829	285	14	,	,	PUNCT
ap-1829	285	15	(	(	PUNCT
ap-1829	285	16	24	24	NUM
ap-1829	285	17	)	)	PUNCT
ap-1829	285	18	where	where	SCONJ
ap-1829	285	19	i	i	PRON
ap-1829	285	20	is	be	AUX
ap-1829	285	21	an	an	DET
ap-1829	285	22	identity	identity	NOUN
ap-1829	285	23	matrix	matrix	NOUN
ap-1829	285	24	.	.	PUNCT
ap-1829	286	1	if	if	SCONJ
ap-1829	286	2	we	we	PRON
ap-1829	286	3	apply	apply	VERB
ap-1829	286	4	the	the	DET
ap-1829	286	5	conjugate	conjugate	ADJ
ap-1829	286	6	gradient	gradient	ADJ
ap-1829	286	7	algorithm	algorithm	NOUN
ap-1829	286	8	for	for	ADP
ap-1829	286	9	normal	normal	ADJ
ap-1829	286	10	equations	equation	NOUN
ap-1829	286	11	to	to	ADP
ap-1829	286	12	the	the	DET
ap-1829	286	13	matrix	matrix	NOUN
ap-1829	286	14	i	i	NOUN
ap-1829	286	15	+	+	CCONJ
ap-1829	286	16	bd−1	bd−1	PROPN
ap-1829	286	17	from	from	ADP
ap-1829	286	18	(	(	PUNCT
ap-1829	286	19	24	24	NUM
ap-1829	286	20	)	)	PUNCT
ap-1829	286	21	,	,	PUNCT
ap-1829	286	22	then	then	ADV
ap-1829	286	23	the	the	DET
ap-1829	286	24	following	follow	VERB
ap-1829	286	25	is	be	AUX
ap-1829	286	26	obtained	obtain	VERB
ap-1829	286	27	g	g	NOUN
ap-1829	286	28	=	=	PUNCT
ap-1829	286	29	(	(	PUNCT
ap-1829	286	30	i	i	PRON
ap-1829	286	31	+	+	PUNCT
ap-1829	286	32	bd−1)t	bd−1)t	PUNCT
ap-1829	287	1	(	(	PUNCT
ap-1829	287	2	i	i	PRON
ap-1829	287	3	+	+	CCONJ
ap-1829	287	4	bd−1	bd−1	PROPN
ap-1829	287	5	)	)	PUNCT
ap-1829	287	6	=	=	PUNCT
ap-1829	288	1	=	=	PUNCT
ap-1829	288	2	i	i	PRON
ap-1829	288	3	+	+	X
ap-1829	288	4	(	(	PUNCT
ap-1829	288	5	bd−1)t	bd−1)t	VERB
ap-1829	288	6	+	+	CCONJ
ap-1829	288	7	bd−1	bd−1	PROPN
ap-1829	288	8	+	+	PROPN
ap-1829	288	9	(	(	PUNCT
ap-1829	288	10	bd−1)tbd−1	bd−1)tbd−1	PROPN
ap-1829	288	11	,	,	PUNCT
ap-1829	288	12	(	(	PUNCT
ap-1829	288	13	25	25	NUM
ap-1829	288	14	)	)	PUNCT
ap-1829	288	15	where	where	SCONJ
ap-1829	288	16	g	g	PROPN
ap-1829	288	17	is	be	AUX
ap-1829	288	18	the	the	DET
ap-1829	288	19	matrix	matrix	NOUN
ap-1829	288	20	that	that	PRON
ap-1829	288	21	is	be	AUX
ap-1829	288	22	processed	process	VERB
ap-1829	288	23	in	in	ADP
ap-1829	288	24	the	the	DET
ap-1829	288	25	conjugate	conjugate	ADJ
ap-1829	288	26	gradient	gradient	NOUN
ap-1829	288	27	algorithm	algorithm	NOUN
ap-1829	288	28	.	.	PUNCT
ap-1829	289	1	based	base	VERB
ap-1829	289	2	on	on	ADP
ap-1829	289	3	the	the	DET
ap-1829	289	4	hypothesis	hypothesis	NOUN
ap-1829	289	5	of	of	ADP
ap-1829	289	6	the	the	DET
ap-1829	289	7	strong	strong	ADJ
ap-1829	289	8	diagonal	diagonal	ADJ
ap-1829	289	9	dominance	dominance	NOUN
ap-1829	289	10	of	of	ADP
ap-1829	289	11	matrix	matrix	NOUN
ap-1829	289	12	a	a	PRON
ap-1829	289	13	,	,	PUNCT
ap-1829	289	14	the	the	DET
ap-1829	289	15	frobenius	frobenius	ADJ
ap-1829	289	16	norm	norm	NOUN
ap-1829	289	17	of	of	ADP
ap-1829	289	18	‖bd−1‖	‖bd−1‖	PROPN
ap-1829	289	19	is	be	AUX
ap-1829	289	20	small	small	ADJ
ap-1829	289	21	‖bd−1‖	‖bd−1‖	PROPN
ap-1829	289	22	�	�	PROPN
ap-1829	289	23	1.0	1.0	NUM
ap-1829	289	24	,	,	PUNCT
ap-1829	289	25	(	(	PUNCT
ap-1829	289	26	26	26	NUM
ap-1829	289	27	)	)	PUNCT
ap-1829	289	28	and	and	CCONJ
ap-1829	289	29	thus	thus	ADV
ap-1829	289	30	it	it	PRON
ap-1829	289	31	could	could	AUX
ap-1829	289	32	be	be	AUX
ap-1829	289	33	concluded	conclude	VERB
ap-1829	289	34	that	that	SCONJ
ap-1829	289	35	frobenius	frobenius	ADJ
ap-1829	289	36	norm	norm	NOUN
ap-1829	289	37	of	of	ADP
ap-1829	289	38	the	the	DET
ap-1829	289	39	matrix	matrix	NOUN
ap-1829	289	40	g	g	NOUN
ap-1829	289	41	from	from	ADP
ap-1829	289	42	(	(	PUNCT
ap-1829	289	43	25	25	NUM
ap-1829	289	44	)	)	PUNCT
ap-1829	289	45	must	must	AUX
ap-1829	289	46	be	be	AUX
ap-1829	289	47	close	close	ADJ
ap-1829	289	48	to	to	ADP
ap-1829	289	49	1.0	1.0	NUM
ap-1829	289	50	.	.	PUNCT
ap-1829	290	1	this	this	DET
ap-1829	290	2	conclusion	conclusion	NOUN
ap-1829	290	3	will	will	AUX
ap-1829	290	4	be	be	AUX
ap-1829	290	5	deeply	deeply	ADV
ap-1829	290	6	explained	explain	VERB
ap-1829	290	7	.	.	PUNCT
ap-1829	291	1	let	let	VERB
ap-1829	291	2	us	we	PRON
ap-1829	291	3	consider	consider	VERB
ap-1829	291	4	matrix	matrix	NOUN
ap-1829	291	5	f	f	NOUN
ap-1829	291	6	as	as	ADP
ap-1829	291	7	f	f	PROPN
ap-1829	291	8	=	=	SYM
ap-1829	291	9	g−	g−	PROPN
ap-1829	292	1	i	i	PRON
ap-1829	292	2	,	,	PUNCT
ap-1829	292	3	(	(	PUNCT
ap-1829	292	4	27	27	NUM
ap-1829	292	5	)	)	PUNCT
ap-1829	292	6	and	and	CCONJ
ap-1829	292	7	thus	thus	ADV
ap-1829	292	8	f	f	X
ap-1829	292	9	=	=	PUNCT
ap-1829	292	10	(	(	PUNCT
ap-1829	292	11	bd−1)t	bd−1)t	PROPN
ap-1829	293	1	+	+	CCONJ
ap-1829	293	2	bd−1	bd−1	PROPN
ap-1829	293	3	+	+	CCONJ
ap-1829	293	4	(	(	PUNCT
ap-1829	293	5	bd−1)tbd−1	bd−1)tbd−1	PROPN
ap-1829	293	6	.	.	PUNCT
ap-1829	294	1	(	(	PUNCT
ap-1829	294	2	28	28	NUM
ap-1829	294	3	)	)	PUNCT
ap-1829	294	4	then	then	ADV
ap-1829	294	5	the	the	DET
ap-1829	294	6	frobenius	frobenius	ADJ
ap-1829	294	7	norm	norm	NOUN
ap-1829	294	8	of	of	ADP
ap-1829	294	9	matrix	matrix	NOUN
ap-1829	294	10	f	f	X
ap-1829	294	11	is	be	AUX
ap-1829	294	12	referred	refer	VERB
ap-1829	294	13	to	to	PART
ap-1829	294	14	fne	fne	VERB
ap-1829	294	15	=	=	PUNCT
ap-1829	294	16	‖f‖.	‖f‖.	PART
ap-1829	294	17	(	(	PUNCT
ap-1829	294	18	29	29	NUM
ap-1829	294	19	)	)	PUNCT
ap-1829	294	20	we	we	PRON
ap-1829	294	21	have	have	AUX
ap-1829	294	22	already	already	ADV
ap-1829	294	23	assumed	assume	VERB
ap-1829	294	24	the	the	DET
ap-1829	294	25	frobenius	frobenius	ADJ
ap-1829	294	26	norm	norm	NOUN
ap-1829	294	27	of	of	ADP
ap-1829	294	28	‖bd−1‖	‖bd−1‖	PROPN
ap-1829	294	29	to	to	PART
ap-1829	294	30	be	be	AUX
ap-1829	294	31	small	small	ADJ
ap-1829	294	32	,	,	PUNCT
ap-1829	294	33	see	see	VERB
ap-1829	294	34	(	(	PUNCT
ap-1829	294	35	26	26	NUM
ap-1829	294	36	)	)	PUNCT
ap-1829	294	37	,	,	PUNCT
ap-1829	294	38	due	due	ADP
ap-1829	294	39	to	to	ADP
ap-1829	294	40	the	the	DET
ap-1829	294	41	triangle	triangle	NOUN
ap-1829	294	42	inequality	inequality	NOUN
ap-1829	294	43	and	and	CCONJ
ap-1829	294	44	due	due	ADJ
ap-1829	294	45	the	the	DET
ap-1829	294	46	submultiplicativity	submultiplicativity	NOUN
ap-1829	294	47	of	of	ADP
ap-1829	294	48	the	the	DET
ap-1829	294	49	frobenius	frobenius	ADJ
ap-1829	294	50	norm	norm	NOUN
ap-1829	294	51	we	we	PRON
ap-1829	294	52	can	can	AUX
ap-1829	294	53	conclude	conclude	VERB
ap-1829	294	54	that	that	PRON
ap-1829	294	55	fne	fne	VERB
ap-1829	295	1	≤	≤	NUM
ap-1829	295	2	3‖bd−1‖.	3‖bd−1‖.	PROPN
ap-1829	295	3	(	(	PUNCT
ap-1829	295	4	30	30	NUM
ap-1829	295	5	)	)	PUNCT
ap-1829	295	6	in	in	ADP
ap-1829	295	7	order	order	NOUN
ap-1829	295	8	to	to	PART
ap-1829	295	9	estimate	estimate	VERB
ap-1829	295	10	the	the	DET
ap-1829	295	11	efficiency	efficiency	NOUN
ap-1829	295	12	of	of	ADP
ap-1829	295	13	the	the	DET
ap-1829	295	14	conjugate	conjugate	ADJ
ap-1829	295	15	gradient	gradient	NOUN
ap-1829	295	16	solver	solver	NOUN
ap-1829	295	17	applied	apply	VERB
ap-1829	295	18	to	to	ADP
ap-1829	295	19	the	the	DET
ap-1829	295	20	matrix	matrix	NOUN
ap-1829	295	21	g	g	NOUN
ap-1829	295	22	from	from	ADP
ap-1829	295	23	(	(	PUNCT
ap-1829	295	24	25	25	NUM
ap-1829	295	25	)	)	PUNCT
ap-1829	295	26	,	,	PUNCT
ap-1829	295	27	we	we	PRON
ap-1829	295	28	should	should	AUX
ap-1829	295	29	estimate	estimate	VERB
ap-1829	295	30	the	the	DET
ap-1829	295	31	condition	condition	NOUN
ap-1829	295	32	numbers	number	NOUN
ap-1829	295	33	of	of	ADP
ap-1829	295	34	matrix	matrix	NOUN
ap-1829	295	35	f	f	NOUN
ap-1829	295	36	from	from	ADP
ap-1829	295	37	(	(	PUNCT
ap-1829	295	38	28	28	NUM
ap-1829	295	39	)	)	PUNCT
ap-1829	295	40	.	.	PUNCT
ap-1829	296	1	it	it	PRON
ap-1829	296	2	is	be	AUX
ap-1829	296	3	well	well	ADV
ap-1829	296	4	known	know	VERB
ap-1829	296	5	that	that	SCONJ
ap-1829	296	6	the	the	DET
ap-1829	296	7	absolute	absolute	ADJ
ap-1829	296	8	values	value	NOUN
ap-1829	296	9	of	of	ADP
ap-1829	296	10	all	all	DET
ap-1829	296	11	eigenvalues	eigenvalue	NOUN
ap-1829	296	12	are	be	AUX
ap-1829	296	13	lower	low	ADJ
ap-1829	296	14	than	than	ADP
ap-1829	296	15	its	its	PRON
ap-1829	296	16	matrix	matrix	NOUN
ap-1829	296	17	norm	norm	NOUN
ap-1829	296	18	(	(	PUNCT
ap-1829	296	19	this	this	PRON
ap-1829	296	20	applies	apply	VERB
ap-1829	296	21	for	for	ADP
ap-1829	296	22	all	all	DET
ap-1829	296	23	commonly	commonly	ADV
ap-1829	296	24	used	use	VERB
ap-1829	296	25	norms	norm	NOUN
ap-1829	296	26	including	include	VERB
ap-1829	296	27	the	the	DET
ap-1829	296	28	frobenius	frobenius	NOUN
ap-1829	296	29	norm	norm	NOUN
ap-1829	296	30	)	)	PUNCT
ap-1829	296	31	.	.	PUNCT
ap-1829	297	1	and	and	CCONJ
ap-1829	297	2	thus	thus	ADV
ap-1829	297	3	the	the	DET
ap-1829	297	4	following	follow	VERB
ap-1829	297	5	applies	applies	PROPN
ap-1829	297	6	σ	σ	PROPN
ap-1829	297	7	(	(	PUNCT
ap-1829	297	8	f	f	X
ap-1829	297	9	)	)	PUNCT
ap-1829	297	10	⊂	⊂	PROPN
ap-1829	297	11	(	(	PUNCT
ap-1829	297	12	−fne,+fne	−fne,+fne	PROPN
ap-1829	297	13	)	)	PUNCT
ap-1829	297	14	.	.	PUNCT
ap-1829	298	1	(	(	PUNCT
ap-1829	298	2	31	31	NUM
ap-1829	298	3	)	)	PUNCT
ap-1829	298	4	and	and	CCONJ
ap-1829	298	5	thus	thus	ADV
ap-1829	298	6	matrix	matrix	VERB
ap-1829	298	7	g	g	NOUN
ap-1829	298	8	from	from	ADP
ap-1829	298	9	(	(	PUNCT
ap-1829	298	10	25	25	NUM
ap-1829	298	11	)	)	PUNCT
ap-1829	298	12	,	,	PUNCT
ap-1829	298	13	which	which	PRON
ap-1829	298	14	is	be	AUX
ap-1829	298	15	related	relate	VERB
ap-1829	298	16	to	to	PART
ap-1829	298	17	matrix	matrix	VERB
ap-1829	298	18	f	f	PROPN
ap-1829	298	19	by	by	ADP
ap-1829	298	20	definition	definition	NOUN
ap-1829	298	21	(	(	PUNCT
ap-1829	298	22	27	27	NUM
ap-1829	298	23	)	)	PUNCT
ap-1829	298	24	,	,	PUNCT
ap-1829	298	25	has	have	AUX
ap-1829	298	26	eigenvalues	eigenvalue	VERB
ap-1829	298	27	within	within	ADP
ap-1829	298	28	the	the	DET
ap-1829	298	29	range	range	NOUN
ap-1829	298	30	σ	σ	PROPN
ap-1829	298	31	(	(	PUNCT
ap-1829	298	32	g	g	NOUN
ap-1829	298	33	)	)	PUNCT
ap-1829	298	34	⊂	⊂	PROPN
ap-1829	298	35	(	(	PUNCT
ap-1829	298	36	1−	1−	NUM
ap-1829	298	37	fne	fne	ADJ
ap-1829	298	38	,	,	PUNCT
ap-1829	298	39	1	1	NUM
ap-1829	298	40	+	+	CCONJ
ap-1829	298	41	fne	fne	ADJ
ap-1829	298	42	)	)	PUNCT
ap-1829	298	43	.	.	PUNCT
ap-1829	299	1	(	(	PUNCT
ap-1829	299	2	32	32	NUM
ap-1829	299	3	)	)	PUNCT
ap-1829	299	4	the	the	DET
ap-1829	299	5	condition	condition	NOUN
ap-1829	299	6	number	number	NOUN
ap-1829	299	7	is	be	AUX
ap-1829	299	8	evaluated	evaluate	VERB
ap-1829	299	9	as	as	ADP
ap-1829	299	10	κ	κ	NOUN
ap-1829	299	11	=	=	SYM
ap-1829	299	12	1	1	NUM
ap-1829	300	1	+	+	CCONJ
ap-1829	300	2	λf	λf	PROPN
ap-1829	300	3	max	max	PROPN
ap-1829	300	4	1−	1−	NUM
ap-1829	300	5	λf	λf	PROPN
ap-1829	300	6	min	min	NOUN
ap-1829	300	7	,	,	PUNCT
ap-1829	300	8	(	(	PUNCT
ap-1829	300	9	33	33	NUM
ap-1829	300	10	)	)	PUNCT
ap-1829	300	11	where	where	SCONJ
ap-1829	300	12	κ	κ	NOUN
ap-1829	300	13	is	be	AUX
ap-1829	300	14	the	the	DET
ap-1829	300	15	condition	condition	NOUN
ap-1829	300	16	number	number	NOUN
ap-1829	300	17	of	of	ADP
ap-1829	300	18	matrix	matrix	NOUN
ap-1829	300	19	g	g	NOUN
ap-1829	300	20	,	,	PUNCT
ap-1829	300	21	λf	λf	PROPN
ap-1829	300	22	min	min	NOUN
ap-1829	300	23	is	be	AUX
ap-1829	300	24	the	the	DET
ap-1829	300	25	minimal	minimal	ADJ
ap-1829	300	26	eigen	eigen	PROPN
ap-1829	300	27	value	value	NOUN
ap-1829	300	28	of	of	ADP
ap-1829	300	29	matrix	matrix	NOUN
ap-1829	300	30	f	f	NOUN
ap-1829	300	31	,	,	PUNCT
ap-1829	300	32	and	and	CCONJ
ap-1829	300	33	λf	λf	PROPN
ap-1829	300	34	max	max	PROPN
ap-1829	300	35	is	be	AUX
ap-1829	300	36	the	the	DET
ap-1829	300	37	maximal	maximal	ADJ
ap-1829	300	38	eigen	eigen	NOUN
ap-1829	300	39	value	value	NOUN
ap-1829	300	40	of	of	ADP
ap-1829	300	41	matrix	matrix	NOUN
ap-1829	300	42	f	f	NOUN
ap-1829	300	43	,	,	PUNCT
ap-1829	300	44	and	and	CCONJ
ap-1829	300	45	thus	thus	ADV
ap-1829	300	46	1	1	NUM
ap-1829	300	47	+	+	CCONJ
ap-1829	300	48	λf	λf	PROPN
ap-1829	300	49	max	max	PROPN
ap-1829	300	50	1−	1−	NUM
ap-1829	300	51	λf	λf	PROPN
ap-1829	300	52	min	min	NOUN
ap-1829	300	53	<	<	X
ap-1829	300	54	1	1	NUM
ap-1829	301	1	+	+	CCONJ
ap-1829	301	2	fne	fne	ADJ
ap-1829	301	3	1−	1−	NUM
ap-1829	301	4	fne	fne	INTJ
ap-1829	301	5	.	.	PUNCT
ap-1829	302	1	(	(	PUNCT
ap-1829	302	2	34	34	NUM
ap-1829	302	3	)	)	PUNCT
ap-1829	302	4	353	353	NUM
ap-1829	302	5	michal	michal	PROPN
ap-1829	302	6	kuráž	kuráž	PROPN
ap-1829	302	7	,	,	PUNCT
ap-1829	302	8	petr	petr	PROPN
ap-1829	302	9	mayer	mayer	PROPN
ap-1829	302	10	acta	acta	PROPN
ap-1829	302	11	polytechnica	polytechnica	PROPN
ap-1829	302	12	figure	figure	NOUN
ap-1829	302	13	4	4	NUM
ap-1829	302	14	.	.	PUNCT
ap-1829	302	15	scheme	scheme	NOUN
ap-1829	302	16	of	of	ADP
ap-1829	302	17	the	the	DET
ap-1829	302	18	two	two	NUM
ap-1829	302	19	-	-	PUNCT
ap-1829	302	20	dimensional	dimensional	ADJ
ap-1829	302	21	theoretical	theoretical	ADJ
ap-1829	302	22	experiment	experiment	NOUN
ap-1829	302	23	.	.	PUNCT
ap-1829	303	1	in	in	ADP
ap-1829	303	2	order	order	NOUN
ap-1829	303	3	to	to	PART
ap-1829	303	4	fulfill	fulfill	VERB
ap-1829	303	5	the	the	DET
ap-1829	303	6	proposed	propose	VERB
ap-1829	303	7	prerequisite	prerequisite	NOUN
ap-1829	303	8	,	,	PUNCT
ap-1829	303	9	the	the	DET
ap-1829	303	10	norm	norm	NOUN
ap-1829	303	11	‖bd−1‖	‖bd−1‖	PROPN
ap-1829	303	12	must	must	AUX
ap-1829	303	13	be	be	AUX
ap-1829	303	14	small	small	ADJ
ap-1829	303	15	,	,	PUNCT
ap-1829	303	16	but	but	CCONJ
ap-1829	303	17	as	as	SCONJ
ap-1829	303	18	already	already	ADV
ap-1829	303	19	mentioned	mention	VERB
ap-1829	303	20	the	the	DET
ap-1829	303	21	value	value	NOUN
ap-1829	303	22	of	of	ADP
ap-1829	303	23	this	this	DET
ap-1829	303	24	norm	norm	NOUN
ap-1829	303	25	for	for	ADP
ap-1829	303	26	our	our	PRON
ap-1829	303	27	richards	richard	NOUN
ap-1829	303	28	equation	equation	NOUN
ap-1829	303	29	problems	problem	NOUN
ap-1829	303	30	was	be	AUX
ap-1829	303	31	typically	typically	ADV
ap-1829	303	32	observed	observe	VERB
ap-1829	303	33	within	within	ADP
ap-1829	303	34	the	the	DET
ap-1829	303	35	range	range	NOUN
ap-1829	303	36	‖bd−1‖	‖bd−1‖	PROPN
ap-1829	303	37	∈	∈	PROPN
ap-1829	303	38	(	(	PUNCT
ap-1829	303	39	1	1	NUM
ap-1829	303	40	·	·	SYM
ap-1829	303	41	10−12	10−12	NOUN
ap-1829	303	42	,	,	PUNCT
ap-1829	303	43	1	1	NUM
ap-1829	303	44	·	·	SYM
ap-1829	303	45	10−8	10−8	NUM
ap-1829	303	46	)	)	PUNCT
ap-1829	303	47	.	.	PUNCT
ap-1829	304	1	(	(	PUNCT
ap-1829	304	2	35	35	NUM
ap-1829	304	3	)	)	PUNCT
ap-1829	304	4	the	the	DET
ap-1829	304	5	conjugate	conjugate	ADJ
ap-1829	304	6	gradient	gradient	NOUN
ap-1829	304	7	method	method	NOUN
ap-1829	304	8	for	for	ADP
ap-1829	304	9	normal	normal	ADJ
ap-1829	304	10	equations	equation	NOUN
ap-1829	304	11	is	be	AUX
ap-1829	304	12	not	not	PART
ap-1829	304	13	a	a	DET
ap-1829	304	14	typical	typical	ADJ
ap-1829	304	15	choice	choice	NOUN
ap-1829	304	16	due	due	ADP
ap-1829	304	17	to	to	ADP
ap-1829	304	18	squaring	square	VERB
ap-1829	304	19	the	the	DET
ap-1829	304	20	condition	condition	NOUN
ap-1829	304	21	number	number	NOUN
ap-1829	304	22	.	.	PUNCT
ap-1829	305	1	the	the	DET
ap-1829	305	2	typical	typical	ADJ
ap-1829	305	3	solution	solution	NOUN
ap-1829	305	4	is	be	AUX
ap-1829	305	5	based	base	VERB
ap-1829	305	6	on	on	ADP
ap-1829	305	7	gmres	gmre	NOUN
ap-1829	305	8	or	or	CCONJ
ap-1829	305	9	bicgstab	bicgstab	NOUN
ap-1829	305	10	.	.	PUNCT
ap-1829	306	1	gmres	gmre	NOUN
ap-1829	306	2	is	be	AUX
ap-1829	306	3	an	an	DET
ap-1829	306	4	optimal	optimal	ADJ
ap-1829	306	5	method	method	NOUN
ap-1829	306	6	on	on	ADP
ap-1829	306	7	the	the	DET
ap-1829	306	8	krylov	krylov	NOUN
ap-1829	306	9	subspace	subspace	NOUN
ap-1829	306	10	generated	generate	VERB
ap-1829	306	11	by	by	ADP
ap-1829	306	12	the	the	DET
ap-1829	306	13	initial	initial	ADJ
ap-1829	306	14	residual	residual	ADJ
ap-1829	306	15	r0	r0	NOUN
ap-1829	306	16	and	and	CCONJ
ap-1829	306	17	matrix	matrix	NOUN
ap-1829	306	18	a.	a.	NOUN
ap-1829	306	19	but	but	CCONJ
ap-1829	306	20	its	its	PRON
ap-1829	306	21	great	great	ADJ
ap-1829	306	22	disadvantage	disadvantage	NOUN
ap-1829	306	23	is	be	AUX
ap-1829	306	24	that	that	SCONJ
ap-1829	306	25	long	long	ADJ
ap-1829	306	26	recurrences	recurrence	NOUN
ap-1829	306	27	are	be	AUX
ap-1829	306	28	required	require	VERB
ap-1829	306	29	,	,	PUNCT
ap-1829	306	30	so	so	CCONJ
ap-1829	306	31	it	it	PRON
ap-1829	306	32	is	be	AUX
ap-1829	306	33	almost	almost	ADV
ap-1829	306	34	impossible	impossible	ADJ
ap-1829	306	35	to	to	PART
ap-1829	306	36	use	use	VERB
ap-1829	306	37	the	the	DET
ap-1829	306	38	original	original	ADJ
ap-1829	306	39	form	form	NOUN
ap-1829	306	40	of	of	ADP
ap-1829	306	41	gmres	gmre	NOUN
ap-1829	306	42	,	,	PUNCT
ap-1829	306	43	as	as	SCONJ
ap-1829	306	44	the	the	DET
ap-1829	306	45	long	long	ADJ
ap-1829	306	46	recurrences	recurrence	NOUN
ap-1829	306	47	may	may	AUX
ap-1829	306	48	cause	cause	VERB
ap-1829	306	49	serious	serious	ADJ
ap-1829	306	50	problems	problem	NOUN
ap-1829	306	51	with	with	ADP
ap-1829	306	52	computer	computer	NOUN
ap-1829	306	53	memory	memory	NOUN
ap-1829	306	54	allocation	allocation	NOUN
ap-1829	306	55	.	.	PUNCT
ap-1829	307	1	gmres	gmre	NOUN
ap-1829	307	2	is	be	AUX
ap-1829	307	3	typically	typically	ADV
ap-1829	307	4	used	use	VERB
ap-1829	307	5	in	in	ADP
ap-1829	307	6	a	a	DET
ap-1829	307	7	variety	variety	NOUN
ap-1829	307	8	of	of	ADP
ap-1829	307	9	modifications	modification	NOUN
ap-1829	307	10	,	,	PUNCT
ap-1829	307	11	as	as	SCONJ
ap-1829	307	12	restarts	restart	NOUN
ap-1829	307	13	or	or	CCONJ
ap-1829	307	14	shorten	shorten	VERB
ap-1829	307	15	recurrences	recurrence	NOUN
ap-1829	307	16	.	.	PUNCT
ap-1829	308	1	as	as	SCONJ
ap-1829	308	2	presented	present	VERB
ap-1829	308	3	by	by	ADP
ap-1829	308	4	greenbaum	greenbaum	PROPN
ap-1829	308	5	et	et	PROPN
ap-1829	308	6	al	al	PROPN
ap-1829	308	7	.	.	PUNCT
ap-1829	309	1	[	[	X
ap-1829	309	2	22	22	NUM
ap-1829	309	3	]	]	PUNCT
ap-1829	309	4	the	the	DET
ap-1829	309	5	convergence	convergence	NOUN
ap-1829	309	6	rate	rate	NOUN
ap-1829	309	7	does	do	AUX
ap-1829	309	8	not	not	PART
ap-1829	309	9	depend	depend	VERB
ap-1829	309	10	on	on	ADP
ap-1829	309	11	the	the	DET
ap-1829	309	12	eigenvalues	eigenvalue	NOUN
ap-1829	309	13	,	,	PUNCT
ap-1829	309	14	and	and	CCONJ
ap-1829	309	15	thus	thus	ADV
ap-1829	309	16	achieving	achieve	VERB
ap-1829	309	17	an	an	DET
ap-1829	309	18	accurate	accurate	ADJ
ap-1829	309	19	solution	solution	NOUN
ap-1829	309	20	in	in	ADP
ap-1829	309	21	restarted	restart	VERB
ap-1829	309	22	gmres	gmre	NOUN
ap-1829	309	23	is	be	AUX
ap-1829	309	24	uncertain	uncertain	ADJ
ap-1829	309	25	(	(	PUNCT
ap-1829	309	26	at	at	ADP
ap-1829	309	27	least	least	ADJ
ap-1829	309	28	on	on	ADP
ap-1829	309	29	theoretical	theoretical	ADJ
ap-1829	309	30	problems	problem	NOUN
ap-1829	309	31	)	)	PUNCT
ap-1829	309	32	.	.	PUNCT
ap-1829	310	1	the	the	DET
ap-1829	310	2	bicgstab	bicgstab	ADJ
ap-1829	310	3	method	method	NOUN
ap-1829	310	4	uses	use	VERB
ap-1829	310	5	short	short	ADJ
ap-1829	310	6	recurrences	recurrence	NOUN
ap-1829	310	7	,	,	PUNCT
ap-1829	310	8	but	but	CCONJ
ap-1829	310	9	its	its	PRON
ap-1829	310	10	great	great	ADJ
ap-1829	310	11	disadvantage	disadvantage	NOUN
ap-1829	310	12	is	be	AUX
ap-1829	310	13	the	the	DET
ap-1829	310	14	possibility	possibility	NOUN
ap-1829	310	15	of	of	ADP
ap-1829	310	16	a	a	DET
ap-1829	310	17	so	so	ADV
ap-1829	310	18	-	-	PUNCT
ap-1829	310	19	called	call	VERB
ap-1829	310	20	break	break	NOUN
ap-1829	310	21	-	-	PUNCT
ap-1829	310	22	down	down	NOUN
ap-1829	310	23	.	.	PUNCT
ap-1829	311	1	the	the	DET
ap-1829	311	2	simple	simple	ADJ
ap-1829	311	3	conjugate	conjugate	ADJ
ap-1829	311	4	gradient	gradient	NOUN
ap-1829	311	5	method	method	NOUN
ap-1829	311	6	for	for	ADP
ap-1829	311	7	normal	normal	ADJ
ap-1829	311	8	equations	equation	NOUN
ap-1829	311	9	does	do	AUX
ap-1829	311	10	not	not	PART
ap-1829	311	11	suffer	suffer	VERB
ap-1829	311	12	from	from	ADP
ap-1829	311	13	any	any	PRON
ap-1829	311	14	these	these	DET
ap-1829	311	15	disadvantages	disadvantage	NOUN
ap-1829	311	16	.	.	PUNCT
ap-1829	312	1	the	the	DET
ap-1829	312	2	only	only	ADJ
ap-1829	312	3	disadvantage	disadvantage	NOUN
ap-1829	312	4	is	be	AUX
ap-1829	312	5	squaring	square	VERB
ap-1829	312	6	the	the	DET
ap-1829	312	7	condition	condition	NOUN
ap-1829	312	8	number	number	NOUN
ap-1829	312	9	,	,	PUNCT
ap-1829	312	10	but	but	CCONJ
ap-1829	312	11	on	on	ADP
ap-1829	312	12	the	the	DET
ap-1829	312	13	basis	basis	NOUN
ap-1829	312	14	of	of	ADP
ap-1829	312	15	the	the	DET
ap-1829	312	16	given	give	VERB
ap-1829	312	17	hypothesis	hypothesis	NOUN
ap-1829	312	18	for	for	ADP
ap-1829	312	19	this	this	DET
ap-1829	312	20	particular	particular	ADJ
ap-1829	312	21	class	class	NOUN
ap-1829	312	22	of	of	ADP
ap-1829	312	23	problems	problem	NOUN
ap-1829	312	24	worsening	worsen	VERB
ap-1829	312	25	the	the	DET
ap-1829	312	26	condition	condition	NOUN
ap-1829	312	27	number	number	NOUN
ap-1829	312	28	is	be	AUX
ap-1829	312	29	negligible	negligible	ADJ
ap-1829	312	30	,	,	PUNCT
ap-1829	312	31	and	and	CCONJ
ap-1829	312	32	thus	thus	ADV
ap-1829	312	33	this	this	DET
ap-1829	312	34	only	only	ADJ
ap-1829	312	35	disadvantage	disadvantage	NOUN
ap-1829	312	36	is	be	AUX
ap-1829	312	37	absent	absent	ADJ
ap-1829	312	38	here	here	ADV
ap-1829	312	39	.	.	PUNCT
ap-1829	313	1	the	the	DET
ap-1829	313	2	conjugate	conjugate	ADJ
ap-1829	313	3	gradient	gradient	NOUN
ap-1829	313	4	method	method	NOUN
ap-1829	313	5	for	for	ADP
ap-1829	313	6	normal	normal	ADJ
ap-1829	313	7	equations	equation	NOUN
ap-1829	313	8	is	be	AUX
ap-1829	313	9	implementary	implementary	ADJ
ap-1829	313	10	simple	simple	NOUN
ap-1829	313	11	,	,	PUNCT
ap-1829	313	12	and	and	CCONJ
ap-1829	313	13	as	as	SCONJ
ap-1829	313	14	explained	explain	VERB
ap-1829	313	15	for	for	ADP
ap-1829	313	16	diagonally	diagonally	ADV
ap-1829	313	17	scaled	scale	VERB
ap-1829	313	18	diagonally	diagonally	ADV
ap-1829	313	19	dominant	dominant	ADJ
ap-1829	313	20	problems	problem	NOUN
ap-1829	313	21	,	,	PUNCT
ap-1829	313	22	it	it	PRON
ap-1829	313	23	is	be	AUX
ap-1829	313	24	also	also	ADV
ap-1829	313	25	an	an	DET
ap-1829	313	26	efficient	efficient	ADJ
ap-1829	313	27	algorithm	algorithm	NOUN
ap-1829	313	28	.	.	PUNCT
ap-1829	314	1	this	this	DET
ap-1829	314	2	method	method	NOUN
ap-1829	314	3	was	be	AUX
ap-1829	314	4	implemented	implement	VERB
ap-1829	314	5	into	into	ADP
ap-1829	314	6	drutes	drute	NOUN
ap-1829	314	7	code	code	NOUN
ap-1829	314	8	,	,	PUNCT
ap-1829	314	9	and	and	CCONJ
ap-1829	314	10	bas	bas	PROPN
ap-1829	314	11	been	be	AUX
ap-1829	314	12	used	use	VERB
ap-1829	314	13	successfully	successfully	ADV
ap-1829	314	14	for	for	ADP
ap-1829	314	15	a	a	DET
ap-1829	314	16	variety	variety	NOUN
ap-1829	314	17	of	of	ADP
ap-1829	314	18	theoretical	theoretical	ADJ
ap-1829	314	19	and	and	CCONJ
ap-1829	314	20	practical	practical	ADJ
ap-1829	314	21	problems	problem	NOUN
ap-1829	314	22	.	.	PUNCT
ap-1829	315	1	4.2	4.2	NUM
ap-1829	315	2	.	.	PUNCT
ap-1829	316	1	theoretical	theoretical	ADJ
ap-1829	316	2	case	case	NOUN
ap-1829	316	3	study	study	NOUN
ap-1829	316	4	this	this	DET
ap-1829	316	5	example	example	NOUN
ap-1829	316	6	is	be	AUX
ap-1829	316	7	a	a	DET
ap-1829	316	8	purely	purely	ADV
ap-1829	316	9	theoretical	theoretical	ADJ
ap-1829	316	10	case	case	NOUN
ap-1829	316	11	study	study	NOUN
ap-1829	316	12	.	.	PUNCT
ap-1829	317	1	the	the	DET
ap-1829	317	2	matrix	matrix	NOUN
ap-1829	317	3	and	and	CCONJ
ap-1829	317	4	fracture	fracture	NOUN
ap-1829	317	5	domain	domain	NOUN
ap-1829	317	6	parameters	parameter	NOUN
ap-1829	317	7	are	be	AUX
ap-1829	317	8	consid	consid	PROPN
ap-1829	317	9	1	1	NUM
ap-1829	317	10	10	10	NUM
ap-1829	317	11	100	100	NUM
ap-1829	317	12	1000	1000	NUM
ap-1829	317	13	10000	10000	NUM
ap-1829	317	14	0	0	NUM
ap-1829	317	15	10	10	NUM
ap-1829	317	16	20	20	NUM
ap-1829	317	17	30	30	NUM
ap-1829	317	18	40	40	NUM
ap-1829	317	19	50	50	NUM
ap-1829	317	20	60	60	NUM
ap-1829	317	21	n	n	NUM
ap-1829	317	22	u	u	NOUN
ap-1829	317	23	m	m	NOUN
ap-1829	317	24	b	b	NOUN
ap-1829	317	25	e	e	NOUN
ap-1829	318	1	r	r	NOUN
ap-1829	319	1	o	o	X
ap-1829	320	1	f	f	X
ap-1829	321	1	it	it	PRON
ap-1829	322	1	e	e	X
ap-1829	322	2	ra	ra	NOUN
ap-1829	322	3	ti	ti	INTJ
ap-1829	322	4	o	o	PROPN
ap-1829	323	1	n	n	NOUN
ap-1829	323	2	s	s	NOUN
ap-1829	323	3	time	time	NOUN
ap-1829	323	4	[	[	X
ap-1829	323	5	hrs	hrs	X
ap-1829	323	6	]	]	X
ap-1829	323	7	preconditioning	precondition	VERB
ap-1829	323	8	no	no	DET
ap-1829	323	9	preconditioning	precondition	VERB
ap-1829	323	10	figure	figure	NOUN
ap-1829	323	11	5	5	NUM
ap-1829	323	12	.	.	NOUN
ap-1829	323	13	conjugate	conjugate	ADJ
ap-1829	323	14	gradient	gradient	ADJ
ap-1829	323	15	iterations	iteration	NOUN
ap-1829	323	16	in	in	ADP
ap-1829	323	17	time	time	NOUN
ap-1829	323	18	.	.	PUNCT
ap-1829	324	1	ered	ere	VERB
ap-1829	324	2	identical	identical	ADJ
ap-1829	324	3	here	here	ADV
ap-1829	324	4	,	,	PUNCT
ap-1829	324	5	and	and	CCONJ
ap-1829	324	6	thus	thus	ADV
ap-1829	324	7	the	the	DET
ap-1829	324	8	problem	problem	NOUN
ap-1829	324	9	is	be	AUX
ap-1829	324	10	described	describe	VERB
ap-1829	324	11	by	by	ADP
ap-1829	324	12	the	the	DET
ap-1829	324	13	classical	classical	ADJ
ap-1829	324	14	richards	richard	NOUN
ap-1829	324	15	equation	equation	NOUN
ap-1829	324	16	model	model	NOUN
ap-1829	324	17	only	only	ADV
ap-1829	324	18	.	.	PUNCT
ap-1829	325	1	the	the	DET
ap-1829	325	2	material	material	NOUN
ap-1829	325	3	parameters	parameter	NOUN
ap-1829	325	4	are	be	AUX
ap-1829	325	5	depicted	depict	VERB
ap-1829	325	6	in	in	ADP
ap-1829	325	7	table	table	NOUN
ap-1829	325	8	3	3	NUM
ap-1829	325	9	,	,	PUNCT
ap-1829	325	10	3rd	3rd	ADJ
ap-1829	325	11	line	line	NOUN
ap-1829	325	12	“	"	PUNCT
ap-1829	325	13	gravel	gravel	NOUN
ap-1829	325	14	bar	bar	NOUN
ap-1829	325	15	.	.	PUNCT
ap-1829	325	16	”	"	PUNCT
ap-1829	325	17	.	.	PUNCT
ap-1829	326	1	the	the	DET
ap-1829	326	2	boundary	boundary	ADJ
ap-1829	326	3	condition	condition	NOUN
ap-1829	326	4	setup	setup	NOUN
ap-1829	326	5	is	be	AUX
ap-1829	326	6	stated	state	VERB
ap-1829	326	7	as	as	ADP
ap-1829	326	8	:	:	PUNCT
ap-1829	326	9	h(x	h(x	PROPN
ap-1829	326	10	,	,	PUNCT
ap-1829	326	11	t	t	PROPN
ap-1829	326	12	)	)	PUNCT
ap-1829	326	13	=	=	SYM
ap-1829	327	1	−10.0	−10.0	NOUN
ap-1829	327	2	cm	cm	NUM
ap-1829	327	3	∀(x	∀(x	NOUN
ap-1829	327	4	,	,	PUNCT
ap-1829	327	5	t	t	PROPN
ap-1829	327	6	)	)	PUNCT
ap-1829	327	7	∈	∈	PROPN
ap-1829	327	8	γd	γd	ADP
ap-1829	327	9	×	×	PROPN
ap-1829	327	10	(	(	PUNCT
ap-1829	327	11	0	0	NUM
ap-1829	327	12	,	,	PUNCT
ap-1829	327	13	t	t	X
ap-1829	327	14	]	]	PUNCT
ap-1829	327	15	,	,	PUNCT
ap-1829	327	16	∂h	∂h	PROPN
ap-1829	327	17	∂n	∂n	PROPN
ap-1829	327	18	(	(	PUNCT
ap-1829	327	19	x	x	X
ap-1829	327	20	,	,	PUNCT
ap-1829	327	21	t	t	PROPN
ap-1829	327	22	)	)	PUNCT
ap-1829	327	23	=	=	SYM
ap-1829	327	24	0	0	NUM
ap-1829	328	1	∀(x	∀(x	NUM
ap-1829	328	2	,	,	PUNCT
ap-1829	328	3	t	t	PROPN
ap-1829	328	4	)	)	PUNCT
ap-1829	328	5	∈	∈	PROPN
ap-1829	328	6	γn	γn	ADP
ap-1829	328	7	×	×	NOUN
ap-1829	328	8	(	(	PUNCT
ap-1829	328	9	0	0	NUM
ap-1829	328	10	,	,	PUNCT
ap-1829	328	11	t	t	X
ap-1829	328	12	]	]	PUNCT
ap-1829	328	13	.	.	PUNCT
ap-1829	329	1	(	(	PUNCT
ap-1829	329	2	36	36	NUM
ap-1829	329	3	)	)	PUNCT
ap-1829	329	4	the	the	DET
ap-1829	329	5	initial	initial	ADJ
ap-1829	329	6	condition	condition	NOUN
ap-1829	329	7	setup	setup	NOUN
ap-1829	329	8	is	be	AUX
ap-1829	329	9	stated	state	VERB
ap-1829	329	10	as	as	ADP
ap-1829	329	11	:	:	PUNCT
ap-1829	329	12	h(x	h(x	PROPN
ap-1829	329	13	)	)	PUNCT
ap-1829	330	1	=	=	PUNCT
ap-1829	331	1	−200.0	−200.0	ADJ
ap-1829	331	2	cm	cm	X
ap-1829	331	3	∀x	∀x	X
ap-1829	331	4	∈	∈	PROPN
ap-1829	331	5	ω	ω	NOUN
ap-1829	331	6	.	.	PUNCT
ap-1829	332	1	(	(	PUNCT
ap-1829	332	2	37	37	NUM
ap-1829	332	3	)	)	PUNCT
ap-1829	332	4	the	the	DET
ap-1829	332	5	domain	domain	NOUN
ap-1829	332	6	scheme	scheme	NOUN
ap-1829	332	7	is	be	AUX
ap-1829	332	8	depicted	depict	VERB
ap-1829	332	9	in	in	ADP
ap-1829	332	10	figure	figure	NOUN
ap-1829	332	11	4	4	NUM
ap-1829	332	12	.	.	PUNCT
ap-1829	333	1	the	the	DET
ap-1829	333	2	spatial	spatial	ADJ
ap-1829	333	3	discretization	discretization	NOUN
ap-1829	333	4	was	be	AUX
ap-1829	333	5	a	a	DET
ap-1829	333	6	uniform	uniform	ADJ
ap-1829	333	7	triangular	triangular	NOUN
ap-1829	333	8	mesh	mesh	NOUN
ap-1829	333	9	with	with	ADP
ap-1829	333	10	10201	10201	NUM
ap-1829	333	11	nodes	node	NOUN
ap-1829	333	12	and	and	CCONJ
ap-1829	333	13	20000	20000	NUM
ap-1829	333	14	elements	element	NOUN
ap-1829	333	15	.	.	PUNCT
ap-1829	334	1	4.2.1	4.2.1	NOUN
ap-1829	334	2	.	.	PUNCT
ap-1829	335	1	conditioning	conditioning	NOUN
ap-1829	335	2	improvements	improvement	NOUN
ap-1829	335	3	the	the	DET
ap-1829	335	4	diagonal	diagonal	ADJ
ap-1829	335	5	scaling	scale	VERB
ap-1829	335	6	algorithm	algorithm	NOUN
ap-1829	335	7	greatly	greatly	ADV
ap-1829	335	8	improved	improve	VERB
ap-1829	335	9	the	the	DET
ap-1829	335	10	problem	problem	NOUN
ap-1829	335	11	conditioning	conditioning	NOUN
ap-1829	335	12	.	.	PUNCT
ap-1829	336	1	the	the	DET
ap-1829	336	2	overall	overall	ADJ
ap-1829	336	3	number	number	NOUN
ap-1829	336	4	of	of	ADP
ap-1829	336	5	picard	picard	NOUN
ap-1829	336	6	iterations	iteration	NOUN
ap-1829	336	7	—	—	PUNCT
ap-1829	336	8	linear	linear	ADJ
ap-1829	336	9	equation	equation	NOUN
ap-1829	336	10	solver	solver	NOUN
ap-1829	336	11	calls	call	NOUN
ap-1829	336	12	—	—	PUNCT
ap-1829	336	13	was	be	AUX
ap-1829	336	14	49001	49001	NUM
ap-1829	336	15	.	.	PUNCT
ap-1829	337	1	the	the	DET
ap-1829	337	2	matrix	matrix	NOUN
ap-1829	337	3	of	of	ADP
ap-1829	337	4	dimension	dimension	NOUN
ap-1829	337	5	10100	10100	NUM
ap-1829	337	6	was	be	AUX
ap-1829	337	7	solved	solve	VERB
ap-1829	337	8	by	by	ADP
ap-1829	337	9	the	the	DET
ap-1829	337	10	conjugate	conjugate	ADJ
ap-1829	337	11	gradient	gradient	NOUN
ap-1829	337	12	method	method	NOUN
ap-1829	337	13	for	for	ADP
ap-1829	337	14	a	a	DET
ap-1829	337	15	normal	normal	ADJ
ap-1829	337	16	equation	equation	NOUN
ap-1829	337	17	with	with	ADP
ap-1829	337	18	an	an	DET
ap-1829	337	19	average	average	NOUN
ap-1829	337	20	of	of	ADP
ap-1829	337	21	33	33	NUM
ap-1829	337	22	iterations	iteration	NOUN
ap-1829	337	23	,	,	PUNCT
ap-1829	337	24	and	and	CCONJ
ap-1829	337	25	the	the	DET
ap-1829	337	26	maximal	maximal	ADJ
ap-1829	337	27	number	number	NOUN
ap-1829	337	28	of	of	ADP
ap-1829	337	29	iterations	iteration	NOUN
ap-1829	337	30	required	require	VERB
ap-1829	337	31	per	per	ADP
ap-1829	337	32	cg	cg	NOUN
ap-1829	337	33	solver	solver	NOUN
ap-1829	337	34	call	call	NOUN
ap-1829	337	35	was	be	AUX
ap-1829	337	36	67	67	NUM
ap-1829	337	37	.	.	PUNCT
ap-1829	338	1	the	the	DET
ap-1829	338	2	stopping	stop	VERB
ap-1829	338	3	criterion	criterion	NOUN
ap-1829	338	4	was	be	AUX
ap-1829	338	5	the	the	DET
ap-1829	338	6	residual	residual	ADJ
ap-1829	338	7	size	size	NOUN
ap-1829	338	8	rk	rk	NOUN
ap-1829	338	9	<	<	X
ap-1829	338	10	10−12	10−12	NOUN
ap-1829	338	11	.	.	PUNCT
ap-1829	338	12	table	table	NOUN
ap-1829	338	13	2	2	NUM
ap-1829	338	14	depicts	depict	VERB
ap-1829	338	15	the	the	DET
ap-1829	338	16	results	result	NOUN
ap-1829	338	17	that	that	PRON
ap-1829	338	18	were	be	AUX
ap-1829	338	19	obtained	obtain	VERB
ap-1829	338	20	.	.	PUNCT
ap-1829	339	1	figure	figure	NOUN
ap-1829	339	2	5	5	NUM
ap-1829	339	3	depicts	depict	VERB
ap-1829	339	4	the	the	DET
ap-1829	339	5	plot	plot	NOUN
ap-1829	339	6	of	of	ADP
ap-1829	339	7	the	the	DET
ap-1829	339	8	conjugate	conjugate	ADJ
ap-1829	339	9	gradient	gradient	NOUN
ap-1829	339	10	iterations	iteration	NOUN
ap-1829	339	11	for	for	ADP
ap-1829	339	12	preconditioned	preconditioned	ADJ
ap-1829	339	13	and	and	CCONJ
ap-1829	339	14	non	non	ADJ
ap-1829	339	15	-	-	ADJ
ap-1829	339	16	preconditioned	preconditioned	ADJ
ap-1829	339	17	matrices	matrix	NOUN
ap-1829	339	18	.	.	PUNCT
ap-1829	340	1	as	as	SCONJ
ap-1829	340	2	expected	expect	VERB
ap-1829	340	3	,	,	PUNCT
ap-1829	340	4	the	the	DET
ap-1829	340	5	cg	cg	NOUN
ap-1829	340	6	method	method	NOUN
ap-1829	340	7	for	for	ADP
ap-1829	340	8	a	a	DET
ap-1829	340	9	normal	normal	ADJ
ap-1829	340	10	equation	equation	NOUN
ap-1829	340	11	without	without	ADP
ap-1829	340	12	preconditioning	precondition	VERB
ap-1829	340	13	converges	converge	NOUN
ap-1829	340	14	so	so	ADV
ap-1829	340	15	slowly	slowly	ADV
ap-1829	340	16	that	that	SCONJ
ap-1829	340	17	its	its	PRON
ap-1829	340	18	application	application	NOUN
ap-1829	340	19	can	can	AUX
ap-1829	340	20	be	be	AUX
ap-1829	340	21	concluded	conclude	VERB
ap-1829	340	22	as	as	ADP
ap-1829	340	23	an	an	DET
ap-1829	340	24	inappropriateconsidered	inappropriateconsidered	ADJ
ap-1829	340	25	inappropriate	inappropriate	NOUN
ap-1829	340	26	.	.	PUNCT
ap-1829	341	1	this	this	PRON
ap-1829	341	2	is	be	AUX
ap-1829	341	3	a	a	DET
ap-1829	341	4	wellknown	wellknown	ADJ
ap-1829	341	5	fact	fact	NOUN
ap-1829	341	6	,	,	PUNCT
ap-1829	341	7	but	but	CCONJ
ap-1829	341	8	simple	simple	ADJ
ap-1829	341	9	diagonal	diagonal	ADJ
ap-1829	341	10	scaling	scaling	NOUN
ap-1829	341	11	enables	enable	VERB
ap-1829	341	12	fast	fast	ADJ
ap-1829	341	13	convergence	convergence	NOUN
ap-1829	341	14	.	.	PUNCT
ap-1829	342	1	4.3	4.3	NUM
ap-1829	342	2	.	.	PUNCT
ap-1829	342	3	practical	practical	ADJ
ap-1829	342	4	case	case	NOUN
ap-1829	342	5	study	study	NOUN
ap-1829	342	6	this	this	DET
ap-1829	342	7	example	example	NOUN
ap-1829	342	8	is	be	AUX
ap-1829	342	9	motivated	motivate	VERB
ap-1829	342	10	by	by	ADP
ap-1829	342	11	an	an	DET
ap-1829	342	12	existing	exist	VERB
ap-1829	342	13	nuclear	nuclear	ADJ
ap-1829	342	14	waste	waste	NOUN
ap-1829	342	15	repository	repository	NOUN
ap-1829	342	16	for	for	ADP
ap-1829	342	17	low	low	ADJ
ap-1829	342	18	-	-	PUNCT
ap-1829	342	19	level	level	NOUN
ap-1829	342	20	and	and	CCONJ
ap-1829	342	21	intermediate	intermediate	ADJ
ap-1829	342	22	-	-	PUNCT
ap-1829	342	23	level	level	NOUN
ap-1829	342	24	waste	waste	NOUN
ap-1829	342	25	.	.	PUNCT
ap-1829	343	1	the	the	DET
ap-1829	343	2	name	name	NOUN
ap-1829	343	3	of	of	ADP
ap-1829	343	4	the	the	DET
ap-1829	343	5	repository	repository	NOUN
ap-1829	343	6	is	be	AUX
ap-1829	343	7	richard	richard	PROPN
ap-1829	343	8	and	and	CCONJ
ap-1829	343	9	it	it	PRON
ap-1829	343	10	is	be	AUX
ap-1829	343	11	situated	situate	VERB
ap-1829	343	12	near	near	ADP
ap-1829	343	13	litoměřice	litoměřice	ADJ
ap-1829	343	14	,	,	PUNCT
ap-1829	343	15	czech	czech	PROPN
ap-1829	343	16	republic	republic	NOUN
ap-1829	343	17	.	.	PUNCT
ap-1829	344	1	the	the	DET
ap-1829	344	2	repository	repository	NOUN
ap-1829	344	3	is	be	AUX
ap-1829	344	4	located	locate	VERB
ap-1829	344	5	within	within	ADP
ap-1829	344	6	a	a	DET
ap-1829	344	7	deep	deep	ADJ
ap-1829	344	8	rock	rock	NOUN
ap-1829	344	9	formation	formation	NOUN
ap-1829	344	10	354	354	NUM
ap-1829	344	11	vol	vol	NOUN
ap-1829	344	12	.	.	PUNCT
ap-1829	345	1	53	53	NUM
ap-1829	345	2	no	no	NOUN
ap-1829	345	3	.	.	PUNCT
ap-1829	346	1	4/2013	4/2013	NOUN
ap-1829	346	2	algorithms	algorithm	NOUN
ap-1829	346	3	for	for	ADP
ap-1829	346	4	solving	solve	VERB
ap-1829	346	5	darcian	darcian	NOUN
ap-1829	346	6	flow	flow	NOUN
ap-1829	346	7	in	in	ADP
ap-1829	346	8	structured	structured	ADJ
ap-1829	346	9	porous	porous	ADJ
ap-1829	346	10	media	medium	NOUN
ap-1829	346	11	time	time	NOUN
ap-1829	346	12	no	no	DET
ap-1829	346	13	preconditioning	precondition	VERB
ap-1829	346	14	preconditioned	precondition	VERB
ap-1829	346	15	λmax	λmax	NOUN
ap-1829	346	16	λmin	λmin	X
ap-1829	346	17	κ	κ	PROPN
ap-1829	346	18	λmax	λmax	PROPN
ap-1829	346	19	λmin	λmin	PROPN
ap-1829	346	20	κ	κ	PROPN
ap-1829	346	21	10−5	10−5	NUM
ap-1829	346	22	7.853	7.853	NUM
ap-1829	346	23	·	·	PUNCT
ap-1829	346	24	10−10	10−10	NUM
ap-1829	346	25	6.376	6.376	NUM
ap-1829	346	26	·	·	PUNCT
ap-1829	346	27	10−12	10−12	NOUN
ap-1829	346	28	123.1612	123.1612	NUM
ap-1829	346	29	0.99999999898	0.99999999898	NUM
ap-1829	346	30	0.9999999919	0.9999999919	NUM
ap-1829	346	31	1.00000000706	1.00000000706	NUM
ap-1829	346	32	0.5	0.5	NUM
ap-1829	346	33	4.578	4.578	NUM
ap-1829	346	34	·	·	SYM
ap-1829	346	35	10−7	10−7	NUM
ap-1829	346	36	1.207	1.207	NUM
ap-1829	346	37	·	·	PUNCT
ap-1829	346	38	10−11	10−11	NUM
ap-1829	346	39	37926.33	37926.33	NUM
ap-1829	346	40	0.9992155771	0.9992155771	NUM
ap-1829	346	41	0.94875498673	0.94875498673	NUM
ap-1829	346	42	1.053186113526	1.053186113526	NUM
ap-1829	346	43	70.5	70.5	NUM
ap-1829	346	44	6.842	6.842	NUM
ap-1829	346	45	·	·	SYM
ap-1829	347	1	10−5	10−5	NUM
ap-1829	347	2	7.040	7.040	NUM
ap-1829	347	3	·	·	PUNCT
ap-1829	347	4	10−10	10−10	NUM
ap-1829	347	5	97199.057	97199.057	NUM
ap-1829	347	6	2.135820803	2.135820803	NUM
ap-1829	347	7	0.28957144730	0.28957144730	NUM
ap-1829	347	8	7.375799041142	7.375799041142	NUM
ap-1829	347	9	154.5	154.5	NUM
ap-1829	347	10	0.000356	0.000356	NUM
ap-1829	347	11	1.773	1.773	NUM
ap-1829	347	12	·	·	PUNCT
ap-1829	348	1	10−8	10−8	NUM
ap-1829	348	2	20109.385	20109.385	NUM
ap-1829	348	3	2.9932628563	2.9932628563	NUM
ap-1829	348	4	0.08109150218	0.08109150218	NUM
ap-1829	348	5	36.91216435282	36.91216435282	NUM
ap-1829	348	6	276.5	276.5	NUM
ap-1829	348	7	0.000103	0.000103	NUM
ap-1829	348	8	3.553	3.553	NUM
ap-1829	348	9	·	·	SYM
ap-1829	348	10	10−9	10−9	NUM
ap-1829	348	11	29069.776	29069.776	NUM
ap-1829	348	12	2.4120151933	2.4120151933	NUM
ap-1829	348	13	0.20777359355	0.20777359355	NUM
ap-1829	348	14	11.60886305218	11.60886305218	NUM
ap-1829	348	15	339.5	339.5	NUM
ap-1829	348	16	0.000257	0.000257	NUM
ap-1829	348	17	1.948	1.948	NUM
ap-1829	348	18	·	·	PUNCT
ap-1829	349	1	10−8	10−8	NUM
ap-1829	349	2	13234.228	13234.228	PROPN
ap-1829	349	3	2.869385334	2.869385334	NUM
ap-1829	349	4	0.1028734952	0.1028734952	NUM
ap-1829	349	5	27.892367499	27.892367499	NUM
ap-1829	349	6	502.5	502.5	NUM
ap-1829	349	7	0.000410	0.000410	NUM
ap-1829	349	8	3.371	3.371	NUM
ap-1829	349	9	·	·	PUNCT
ap-1829	350	1	10−8	10−8	NUM
ap-1829	350	2	12176.805	12176.805	NUM
ap-1829	350	3	3.0701098732	3.0701098732	NUM
ap-1829	350	4	0.06920022271	0.06920022271	NUM
ap-1829	350	5	44.36560682	44.36560682	NOUN
ap-1829	350	6	669.0	669.0	NUM
ap-1829	350	7	5.0563	5.0563	NUM
ap-1829	350	8	·	·	PUNCT
ap-1829	350	9	10−5	10−5	NUM
ap-1829	350	10	1.818	1.818	NUM
ap-1829	350	11	·	·	PUNCT
ap-1829	350	12	10−9	10−9	NUM
ap-1829	350	13	27805.705	27805.705	NUM
ap-1829	350	14	2.01150608	2.01150608	NUM
ap-1829	350	15	0.34435293431	0.34435293431	NUM
ap-1829	350	16	5.841408287719	5.841408287719	NUM
ap-1829	350	17	850.0	850.0	NUM
ap-1829	350	18	0.0005709	0.0005709	NUM
ap-1829	350	19	1.090	1.090	NUM
ap-1829	350	20	·	·	SYM
ap-1829	350	21	10−7	10−7	NUM
ap-1829	350	22	5236.54	5236.54	NUM
ap-1829	350	23	3.196279963	3.196279963	NUM
ap-1829	350	24	0.0527000983	0.0527000983	NUM
ap-1829	350	25	60.65036051186	60.65036051186	NUM
ap-1829	350	26	950.0	950.0	NUM
ap-1829	350	27	0.0007849	0.0007849	NUM
ap-1829	350	28	2.026	2.026	NUM
ap-1829	350	29	·	·	SYM
ap-1829	350	30	10−7	10−7	NUM
ap-1829	351	1	3873.438	3873.438	NUM
ap-1829	351	2	3.3012379801	3.3012379801	NUM
ap-1829	351	3	0.04053514763	0.04053514763	NUM
ap-1829	351	4	81.44137057972	81.44137057972	NUM
ap-1829	351	5	table	table	NOUN
ap-1829	351	6	2	2	NUM
ap-1829	351	7	.	.	PUNCT
ap-1829	351	8	conditioning	conditioning	NOUN
ap-1829	351	9	improvements	improvement	NOUN
ap-1829	351	10	before	before	ADV
ap-1829	351	11	and	and	CCONJ
ap-1829	351	12	after	after	ADP
ap-1829	351	13	right	right	ADJ
ap-1829	351	14	hand	hand	NOUN
ap-1829	351	15	side	side	NOUN
ap-1829	351	16	diagonal	diagonal	ADJ
ap-1829	351	17	scaling	scaling	NOUN
ap-1829	351	18	.	.	PUNCT
ap-1829	352	1	if	if	SCONJ
ap-1829	352	2	λmax	λmax	X
ap-1829	352	3	<	<	X
ap-1829	352	4	1.0	1.0	NUM
ap-1829	352	5	,	,	PUNCT
ap-1829	352	6	then	then	ADV
ap-1829	352	7	most	most	ADV
ap-1829	352	8	likely	likely	ADJ
ap-1829	352	9	more	more	ADJ
ap-1829	352	10	iterations	iteration	NOUN
ap-1829	352	11	are	be	AUX
ap-1829	352	12	required	require	VERB
ap-1829	352	13	to	to	PART
ap-1829	352	14	improve	improve	VERB
ap-1829	352	15	the	the	DET
ap-1829	352	16	accuracy	accuracy	NOUN
ap-1829	352	17	of	of	ADP
ap-1829	352	18	the	the	DET
ap-1829	352	19	eigenvalue	eigenvalue	PROPN
ap-1829	352	20	estimation	estimation	NOUN
ap-1829	352	21	.	.	PUNCT
ap-1829	353	1	figure	figure	NOUN
ap-1829	353	2	6	6	NUM
ap-1829	353	3	.	.	PUNCT
ap-1829	354	1	domain	domain	NOUN
ap-1829	354	2	scheme	scheme	NOUN
ap-1829	354	3	of	of	ADP
ap-1829	354	4	the	the	DET
ap-1829	354	5	repository	repository	NOUN
ap-1829	354	6	problem	problem	NOUN
ap-1829	354	7	.	.	PUNCT
ap-1829	355	1	in	in	ADP
ap-1829	355	2	the	the	DET
ap-1829	355	3	bídnice	bídnice	PROPN
ap-1829	355	4	hill	hill	PROPN
ap-1829	355	5	,	,	PUNCT
ap-1829	355	6	40	40	NUM
ap-1829	355	7	m	m	NOUN
ap-1829	355	8	below	below	ADP
ap-1829	355	9	the	the	DET
ap-1829	355	10	surface	surface	NOUN
ap-1829	355	11	and	and	CCONJ
ap-1829	355	12	70	70	NUM
ap-1829	355	13	m	m	NOUN
ap-1829	355	14	above	above	ADP
ap-1829	355	15	the	the	DET
ap-1829	355	16	ground	ground	NOUN
ap-1829	355	17	water	water	NOUN
ap-1829	355	18	table	table	NOUN
ap-1829	355	19	,	,	PUNCT
ap-1829	355	20	and	and	CCONJ
ap-1829	355	21	it	it	PRON
ap-1829	355	22	is	be	AUX
ap-1829	355	23	surrounded	surround	VERB
ap-1829	355	24	by	by	ADP
ap-1829	355	25	tectonically	tectonically	ADV
ap-1829	355	26	fractured	fractured	ADJ
ap-1829	355	27	claystone	claystone	NOUN
ap-1829	355	28	.	.	PUNCT
ap-1829	356	1	under	under	ADP
ap-1829	356	2	normal	normal	ADJ
ap-1829	356	3	circumstances	circumstance	NOUN
ap-1829	356	4	,	,	PUNCT
ap-1829	356	5	this	this	PRON
ap-1829	356	6	is	be	AUX
ap-1829	356	7	a	a	DET
ap-1829	356	8	very	very	ADV
ap-1829	356	9	stable	stable	ADJ
ap-1829	356	10	unsaturated	unsaturated	ADJ
ap-1829	356	11	environment	environment	NOUN
ap-1829	356	12	.	.	PUNCT
ap-1829	357	1	this	this	PRON
ap-1829	357	2	is	be	AUX
ap-1829	357	3	therefore	therefore	ADV
ap-1829	357	4	a	a	DET
ap-1829	357	5	typical	typical	ADJ
ap-1829	357	6	problem	problem	NOUN
ap-1829	357	7	for	for	ADP
ap-1829	357	8	applying	apply	VERB
ap-1829	357	9	the	the	DET
ap-1829	357	10	richards	richard	NOUN
ap-1829	357	11	equation	equation	NOUN
ap-1829	357	12	model	model	NOUN
ap-1829	357	13	.	.	PUNCT
ap-1829	358	1	in	in	ADP
ap-1829	358	2	order	order	NOUN
ap-1829	358	3	to	to	PART
ap-1829	358	4	protect	protect	VERB
ap-1829	358	5	its	its	PRON
ap-1829	358	6	surroundings	surrounding	NOUN
ap-1829	358	7	from	from	ADP
ap-1829	358	8	radiotoxic	radiotoxic	NOUN
ap-1829	358	9	pollution	pollution	NOUN
ap-1829	358	10	,	,	PUNCT
ap-1829	358	11	the	the	DET
ap-1829	358	12	repository	repository	NOUN
ap-1829	358	13	is	be	AUX
ap-1829	358	14	shielded	shield	VERB
ap-1829	358	15	by	by	ADP
ap-1829	358	16	a	a	DET
ap-1829	358	17	30	30	NUM
ap-1829	358	18	cm	cm	NOUN
ap-1829	358	19	thick	thick	ADJ
ap-1829	358	20	gravel	gravel	NOUN
ap-1829	358	21	layer	layer	NOUN
ap-1829	358	22	that	that	PRON
ap-1829	358	23	acts	act	VERB
ap-1829	358	24	as	as	ADP
ap-1829	358	25	a	a	DET
ap-1829	358	26	capillary	capillary	ADJ
ap-1829	358	27	barrier	barrier	NOUN
ap-1829	358	28	.	.	PUNCT
ap-1829	359	1	the	the	DET
ap-1829	359	2	capillary	capillary	ADJ
ap-1829	359	3	barrier	barrier	NOUN
ap-1829	359	4	effect	effect	NOUN
ap-1829	359	5	is	be	AUX
ap-1829	359	6	based	base	VERB
ap-1829	359	7	on	on	ADP
ap-1829	359	8	the	the	DET
ap-1829	359	9	unsaturated	unsaturated	ADJ
ap-1829	359	10	hydraulic	hydraulic	ADJ
ap-1829	359	11	properties	property	NOUN
ap-1829	359	12	of	of	ADP
ap-1829	359	13	gravel	gravel	NOUN
ap-1829	359	14	.	.	PUNCT
ap-1829	360	1	the	the	DET
ap-1829	360	2	unsaturated	unsaturated	ADJ
ap-1829	360	3	hydraulic	hydraulic	ADJ
ap-1829	360	4	conductivity	conductivity	NOUN
ap-1829	360	5	of	of	ADP
ap-1829	360	6	gravel	gravel	NOUN
ap-1829	360	7	reaches	reach	VERB
ap-1829	360	8	very	very	ADV
ap-1829	360	9	high	high	ADJ
ap-1829	360	10	values	value	NOUN
ap-1829	360	11	at	at	ADP
ap-1829	360	12	and	and	CCONJ
ap-1829	360	13	near	near	ADP
ap-1829	360	14	full	full	ADJ
ap-1829	360	15	saturation	saturation	NOUN
ap-1829	360	16	,	,	PUNCT
ap-1829	360	17	but	but	CCONJ
ap-1829	360	18	with	with	ADP
ap-1829	360	19	decreasing	decrease	VERB
ap-1829	360	20	saturation	saturation	NOUN
ap-1829	360	21	it	it	PRON
ap-1829	360	22	falls	fall	VERB
ap-1829	360	23	steeply	steeply	ADV
ap-1829	360	24	to	to	ADP
ap-1829	360	25	almost	almost	ADV
ap-1829	360	26	zero	zero	NUM
ap-1829	360	27	values	value	NOUN
ap-1829	360	28	.	.	PUNCT
ap-1829	361	1	the	the	DET
ap-1829	361	2	problem	problem	NOUN
ap-1829	361	3	was	be	AUX
ap-1829	361	4	conceptualized	conceptualize	VERB
ap-1829	361	5	by	by	ADP
ap-1829	361	6	model	model	NOUN
ap-1829	361	7	(	(	PUNCT
ap-1829	361	8	1	1	NUM
ap-1829	361	9	)	)	PUNCT
ap-1829	361	10	,	,	PUNCT
ap-1829	361	11	where	where	SCONJ
ap-1829	361	12	the	the	DET
ap-1829	361	13	tectonic	tectonic	ADJ
ap-1829	361	14	fractures	fracture	NOUN
ap-1829	361	15	are	be	AUX
ap-1829	361	16	represented	represent	VERB
ap-1829	361	17	by	by	ADP
ap-1829	361	18	the	the	DET
ap-1829	361	19	fast	fast	ADJ
ap-1829	361	20	domain	domain	NOUN
ap-1829	361	21	(	(	PUNCT
ap-1829	361	22	f	f	NOUN
ap-1829	361	23	)	)	PUNCT
ap-1829	361	24	,	,	PUNCT
ap-1829	361	25	and	and	CCONJ
ap-1829	361	26	the	the	DET
ap-1829	361	27	rock	rock	NOUN
ap-1829	361	28	matrix	matrix	NOUN
ap-1829	361	29	is	be	AUX
ap-1829	361	30	represented	represent	VERB
ap-1829	361	31	by	by	ADP
ap-1829	361	32	the	the	DET
ap-1829	361	33	matrix	matrix	NOUN
ap-1829	361	34	domain	domain	NOUN
ap-1829	361	35	(	(	PUNCT
ap-1829	361	36	m	m	NOUN
ap-1829	361	37	)	)	PUNCT
ap-1829	361	38	,	,	PUNCT
ap-1829	361	39	the	the	DET
ap-1829	361	40	material	material	NOUN
ap-1829	361	41	properties	property	NOUN
ap-1829	361	42	are	be	AUX
ap-1829	361	43	depicted	depict	VERB
ap-1829	361	44	in	in	ADP
ap-1829	361	45	table	table	NOUN
ap-1829	361	46	3	3	NUM
ap-1829	361	47	,	,	PUNCT
ap-1829	361	48	and	and	CCONJ
ap-1829	361	49	the	the	DET
ap-1829	361	50	domain	domain	NOUN
ap-1829	361	51	scheme	scheme	NOUN
ap-1829	361	52	is	be	AUX
ap-1829	361	53	depicted	depict	VERB
ap-1829	361	54	in	in	ADP
ap-1829	361	55	figure	figure	NOUN
ap-1829	361	56	6	6	NUM
ap-1829	361	57	.	.	PUNCT
ap-1829	362	1	the	the	DET
ap-1829	362	2	coupling	couple	VERB
ap-1829	362	3	parameters	parameter	NOUN
ap-1829	362	4	of	of	ADP
ap-1829	362	5	the	the	DET
ap-1829	362	6	model	model	NOUN
ap-1829	362	7	(	(	PUNCT
ap-1829	362	8	1	1	X
ap-1829	362	9	)	)	PUNCT
ap-1829	362	10	were	be	AUX
ap-1829	362	11	identified	identify	VERB
ap-1829	362	12	in	in	ADP
ap-1829	362	13	[	[	X
ap-1829	362	14	9	9	NUM
ap-1829	362	15	]	]	PUNCT
ap-1829	362	16	,	,	PUNCT
ap-1829	362	17	and	and	CCONJ
ap-1829	362	18	are	be	AUX
ap-1829	362	19	stated	state	VERB
ap-1829	362	20	as	as	ADP
ap-1829	362	21	:	:	PUNCT
ap-1829	362	22	α	α	NOUN
ap-1829	362	23	=	=	SYM
ap-1829	362	24	8.89911	8.89911	NUM
ap-1829	362	25	cm−1	cm−1	NOUN
ap-1829	362	26	d−1	d−1	PROPN
ap-1829	362	27	,	,	PUNCT
ap-1829	362	28	and	and	CCONJ
ap-1829	362	29	ωf	ωf	PROPN
ap-1829	362	30	=	=	PROPN
ap-1829	362	31	0.0292884	0.0292884	NUM
ap-1829	362	32	.	.	PUNCT
ap-1829	363	1	the	the	DET
ap-1829	363	2	hydraulic	hydraulic	ADJ
ap-1829	363	3	parameters	parameter	NOUN
ap-1829	363	4	(	(	PUNCT
ap-1829	363	5	parameters	parameter	NOUN
ap-1829	363	6	of	of	ADP
ap-1829	363	7	the	the	DET
ap-1829	363	8	van	van	PROPN
ap-1829	363	9	genuchten	genuchten	NOUN
ap-1829	363	10	and	and	CCONJ
ap-1829	363	11	the	the	DET
ap-1829	363	12	mualem	mualem	NOUN
ap-1829	363	13	function	function	NOUN
ap-1829	363	14	)	)	PUNCT
ap-1829	363	15	are	be	AUX
ap-1829	363	16	depicted	depict	VERB
ap-1829	363	17	in	in	ADP
ap-1829	363	18	table	table	NOUN
ap-1829	363	19	3	3	NUM
ap-1829	363	20	,	,	PUNCT
ap-1829	363	21	and	and	CCONJ
ap-1829	363	22	figure	figure	VERB
ap-1829	363	23	1	1	NUM
ap-1829	363	24	is	be	AUX
ap-1829	363	25	a	a	DET
ap-1829	363	26	plot	plot	NOUN
ap-1829	363	27	of	of	ADP
ap-1829	363	28	the	the	DET
ap-1829	363	29	constitutive	constitutive	ADJ
ap-1829	363	30	functions	function	NOUN
ap-1829	363	31	.	.	PUNCT
ap-1829	364	1	the	the	DET
ap-1829	364	2	repository	repository	NOUN
ap-1829	364	3	interior	interior	ADJ
ap-1829	364	4	–	–	PUNCT
ap-1829	364	5	concrete	concrete	ADJ
ap-1829	364	6	,	,	PUNCT
ap-1829	364	7	and	and	CCONJ
ap-1829	364	8	the	the	DET
ap-1829	364	9	repository	repository	NOUN
ap-1829	364	10	barrier	barrier	NOUN
ap-1829	364	11	–	–	PUNCT
ap-1829	364	12	gravel	gravel	NOUN
ap-1829	364	13	,	,	PUNCT
ap-1829	364	14	were	be	AUX
ap-1829	364	15	obviously	obviously	ADV
ap-1829	364	16	formed	form	VERB
ap-1829	364	17	out	out	ADP
ap-1829	364	18	of	of	ADP
ap-1829	364	19	identical	identical	ADJ
ap-1829	364	20	material	material	NOUN
ap-1829	364	21	in	in	ADP
ap-1829	364	22	both	both	CCONJ
ap-1829	364	23	the	the	DET
ap-1829	364	24	matrix	matrix	NOUN
ap-1829	364	25	domain	domain	NOUN
ap-1829	364	26	and	and	CCONJ
ap-1829	364	27	the	the	DET
ap-1829	364	28	fracture	fracture	NOUN
ap-1829	364	29	domain	domain	NOUN
ap-1829	364	30	.	.	PUNCT
ap-1829	365	1	the	the	DET
ap-1829	365	2	different	different	ADJ
ap-1829	365	3	material	material	NOUN
ap-1829	365	4	conditions	condition	NOUN
ap-1829	365	5	scattered	scatter	VERB
ap-1829	365	6	into	into	ADP
ap-1829	365	7	the	the	DET
ap-1829	365	8	matrix	matrix	NOUN
ap-1829	365	9	and	and	CCONJ
ap-1829	365	10	fracture	fracture	NOUN
ap-1829	365	11	domains	domain	NOUN
ap-1829	365	12	appeared	appear	VERB
ap-1829	365	13	in	in	ADP
ap-1829	365	14	the	the	DET
ap-1829	365	15	rock	rock	NOUN
ap-1829	365	16	material	material	NOUN
ap-1829	365	17	.	.	PUNCT
ap-1829	366	1	the	the	DET
ap-1829	366	2	initial	initial	ADJ
ap-1829	366	3	condition	condition	NOUN
ap-1829	366	4	was	be	AUX
ap-1829	366	5	defined	define	VERB
ap-1829	366	6	as	as	ADP
ap-1829	366	7	h(x	h(x	PROPN
ap-1829	366	8	,	,	PUNCT
ap-1829	366	9	0	0	NUM
ap-1829	366	10	)	)	PUNCT
ap-1829	367	1	=	=	VERB
ap-1829	367	2	−200.0	−200.0	ADJ
ap-1829	367	3	cm	cm	X
ap-1829	367	4	∀x	∀x	X
ap-1829	367	5	∈	∈	PROPN
ap-1829	367	6	ω	ω	NOUN
ap-1829	367	7	,	,	PUNCT
ap-1829	367	8	(	(	PUNCT
ap-1829	367	9	38	38	NUM
ap-1829	367	10	)	)	PUNCT
ap-1829	367	11	and	and	CCONJ
ap-1829	367	12	the	the	DET
ap-1829	367	13	boundary	boundary	ADJ
ap-1829	367	14	conditions	condition	NOUN
ap-1829	367	15	were	be	AUX
ap-1829	367	16	defined	define	VERB
ap-1829	367	17	as	as	ADP
ap-1829	367	18	•	•	NUM
ap-1829	367	19	γ1	γ1	PROPN
ap-1829	367	20	–	–	PUNCT
ap-1829	367	21	dirichlet	dirichlet	PROPN
ap-1829	367	22	boundary	boundary	ADJ
ap-1829	367	23	condition	condition	NOUN
ap-1829	367	24	of	of	ADP
ap-1829	367	25	pressure	pressure	NOUN
ap-1829	367	26	head	head	NOUN
ap-1829	367	27	+10.0	+10.0	PROPN
ap-1829	367	28	cm	cm	PROPN
ap-1829	367	29	hm	hm	PROPN
ap-1829	367	30	,	,	PUNCT
ap-1829	367	31	f	f	PROPN
ap-1829	367	32	(	(	PUNCT
ap-1829	367	33	x	x	PROPN
ap-1829	367	34	,	,	PUNCT
ap-1829	367	35	t	t	PROPN
ap-1829	367	36	)	)	PUNCT
ap-1829	367	37	=	=	PUNCT
ap-1829	367	38	10.0	10.0	NUM
ap-1829	367	39	cm	cm	NOUN
ap-1829	367	40	x	x	SYM
ap-1829	367	41	∈	∈	PROPN
ap-1829	367	42	γ1	γ1	NOUN
ap-1829	367	43	×	×	NOUN
ap-1829	367	44	[	[	X
ap-1829	367	45	0	0	NUM
ap-1829	367	46	,	,	PUNCT
ap-1829	367	47	t	t	NOUN
ap-1829	367	48	)	)	PUNCT
ap-1829	367	49	(	(	PUNCT
ap-1829	367	50	39	39	NUM
ap-1829	367	51	)	)	PUNCT
ap-1829	367	52	•	•	NUM
ap-1829	367	53	γ2,3,4	γ2,3,4	ADJ
ap-1829	367	54	–	–	PUNCT
ap-1829	367	55	homogeneous	homogeneous	ADJ
ap-1829	367	56	neumann	neumann	PROPN
ap-1829	367	57	boundary	boundary	ADJ
ap-1829	367	58	conditions	condition	NOUN
ap-1829	367	59	that	that	PRON
ap-1829	367	60	satisfy	satisfy	VERB
ap-1829	367	61	the	the	DET
ap-1829	367	62	initial	initial	ADJ
ap-1829	367	63	condition	condition	NOUN
ap-1829	367	64	(	(	PUNCT
ap-1829	367	65	free	free	ADJ
ap-1829	367	66	drainage	drainage	NOUN
ap-1829	367	67	boundary	boundary	NOUN
ap-1829	367	68	,	,	PUNCT
ap-1829	367	69	because	because	SCONJ
ap-1829	367	70	in	in	ADP
ap-1829	367	71	general	general	ADJ
ap-1829	367	72	the	the	DET
ap-1829	367	73	neumann	neumann	PROPN
ap-1829	367	74	condition	condition	NOUN
ap-1829	367	75	for	for	ADP
ap-1829	367	76	the	the	DET
ap-1829	367	77	richards	richard	NOUN
ap-1829	367	78	equation	equation	NOUN
ap-1829	367	79	states	state	VERB
ap-1829	367	80	that	that	SCONJ
ap-1829	367	81	qn	qn	NOUN
ap-1829	368	1	=	=	NOUN
ap-1829	368	2	−n(k(h)∇h	−n(k(h)∇h	PROPN
ap-1829	368	3	+	+	NUM
ap-1829	368	4	k(h)(:,2	k(h)(:,2	NOUN
ap-1829	368	5	)	)	PUNCT
ap-1829	368	6	)	)	PUNCT
ap-1829	368	7	,	,	PUNCT
ap-1829	368	8	where	where	SCONJ
ap-1829	368	9	k(h)(:,2	k(h)(:,2	NOUN
ap-1829	368	10	)	)	PUNCT
ap-1829	368	11	is	be	AUX
ap-1829	368	12	the	the	DET
ap-1829	368	13	second	second	ADJ
ap-1829	368	14	column	column	NOUN
ap-1829	368	15	of	of	ADP
ap-1829	368	16	the	the	DET
ap-1829	368	17	hydraulic	hydraulic	ADJ
ap-1829	368	18	conductivity	conductivity	NOUN
ap-1829	368	19	tensor	tensor	NOUN
ap-1829	368	20	in	in	ADP
ap-1829	368	21	the	the	DET
ap-1829	368	22	case	case	NOUN
ap-1829	368	23	of	of	ADP
ap-1829	368	24	<	<	X
ap-1829	368	25	2	2	NUM
ap-1829	368	26	)	)	PUNCT
ap-1829	368	27	the	the	DET
ap-1829	368	28	domain	domain	NOUN
ap-1829	368	29	was	be	AUX
ap-1829	368	30	discretized	discretize	VERB
ap-1829	368	31	by	by	ADP
ap-1829	368	32	a	a	DET
ap-1829	368	33	non	non	ADJ
ap-1829	368	34	-	-	ADJ
ap-1829	368	35	uniform	uniform	ADJ
ap-1829	368	36	triangular	triangular	NOUN
ap-1829	368	37	mesh	mesh	NOUN
ap-1829	368	38	that	that	PRON
ap-1829	368	39	consists	consist	VERB
ap-1829	368	40	of	of	ADP
ap-1829	368	41	12027	12027	NUM
ap-1829	368	42	nodes	node	NOUN
ap-1829	368	43	and	and	CCONJ
ap-1829	368	44	23771	23771	NUM
ap-1829	368	45	elements	element	NOUN
ap-1829	368	46	.	.	PUNCT
ap-1829	369	1	4.4	4.4	NUM
ap-1829	369	2	.	.	PUNCT
ap-1829	370	1	numerical	numerical	ADJ
ap-1829	370	2	properties	property	NOUN
ap-1829	370	3	the	the	DET
ap-1829	370	4	material	material	NOUN
ap-1829	370	5	properties	property	NOUN
ap-1829	370	6	of	of	ADP
ap-1829	370	7	this	this	DET
ap-1829	370	8	problem	problem	NOUN
ap-1829	370	9	cover	cover	VERB
ap-1829	370	10	several	several	ADJ
ap-1829	370	11	orders	order	NOUN
ap-1829	370	12	of	of	ADP
ap-1829	370	13	magnitude	magnitude	NOUN
ap-1829	370	14	,	,	PUNCT
ap-1829	370	15	and	and	CCONJ
ap-1829	370	16	thus	thus	ADV
ap-1829	370	17	finite	finite	VERB
ap-1829	370	18	element	element	NOUN
ap-1829	370	19	approximation	approximation	NOUN
ap-1829	370	20	forms	form	VERB
ap-1829	370	21	ill	ill	ADV
ap-1829	370	22	-	-	PUNCT
ap-1829	370	23	posed	pose	VERB
ap-1829	370	24	matrices	matrix	NOUN
ap-1829	370	25	.	.	PUNCT
ap-1829	371	1	in	in	ADP
ap-1829	371	2	order	order	NOUN
ap-1829	371	3	to	to	PART
ap-1829	371	4	evaluate	evaluate	VERB
ap-1829	371	5	the	the	DET
ap-1829	371	6	efficiency	efficiency	NOUN
ap-1829	371	7	of	of	ADP
ap-1829	371	8	the	the	DET
ap-1829	371	9	preconditioner	preconditioner	NOUN
ap-1829	371	10	that	that	PRON
ap-1829	371	11	is	be	AUX
ap-1829	371	12	applied	apply	VERB
ap-1829	371	13	here	here	ADV
ap-1829	371	14	,	,	PUNCT
ap-1829	371	15	several	several	ADJ
ap-1829	371	16	early	early	ADJ
ap-1829	371	17	states	state	NOUN
ap-1829	371	18	were	be	AUX
ap-1829	371	19	solved	solve	VERB
ap-1829	371	20	both	both	CCONJ
ap-1829	371	21	with	with	ADP
ap-1829	371	22	and	and	CCONJ
ap-1829	371	23	without	without	ADP
ap-1829	371	24	preconditioned	preconditioned	ADJ
ap-1829	371	25	matrices	matrix	NOUN
ap-1829	371	26	.	.	PUNCT
ap-1829	372	1	when	when	SCONJ
ap-1829	372	2	the	the	DET
ap-1829	372	3	stopping	stop	VERB
ap-1829	372	4	criterion	criterion	NOUN
ap-1829	372	5	definition	definition	NOUN
ap-1829	372	6	from	from	ADP
ap-1829	372	7	the	the	DET
ap-1829	372	8	previous	previous	ADJ
ap-1829	372	9	paragraph	paragraph	NOUN
ap-1829	372	10	was	be	AUX
ap-1829	372	11	used	use	VERB
ap-1829	372	12	,	,	PUNCT
ap-1829	372	13	it	it	PRON
ap-1829	372	14	was	be	AUX
ap-1829	372	15	observed	observe	VERB
ap-1829	372	16	that	that	SCONJ
ap-1829	372	17	for	for	ADP
ap-1829	372	18	non	non	ADJ
ap-1829	372	19	-	-	ADJ
ap-1829	372	20	preconditioned	preconditioned	ADJ
ap-1829	372	21	matrices	matrix	NOUN
ap-1829	372	22	the	the	DET
ap-1829	372	23	number	number	NOUN
ap-1829	372	24	of	of	ADP
ap-1829	372	25	iterations	iteration	NOUN
ap-1829	372	26	reached	reach	VERB
ap-1829	372	27	an	an	DET
ap-1829	372	28	average	average	ADJ
ap-1829	372	29	355	355	NUM
ap-1829	372	30	michal	michal	NOUN
ap-1829	372	31	kuráž	kuráž	PROPN
ap-1829	372	32	,	,	PUNCT
ap-1829	372	33	petr	petr	PROPN
ap-1829	372	34	mayer	mayer	PROPN
ap-1829	372	35	acta	acta	PROPN
ap-1829	372	36	polytechnica	polytechnica	PROPN
ap-1829	372	37	material	material	PROPN
ap-1829	373	1	ks	ks	PROPN
ap-1829	374	1	[	[	X
ap-1829	374	2	cmd−1	cmd−1	X
ap-1829	374	3	]	]	X
ap-1829	374	4	θr	θr	PRON
ap-1829	375	1	[	[	X
ap-1829	375	2	–	–	PUNCT
ap-1829	375	3	]	]	X
ap-1829	375	4	θs	θs	X
ap-1829	376	1	[	[	X
ap-1829	376	2	–	–	PUNCT
ap-1829	376	3	]	]	PUNCT
ap-1829	376	4	αvg	αvg	NOUN
ap-1829	377	1	[	[	X
ap-1829	377	2	cm−1	cm−1	NOUN
ap-1829	377	3	]	]	PUNCT
ap-1829	377	4	nvg	nvg	PROPN
ap-1829	377	5	[	[	X
ap-1829	377	6	–	–	PUNCT
ap-1829	377	7	]	]	PUNCT
ap-1829	377	8	mvg	mvg	PROPN
ap-1829	378	1	[	[	X
ap-1829	378	2	–	–	PUNCT
ap-1829	378	3	]	]	PUNCT
ap-1829	378	4	ss	ss	NOUN
ap-1829	379	1	[	[	X
ap-1829	379	2	cm−1	cm−1	NOUN
ap-1829	379	3	]	]	PUNCT
ap-1829	379	4	claystone	claystone	NOUN
ap-1829	379	5	–	–	PUNCT
ap-1829	379	6	“	"	PUNCT
ap-1829	379	7	m	m	NOUN
ap-1829	379	8	”	"	PUNCT
ap-1829	379	9	0.0864	0.0864	NUM
ap-1829	379	10	0.064	0.064	NUM
ap-1829	379	11	0.14	0.14	NUM
ap-1829	379	12	0.01	0.01	NUM
ap-1829	379	13	2.5	2.5	NUM
ap-1829	379	14	0.864	0.864	NUM
ap-1829	379	15	0.1	0.1	NUM
ap-1829	379	16	claystone	claystone	NOUN
ap-1829	379	17	–	–	PUNCT
ap-1829	379	18	“	"	PUNCT
ap-1829	379	19	f	f	X
ap-1829	379	20	”	"	PUNCT
ap-1829	379	21	15.9464	15.9464	NUM
ap-1829	379	22	0.0	0.0	NUM
ap-1829	379	23	0.91087	0.91087	NUM
ap-1829	379	24	0.00682	0.00682	NUM
ap-1829	379	25	5.4829	5.4829	NUM
ap-1829	379	26	0.43369	0.43369	NUM
ap-1829	379	27	0.1	0.1	NUM
ap-1829	379	28	gravel	gravel	NOUN
ap-1829	379	29	bar	bar	NOUN
ap-1829	379	30	.	.	PUNCT
ap-1829	380	1	712.8	712.8	NUM
ap-1829	380	2	0.0	0.0	NUM
ap-1829	380	3	0.43	0.43	NUM
ap-1829	380	4	1.0	1.0	NUM
ap-1829	380	5	2.0	2.0	NUM
ap-1829	380	6	0.626	0.626	NUM
ap-1829	380	7	0.2	0.2	NUM
ap-1829	380	8	concrete	concrete	ADJ
ap-1829	380	9	fill	fill	NOUN
ap-1829	380	10	1.68	1.68	NUM
ap-1829	380	11	0.089	0.089	NUM
ap-1829	380	12	0.43	0.43	NUM
ap-1829	380	13	0.01	0.01	NUM
ap-1829	380	14	1.23	1.23	NUM
ap-1829	380	15	0.187	0.187	NUM
ap-1829	380	16	0.03	0.03	NUM
ap-1829	380	17	table	table	NOUN
ap-1829	380	18	3	3	NUM
ap-1829	380	19	.	.	PUNCT
ap-1829	381	1	the	the	DET
ap-1829	381	2	material	material	NOUN
ap-1829	381	3	properties	property	NOUN
ap-1829	381	4	table	table	VERB
ap-1829	381	5	.	.	PUNCT
ap-1829	382	1	0	0	NUM
ap-1829	383	1	50	50	NUM
ap-1829	383	2	100	100	NUM
ap-1829	383	3	150	150	NUM
ap-1829	383	4	200	200	NUM
ap-1829	383	5	250	250	NUM
ap-1829	383	6	300	300	NUM
ap-1829	383	7	350	350	NUM
ap-1829	383	8	400	400	NUM
ap-1829	383	9	0	0	NUM
ap-1829	383	10	25	25	NUM
ap-1829	383	11	50	50	NUM
ap-1829	383	12	75	75	NUM
ap-1829	383	13	100	100	NUM
ap-1829	383	14	p	p	NOUN
ap-1829	383	15	c	c	NOUN
ap-1829	383	16	g	g	NOUN
ap-1829	384	1	i	i	PRON
ap-1829	384	2	te	te	INTJ
ap-1829	384	3	ra	ra	INTJ
ap-1829	384	4	ti	ti	INTJ
ap-1829	384	5	o	o	PROPN
ap-1829	385	1	n	n	PROPN
ap-1829	385	2	s	s	NOUN
ap-1829	385	3	time	time	NOUN
ap-1829	385	4	[	[	X
ap-1829	385	5	days	day	NOUN
ap-1829	385	6	]	]	X
ap-1829	385	7	right	right	ADJ
ap-1829	385	8	hand	hand	NOUN
ap-1829	385	9	s.	s.	PROPN
ap-1829	385	10	precond	precond	PROPN
ap-1829	385	11	.	.	PUNCT
ap-1829	386	1	left	leave	VERB
ap-1829	386	2	hand	hand	NOUN
ap-1829	386	3	s.	s.	PROPN
ap-1829	386	4	precond	precond	PROPN
ap-1829	386	5	.	.	PUNCT
ap-1829	387	1	figure	figure	NOUN
ap-1829	387	2	7	7	NUM
ap-1829	387	3	.	.	PUNCT
ap-1829	387	4	number	number	NOUN
ap-1829	387	5	of	of	ADP
ap-1829	387	6	iterations	iteration	NOUN
ap-1829	387	7	required	require	VERB
ap-1829	387	8	by	by	ADP
ap-1829	387	9	the	the	DET
ap-1829	387	10	conjugate	conjugate	ADJ
ap-1829	387	11	gradient	gradient	ADJ
ap-1829	387	12	algorithm	algorithm	NOUN
ap-1829	387	13	to	to	PART
ap-1829	387	14	converge	converge	VERB
ap-1829	387	15	for	for	ADP
ap-1829	387	16	the	the	DET
ap-1829	387	17	repository	repository	NOUN
ap-1829	387	18	problem	problem	NOUN
ap-1829	387	19	.	.	PUNCT
ap-1829	388	1	value	value	NOUN
ap-1829	388	2	of	of	ADP
ap-1829	388	3	17687	17687	NUM
ap-1829	388	4	.	.	PUNCT
ap-1829	389	1	in	in	ADP
ap-1829	389	2	the	the	DET
ap-1829	389	3	case	case	NOUN
ap-1829	389	4	of	of	ADP
ap-1829	389	5	a	a	DET
ap-1829	389	6	preconditioned	preconditioned	ADJ
ap-1829	389	7	state	state	NOUN
ap-1829	389	8	,	,	PUNCT
ap-1829	389	9	the	the	DET
ap-1829	389	10	average	average	ADJ
ap-1829	389	11	number	number	NOUN
ap-1829	389	12	of	of	ADP
ap-1829	389	13	iterations	iteration	NOUN
ap-1829	389	14	was	be	AUX
ap-1829	389	15	18	18	NUM
ap-1829	389	16	.	.	PUNCT
ap-1829	390	1	the	the	DET
ap-1829	390	2	matrix	matrix	NOUN
ap-1829	390	3	dimension	dimension	NOUN
ap-1829	390	4	was	be	AUX
ap-1829	390	5	23898	23898	NUM
ap-1829	390	6	.	.	PUNCT
ap-1829	391	1	thus	thus	ADV
ap-1829	391	2	,	,	PUNCT
ap-1829	391	3	for	for	ADP
ap-1829	391	4	this	this	DET
ap-1829	391	5	particular	particular	ADJ
ap-1829	391	6	case	case	NOUN
ap-1829	391	7	,	,	PUNCT
ap-1829	391	8	this	this	DET
ap-1829	391	9	simple	simple	ADJ
ap-1829	391	10	preconditioner	preconditioner	NOUN
ap-1829	391	11	decreased	decrease	VERB
ap-1829	391	12	the	the	DET
ap-1829	391	13	total	total	ADJ
ap-1829	391	14	number	number	NOUN
ap-1829	391	15	of	of	ADP
ap-1829	391	16	iterations	iteration	NOUN
ap-1829	391	17	required	require	VERB
ap-1829	391	18	to	to	PART
ap-1829	391	19	solve	solve	VERB
ap-1829	391	20	the	the	DET
ap-1829	391	21	unsteady	unsteady	ADJ
ap-1829	391	22	problem	problem	NOUN
ap-1829	391	23	by	by	ADP
ap-1829	391	24	a	a	DET
ap-1829	391	25	multiple	multiple	NOUN
ap-1829	391	26	of	of	ADP
ap-1829	391	27	approximately	approximately	ADV
ap-1829	391	28	10−3	10−3	NUM
ap-1829	391	29	.	.	PUNCT
ap-1829	392	1	as	as	SCONJ
ap-1829	392	2	was	be	AUX
ap-1829	392	3	mentioned	mention	VERB
ap-1829	392	4	above	above	ADV
ap-1829	392	5	,	,	PUNCT
ap-1829	392	6	this	this	DET
ap-1829	392	7	proposed	propose	VERB
ap-1829	392	8	method	method	NOUN
ap-1829	392	9	suffers	suffer	VERB
ap-1829	392	10	from	from	ADP
ap-1829	392	11	a	a	DET
ap-1829	392	12	noticeable	noticeable	ADJ
ap-1829	392	13	disadvantage	disadvantage	NOUN
ap-1829	392	14	–	–	PUNCT
ap-1829	392	15	for	for	ADP
ap-1829	392	16	symmetric	symmetric	ADJ
ap-1829	392	17	problems	problem	NOUN
ap-1829	392	18	the	the	DET
ap-1829	392	19	matrix	matrix	NOUN
ap-1829	392	20	is	be	AUX
ap-1829	392	21	converted	convert	VERB
ap-1829	392	22	into	into	ADP
ap-1829	392	23	a	a	DET
ap-1829	392	24	non	non	ADJ
ap-1829	392	25	-	-	ADJ
ap-1829	392	26	symmetric	symmetric	ADJ
ap-1829	392	27	matrix	matrix	NOUN
ap-1829	392	28	.	.	PUNCT
ap-1829	393	1	thus	thus	ADV
ap-1829	393	2	the	the	DET
ap-1829	393	3	diagonal	diagonal	ADJ
ap-1829	393	4	scaling	scaling	NOUN
ap-1829	393	5	was	be	AUX
ap-1829	393	6	also	also	ADV
ap-1829	393	7	assumed	assume	VERB
ap-1829	393	8	in	in	ADP
ap-1829	393	9	a	a	DET
ap-1829	393	10	different	different	ADJ
ap-1829	393	11	way	way	NOUN
ap-1829	393	12	–	–	PUNCT
ap-1829	393	13	from	from	ADP
ap-1829	393	14	the	the	DET
ap-1829	393	15	left	left	ADJ
ap-1829	393	16	hand	hand	NOUN
ap-1829	393	17	side	side	NOUN
ap-1829	393	18	aprcd	aprcd	PROPN
ap-1829	393	19	=	=	SYM
ap-1829	393	20	d×a	d×a	PROPN
ap-1829	393	21	,	,	PUNCT
ap-1829	393	22	(	(	PUNCT
ap-1829	393	23	40	40	NUM
ap-1829	393	24	)	)	PUNCT
ap-1829	393	25	and	and	CCONJ
ap-1829	393	26	then	then	ADV
ap-1829	393	27	the	the	DET
ap-1829	393	28	scaling	scaling	NOUN
ap-1829	393	29	can	can	AUX
ap-1829	393	30	be	be	AUX
ap-1829	393	31	described	describe	VERB
ap-1829	393	32	by	by	ADP
ap-1829	393	33	the	the	DET
ap-1829	393	34	following	follow	VERB
ap-1829	393	35	scheme	scheme	NOUN
ap-1829	393	36			PROPN
ap-1829	393	37	a11	a11	PROPN
ap-1829	393	38	a12	a12	PROPN
ap-1829	393	39	.	.	PUNCT
ap-1829	393	40	.	.	PUNCT
ap-1829	393	41	.	.	PUNCT
ap-1829	394	1	a1n	a1n	PRON
ap-1829	394	2	a21	a21	PROPN
ap-1829	394	3	a22	a22	PROPN
ap-1829	394	4	.	.	PUNCT
ap-1829	394	5	.	.	PUNCT
ap-1829	394	6	.	.	PUNCT
ap-1829	395	1	a2n	a2n	PROPN
ap-1829	395	2	...	...	PUNCT
ap-1829	395	3	...	...	PUNCT
ap-1829	395	4	.	.	PUNCT
ap-1829	395	5	.	.	PUNCT
ap-1829	395	6	.	.	PUNCT
ap-1829	395	7	...	...	PUNCT
ap-1829	396	1	an1	an1	PROPN
ap-1829	396	2	an2	an2	PROPN
ap-1829	396	3	.	.	PUNCT
ap-1829	396	4	.	.	PUNCT
ap-1829	396	5	.	.	PUNCT
ap-1829	397	1	ann	ann	PROPN
ap-1829	397	2			PROPN
ap-1829	397	3	→	→	SYM
ap-1829	397	4			PROPN
ap-1829	397	5	1.0	1.0	NUM
ap-1829	397	6	a12	a12	PROPN
ap-1829	397	7	a11	a11	PROPN
ap-1829	397	8	.	.	PUNCT
ap-1829	397	9	.	.	PUNCT
ap-1829	397	10	.	.	PUNCT
ap-1829	398	1	a1n	a1n	PRON
ap-1829	398	2	a11	a11	PROPN
ap-1829	398	3	a21	a21	PROPN
ap-1829	398	4	a22	a22	PROPN
ap-1829	398	5	1.0	1.0	NUM
ap-1829	398	6	.	.	PUNCT
ap-1829	398	7	.	.	PUNCT
ap-1829	398	8	.	.	PUNCT
ap-1829	399	1	a2n	a2n	PROPN
ap-1829	399	2	a22	a22	PROPN
ap-1829	399	3	...	...	PUNCT
ap-1829	399	4	...	...	PUNCT
ap-1829	399	5	.	.	PUNCT
ap-1829	399	6	.	.	PUNCT
ap-1829	399	7	.	.	PUNCT
ap-1829	399	8	...	...	PUNCT
ap-1829	400	1	an1	an1	X
ap-1829	401	1	ann	ann	PROPN
ap-1829	401	2	an2	an2	PROPN
ap-1829	401	3	ann	ann	PROPN
ap-1829	401	4	.	.	PUNCT
ap-1829	401	5	.	.	PUNCT
ap-1829	402	1	.	.	PUNCT
ap-1829	403	1	1.0	1.0	NUM
ap-1829	403	2			NUM
ap-1829	403	3	(	(	PUNCT
ap-1829	403	4	41	41	NUM
ap-1829	403	5	)	)	PUNCT
ap-1829	403	6	it	it	PRON
ap-1829	403	7	is	be	AUX
ap-1829	403	8	well	well	ADV
ap-1829	403	9	known	know	VERB
ap-1829	403	10	,	,	PUNCT
ap-1829	403	11	see	see	VERB
ap-1829	403	12	eg	eg	NOUN
ap-1829	403	13	.	.	PUNCT
ap-1829	404	1	[	[	X
ap-1829	404	2	23	23	NUM
ap-1829	404	3	]	]	PUNCT
ap-1829	404	4	,	,	PUNCT
ap-1829	404	5	that	that	SCONJ
ap-1829	404	6	if	if	SCONJ
ap-1829	404	7	a	a	PRON
ap-1829	404	8	were	be	AUX
ap-1829	404	9	a	a	DET
ap-1829	404	10	symmetric	symmetric	ADJ
ap-1829	404	11	positive	positive	ADJ
ap-1829	404	12	definite	definite	ADJ
ap-1829	404	13	matrix	matrix	NOUN
ap-1829	404	14	,	,	PUNCT
ap-1829	404	15	then	then	ADV
ap-1829	404	16	the	the	DET
ap-1829	404	17	left	left	ADJ
ap-1829	404	18	and	and	CCONJ
ap-1829	404	19	right	right	ADJ
ap-1829	404	20	hand	hand	NOUN
ap-1829	404	21	side	side	NOUN
ap-1829	404	22	preconditioners	preconditioner	NOUN
ap-1829	404	23	would	would	AUX
ap-1829	404	24	be	be	AUX
ap-1829	404	25	equivalent	equivalent	ADJ
ap-1829	404	26	.	.	PUNCT
ap-1829	405	1	it	it	PRON
ap-1829	405	2	should	should	AUX
ap-1829	405	3	be	be	AUX
ap-1829	405	4	further	far	ADV
ap-1829	405	5	noted	note	VERB
ap-1829	405	6	,	,	PUNCT
ap-1829	405	7	that	that	SCONJ
ap-1829	405	8	the	the	DET
ap-1829	405	9	left	left	ADJ
ap-1829	405	10	hand	hand	NOUN
ap-1829	405	11	side	side	NOUN
ap-1829	405	12	z	z	PROPN
ap-1829	406	1	[	[	X
ap-1829	406	2	cm	cm	X
ap-1829	406	3	]	]	X
ap-1829	406	4	−3400	−3400	NOUN
ap-1829	406	5	−3200	−3200	PROPN
ap-1829	406	6	−3000	−3000	VERB
ap-1829	406	7	−2800	−2800	NOUN
ap-1829	406	8	−2600	−2600	PROPN
ap-1829	406	9	−2400	−2400	NOUN
ap-1829	406	10	−2200	−2200	NOUN
ap-1829	406	11	h	h	NOUN
ap-1829	407	1	[	[	X
ap-1829	407	2	cm	cm	X
ap-1829	407	3	]	]	SYM
ap-1829	407	4	800	800	NUM
ap-1829	407	5	1000	1000	NUM
ap-1829	407	6	1200	1200	NUM
ap-1829	407	7	1400	1400	NUM
ap-1829	407	8	1600	1600	NUM
ap-1829	407	9	1800	1800	NUM
ap-1829	407	10	2000	2000	NUM
ap-1829	407	11	2200	2200	NUM
ap-1829	407	12	2400	2400	NUM
ap-1829	407	13	2600	2600	NUM
ap-1829	407	14	2800x	2800x	NUM
ap-1829	407	15	−2e+02	−2e+02	PROPN
ap-1829	407	16	−1.5e+02	−1.5e+02	NOUN
ap-1829	407	17	−95	−95	PROPN
ap-1829	407	18	−43	−43	PROPN
ap-1829	407	19	10	10	NUM
ap-1829	407	20	figure	figure	NOUN
ap-1829	407	21	8	8	NUM
ap-1829	407	22	.	.	PUNCT
ap-1829	408	1	intense	intense	ADJ
ap-1829	408	2	initial	initial	ADJ
ap-1829	408	3	infiltration	infiltration	NOUN
ap-1829	408	4	–	–	PUNCT
ap-1829	408	5	the	the	DET
ap-1829	408	6	dirichlet	dirichlet	PROPN
ap-1829	408	7	boundary	boundary	PROPN
ap-1829	408	8	condition	condition	NOUN
ap-1829	408	9	does	do	AUX
ap-1829	408	10	not	not	PART
ap-1829	408	11	satisfy	satisfy	VERB
ap-1829	408	12	the	the	DET
ap-1829	408	13	initial	initial	ADJ
ap-1829	408	14	condition	condition	NOUN
ap-1829	408	15	,	,	PUNCT
ap-1829	408	16	such	such	ADJ
ap-1829	408	17	discontinuity	discontinuity	NOUN
ap-1829	408	18	causes	cause	VERB
ap-1829	408	19	intense	intense	ADJ
ap-1829	408	20	processes	process	NOUN
ap-1829	408	21	in	in	ADP
ap-1829	408	22	the	the	DET
ap-1829	408	23	initial	initial	ADJ
ap-1829	408	24	states	state	NOUN
ap-1829	408	25	.	.	PUNCT
ap-1829	409	1	preconditioner	preconditioner	NOUN
ap-1829	409	2	in	in	ADP
ap-1829	409	3	the	the	DET
ap-1829	409	4	context	context	NOUN
ap-1829	409	5	of	of	ADP
ap-1829	409	6	the	the	DET
ap-1829	409	7	conjugate	conjugate	ADJ
ap-1829	409	8	gradient	gradient	NOUN
ap-1829	409	9	method	method	NOUN
ap-1829	409	10	for	for	SCONJ
ap-1829	409	11	normal	normal	ADJ
ap-1829	409	12	equations	equation	NOUN
ap-1829	409	13	forms	form	NOUN
ap-1829	409	14	atdtda	atdtda	VERB
ap-1829	409	15	,	,	PUNCT
ap-1829	409	16	and	and	CCONJ
ap-1829	409	17	this	this	DET
ap-1829	409	18	form	form	NOUN
ap-1829	409	19	is	be	AUX
ap-1829	409	20	not	not	PART
ap-1829	409	21	commonly	commonly	ADV
ap-1829	409	22	used	use	VERB
ap-1829	409	23	.	.	PUNCT
ap-1829	410	1	this	this	DET
ap-1829	410	2	preconditioner	preconditioner	NOUN
ap-1829	410	3	was	be	AUX
ap-1829	410	4	again	again	ADV
ap-1829	410	5	evaluated	evaluate	VERB
ap-1829	410	6	in	in	ADP
ap-1829	410	7	our	our	PRON
ap-1829	410	8	repository	repository	NOUN
ap-1829	410	9	study	study	NOUN
ap-1829	410	10	.	.	PUNCT
ap-1829	411	1	it	it	PRON
ap-1829	411	2	was	be	AUX
ap-1829	411	3	observed	observe	VERB
ap-1829	411	4	that	that	SCONJ
ap-1829	411	5	the	the	DET
ap-1829	411	6	left	left	ADJ
ap-1829	411	7	hand	hand	NOUN
ap-1829	411	8	and	and	CCONJ
ap-1829	411	9	right	right	ADJ
ap-1829	411	10	hand	hand	NOUN
ap-1829	411	11	side	side	NOUN
ap-1829	411	12	preconditioners	preconditioner	NOUN
ap-1829	411	13	both	both	PRON
ap-1829	411	14	behave	behave	VERB
ap-1829	411	15	similarly	similarly	ADV
ap-1829	411	16	if	if	SCONJ
ap-1829	411	17	the	the	DET
ap-1829	411	18	solution	solution	NOUN
ap-1829	411	19	is	be	AUX
ap-1829	411	20	"	"	PUNCT
ap-1829	411	21	smooth	smooth	ADJ
ap-1829	411	22	"	"	PUNCT
ap-1829	411	23	,	,	PUNCT
ap-1829	411	24	while	while	SCONJ
ap-1829	411	25	for	for	ADP
ap-1829	411	26	less	less	ADV
ap-1829	411	27	smooth	smooth	ADJ
ap-1829	411	28	solutions	solution	NOUN
ap-1829	411	29	the	the	DET
ap-1829	411	30	right	right	ADJ
ap-1829	411	31	hand	hand	NOUN
ap-1829	411	32	side	side	NOUN
ap-1829	411	33	preconditioner	preconditioner	NOUN
ap-1829	411	34	offers	offer	VERB
ap-1829	411	35	better	well	ADJ
ap-1829	411	36	performance	performance	NOUN
ap-1829	411	37	,	,	PUNCT
ap-1829	411	38	see	see	VERB
ap-1829	411	39	figure	figure	NOUN
ap-1829	411	40	7	7	NUM
ap-1829	411	41	.	.	PUNCT
ap-1829	412	1	the	the	DET
ap-1829	412	2	"	"	PUNCT
ap-1829	412	3	smoothness	smoothness	NOUN
ap-1829	412	4	"	"	PUNCT
ap-1829	412	5	of	of	ADP
ap-1829	412	6	the	the	DET
ap-1829	412	7	solution	solution	NOUN
ap-1829	412	8	was	be	AUX
ap-1829	412	9	defined	define	VERB
ap-1829	412	10	by	by	ADP
ap-1829	412	11	the	the	DET
ap-1829	412	12	criterion	criterion	NOUN
ap-1829	412	13	sm	sm	INTJ
ap-1829	413	1	=	=	PUNCT
ap-1829	413	2	n−1∑	n−1∑	PROPN
ap-1829	413	3	i=1	i=1	PROPN
ap-1829	413	4	|xi+1	|xi+1	PROPN
ap-1829	413	5	−	−	PROPN
ap-1829	413	6	xi|	xi|	PROPN
ap-1829	413	7	,	,	PUNCT
ap-1829	413	8	(	(	PUNCT
ap-1829	413	9	42	42	NUM
ap-1829	413	10	)	)	PUNCT
ap-1829	413	11	where	where	SCONJ
ap-1829	413	12	n	n	NOUN
ap-1829	413	13	is	be	AUX
ap-1829	413	14	matrix	matrix	NOUN
ap-1829	413	15	dimension	dimension	NOUN
ap-1829	413	16	,	,	PUNCT
ap-1829	413	17	x	x	X
ap-1829	413	18	is	be	AUX
ap-1829	413	19	vector	vector	NOUN
ap-1829	413	20	of	of	ADP
ap-1829	413	21	solution	solution	NOUN
ap-1829	413	22	(	(	PUNCT
ap-1829	413	23	ax	ax	NOUN
ap-1829	413	24	=	=	SYM
ap-1829	413	25	b	b	NOUN
ap-1829	413	26	)	)	PUNCT
ap-1829	413	27	,	,	PUNCT
ap-1829	413	28	and	and	CCONJ
ap-1829	413	29	xi	xi	X
ap-1829	413	30	is	be	AUX
ap-1829	413	31	some	some	DET
ap-1829	413	32	particular	particular	ADJ
ap-1829	413	33	value	value	NOUN
ap-1829	413	34	at	at	ADP
ap-1829	413	35	position	position	NOUN
ap-1829	413	36	i	i	PRON
ap-1829	413	37	from	from	ADP
ap-1829	413	38	the	the	DET
ap-1829	413	39	solution	solution	NOUN
ap-1829	413	40	vector	vector	NOUN
ap-1829	413	41	x.	x.	NOUN
ap-1829	413	42	constant	constant	PROPN
ap-1829	413	43	sm	sm	PROPN
ap-1829	413	44	is	be	AUX
ap-1829	413	45	only	only	ADV
ap-1829	413	46	a	a	DET
ap-1829	413	47	certain	certain	ADJ
ap-1829	413	48	indicator	indicator	NOUN
ap-1829	413	49	of	of	ADP
ap-1829	413	50	the	the	DET
ap-1829	413	51	"	"	PUNCT
ap-1829	413	52	smoothness	smoothness	NOUN
ap-1829	413	53	"	"	PUNCT
ap-1829	413	54	of	of	ADP
ap-1829	413	55	the	the	DET
ap-1829	413	56	values	value	NOUN
ap-1829	413	57	in	in	ADP
ap-1829	413	58	vector	vector	NOUN
ap-1829	413	59	x.	x.	NOUN
ap-1829	413	60	then	then	ADV
ap-1829	413	61	,	,	PUNCT
ap-1829	413	62	as	as	SCONJ
ap-1829	413	63	observed	observe	VERB
ap-1829	413	64	(	(	PUNCT
ap-1829	413	65	see	see	VERB
ap-1829	413	66	figure	figure	NOUN
ap-1829	413	67	7	7	NUM
ap-1829	413	68	)	)	PUNCT
ap-1829	413	69	,	,	PUNCT
ap-1829	413	70	at	at	ADP
ap-1829	413	71	time	time	NOUN
ap-1829	413	72	e.g.	e.g.	ADV
ap-1829	413	73	t	t	NOUN
ap-1829	413	74	=	=	SYM
ap-1829	413	75	2	2	NUM
ap-1829	413	76	days	day	NOUN
ap-1829	413	77	→	→	SYM
ap-1829	414	1	sm	sm	PROPN
ap-1829	415	1	≈	≈	PROPN
ap-1829	415	2	104	104	NUM
ap-1829	415	3	–	–	PUNCT
ap-1829	415	4	the	the	DET
ap-1829	415	5	behavior	behavior	NOUN
ap-1829	415	6	of	of	ADP
ap-1829	415	7	the	the	DET
ap-1829	415	8	two	two	NUM
ap-1829	415	9	methods	method	NOUN
ap-1829	415	10	was	be	AUX
ap-1829	415	11	comparable	comparable	ADJ
ap-1829	415	12	.	.	PUNCT
ap-1829	416	1	however	however	ADV
ap-1829	416	2	,	,	PUNCT
ap-1829	416	3	for	for	ADP
ap-1829	416	4	some	some	DET
ap-1829	416	5	later	later	ADJ
ap-1829	416	6	simulation	simulation	NOUN
ap-1829	416	7	time	time	NOUN
ap-1829	416	8	levels	level	NOUN
ap-1829	416	9	the	the	DET
ap-1829	416	10	right	right	ADJ
ap-1829	416	11	hand	hand	NOUN
ap-1829	416	12	side	side	NOUN
ap-1829	416	13	preconditioner	preconditioner	NOUN
ap-1829	416	14	offered	offer	VERB
ap-1829	416	15	better	well	ADJ
ap-1829	416	16	performance	performance	NOUN
ap-1829	416	17	,	,	PUNCT
ap-1829	416	18	e.g.	e.g.	ADV
ap-1829	416	19	at	at	ADP
ap-1829	416	20	time	time	NOUN
ap-1829	416	21	t	t	NOUN
ap-1829	416	22	=	=	SYM
ap-1829	416	23	80	80	NUM
ap-1829	416	24	days	day	NOUN
ap-1829	416	25	→	→	SYM
ap-1829	416	26	sm	sm	PROPN
ap-1829	416	27	=	=	PUNCT
ap-1829	416	28	106	106	NUM
ap-1829	416	29	.	.	PUNCT
ap-1829	417	1	if	if	SCONJ
ap-1829	417	2	the	the	DET
ap-1829	417	3	right	right	ADJ
ap-1829	417	4	hand	hand	NOUN
ap-1829	417	5	side	side	NOUN
ap-1829	417	6	preconditioner	preconditioner	NOUN
ap-1829	417	7	is	be	AUX
ap-1829	417	8	used	use	VERB
ap-1829	417	9	,	,	PUNCT
ap-1829	417	10	together	together	ADV
ap-1829	417	11	with	with	ADP
ap-1829	417	12	the	the	DET
ap-1829	417	13	small	small	ADJ
ap-1829	417	14	time	time	NOUN
ap-1829	417	15	steps	step	NOUN
ap-1829	417	16	involved	involve	VERB
ap-1829	417	17	,	,	PUNCT
ap-1829	417	18	the	the	DET
ap-1829	417	19	"	"	PUNCT
ap-1829	417	20	smoothness	smoothness	NOUN
ap-1829	417	21	"	"	PUNCT
ap-1829	417	22	of	of	ADP
ap-1829	417	23	the	the	DET
ap-1829	417	24	solution	solution	NOUN
ap-1829	417	25	remains	remain	VERB
ap-1829	417	26	hidden	hide	VERB
ap-1829	417	27	in	in	ADP
ap-1829	417	28	the	the	DET
ap-1829	417	29	diagonal	diagonal	ADJ
ap-1829	417	30	matrix	matrix	NOUN
ap-1829	417	31	d.	d.	NOUN
ap-1829	417	32	this	this	PRON
ap-1829	417	33	is	be	AUX
ap-1829	417	34	because	because	SCONJ
ap-1829	417	35	the	the	DET
ap-1829	417	36	solution	solution	NOUN
ap-1829	417	37	xprcd	xprcd	VERB
ap-1829	417	38	of	of	ADP
ap-1829	417	39	matrix	matrix	NOUN
ap-1829	417	40	aprcd	aprcd	PROPN
ap-1829	417	41	is	be	AUX
ap-1829	417	42	related	relate	VERB
ap-1829	417	43	to	to	ADP
ap-1829	417	44	solution	solution	NOUN
ap-1829	417	45	x	x	PUNCT
ap-1829	417	46	of	of	ADP
ap-1829	417	47	matrix	matrix	NOUN
ap-1829	417	48	a	a	PRON
ap-1829	417	49	by	by	ADP
ap-1829	417	50	x	x	X
ap-1829	418	1	=	=	SYM
ap-1829	418	2	d−1	d−1	PROPN
ap-1829	418	3	×	×	PROPN
ap-1829	418	4	xprcd	xprcd	PROPN
ap-1829	418	5	,	,	PUNCT
ap-1829	418	6	(	(	PUNCT
ap-1829	418	7	43	43	NUM
ap-1829	418	8	)	)	PUNCT
ap-1829	418	9	356	356	NUM
ap-1829	418	10	vol	vol	NOUN
ap-1829	418	11	.	.	PUNCT
ap-1829	419	1	53	53	NUM
ap-1829	419	2	no	no	NOUN
ap-1829	419	3	.	.	PUNCT
ap-1829	420	1	4/2013	4/2013	NOUN
ap-1829	420	2	algorithms	algorithm	NOUN
ap-1829	420	3	for	for	ADP
ap-1829	420	4	solving	solve	VERB
ap-1829	420	5	darcian	darcian	NOUN
ap-1829	420	6	flow	flow	NOUN
ap-1829	420	7	in	in	ADP
ap-1829	420	8	structured	structured	ADJ
ap-1829	420	9	porous	porous	ADJ
ap-1829	420	10	media	medium	NOUN
ap-1829	420	11	figure	figure	NOUN
ap-1829	420	12	9	9	NUM
ap-1829	420	13	.	.	PUNCT
ap-1829	421	1	wetting	wet	VERB
ap-1829	421	2	front	front	NOUN
ap-1829	421	3	is	be	AUX
ap-1829	421	4	getting	get	VERB
ap-1829	421	5	closer	close	ADJ
ap-1829	421	6	to	to	ADP
ap-1829	421	7	the	the	DET
ap-1829	421	8	capillary	capillary	ADJ
ap-1829	421	9	barrier	barrier	NOUN
ap-1829	421	10	shield	shield	NOUN
ap-1829	421	11	,	,	PUNCT
ap-1829	421	12	the	the	DET
ap-1829	421	13	repository	repository	NOUN
ap-1829	421	14	is	be	AUX
ap-1829	421	15	being	be	AUX
ap-1829	421	16	bypassed	bypass	VERB
ap-1829	421	17	.	.	PUNCT
ap-1829	422	1	and	and	CCONJ
ap-1829	422	2	thus	thus	ADV
ap-1829	422	3	for	for	ADP
ap-1829	422	4	the	the	DET
ap-1829	422	5	small	small	ADJ
ap-1829	422	6	time	time	NOUN
ap-1829	422	7	steps	step	NOUN
ap-1829	422	8	involved	involve	VERB
ap-1829	422	9	,	,	PUNCT
ap-1829	422	10	together	together	ADV
ap-1829	422	11	with	with	ADP
ap-1829	422	12	an	an	DET
ap-1829	422	13	assumption	assumption	NOUN
ap-1829	422	14	that	that	SCONJ
ap-1829	422	15	the	the	DET
ap-1829	422	16	solution	solution	NOUN
ap-1829	422	17	of	of	ADP
ap-1829	422	18	the	the	DET
ap-1829	422	19	richards	richard	NOUN
ap-1829	422	20	equation	equation	NOUN
ap-1829	422	21	is	be	AUX
ap-1829	422	22	continuous	continuous	ADJ
ap-1829	422	23	,	,	PUNCT
ap-1829	422	24	the	the	DET
ap-1829	422	25	sm	sm	PROPN
ap-1829	422	26	constant	constant	ADJ
ap-1829	422	27	from	from	ADP
ap-1829	422	28	equation	equation	NOUN
ap-1829	422	29	(	(	PUNCT
ap-1829	422	30	42	42	NUM
ap-1829	422	31	)	)	PUNCT
ap-1829	422	32	of	of	ADP
ap-1829	422	33	the	the	DET
ap-1829	422	34	xprcd	xprcd	PROPN
ap-1829	422	35	vector	vector	NOUN
ap-1829	422	36	reaches	reach	VERB
ap-1829	422	37	a	a	DET
ap-1829	422	38	low	low	ADJ
ap-1829	422	39	value	value	NOUN
ap-1829	422	40	.	.	PUNCT
ap-1829	423	1	4.4.1	4.4.1	X
ap-1829	423	2	.	.	PUNCT
ap-1829	423	3	conditioning	conditioning	NOUN
ap-1829	423	4	improvements	improvement	NOUN
ap-1829	423	5	the	the	DET
ap-1829	423	6	unsteady	unsteady	ADJ
ap-1829	423	7	problem	problem	NOUN
ap-1829	423	8	of	of	ADP
ap-1829	423	9	infiltration	infiltration	NOUN
ap-1829	423	10	around	around	ADP
ap-1829	423	11	the	the	DET
ap-1829	423	12	repository	repository	NOUN
ap-1829	423	13	can	can	AUX
ap-1829	423	14	be	be	AUX
ap-1829	423	15	divided	divide	VERB
ap-1829	423	16	into	into	ADP
ap-1829	423	17	the	the	DET
ap-1829	423	18	following	follow	VERB
ap-1829	423	19	periods	period	NOUN
ap-1829	423	20	(	(	PUNCT
ap-1829	423	21	1	1	NUM
ap-1829	423	22	.	.	PUNCT
ap-1829	423	23	)	)	PUNCT
ap-1829	423	24	intense	intense	ADJ
ap-1829	423	25	initial	initial	ADJ
ap-1829	423	26	infiltration	infiltration	NOUN
ap-1829	423	27	–	–	PUNCT
ap-1829	423	28	the	the	DET
ap-1829	423	29	dirichlet	dirichlet	PROPN
ap-1829	423	30	boundary	boundary	PROPN
ap-1829	423	31	condition	condition	NOUN
ap-1829	423	32	does	do	AUX
ap-1829	423	33	not	not	PART
ap-1829	423	34	satisfy	satisfy	VERB
ap-1829	423	35	the	the	DET
ap-1829	423	36	initial	initial	ADJ
ap-1829	423	37	condition	condition	NOUN
ap-1829	423	38	.	.	PUNCT
ap-1829	424	1	such	such	ADJ
ap-1829	424	2	discontinuity	discontinuity	NOUN
ap-1829	424	3	causes	cause	VERB
ap-1829	424	4	intense	intense	ADJ
ap-1829	424	5	processes	process	NOUN
ap-1829	424	6	in	in	ADP
ap-1829	424	7	the	the	DET
ap-1829	424	8	initial	initial	ADJ
ap-1829	424	9	states	state	NOUN
ap-1829	424	10	,	,	PUNCT
ap-1829	424	11	see	see	VERB
ap-1829	424	12	figure	figure	NOUN
ap-1829	424	13	8	8	NUM
ap-1829	424	14	;	;	PUNCT
ap-1829	424	15	(	(	PUNCT
ap-1829	424	16	2	2	NUM
ap-1829	424	17	.	.	PUNCT
ap-1829	424	18	)	)	PUNCT
ap-1829	425	1	the	the	DET
ap-1829	425	2	wetting	wet	VERB
ap-1829	425	3	front	front	NOUN
ap-1829	425	4	is	be	AUX
ap-1829	425	5	getting	get	VERB
ap-1829	425	6	closer	close	ADJ
ap-1829	425	7	to	to	ADP
ap-1829	425	8	the	the	DET
ap-1829	425	9	capillary	capillary	ADJ
ap-1829	425	10	barrier	barrier	NOUN
ap-1829	425	11	shield	shield	NOUN
ap-1829	425	12	,	,	PUNCT
ap-1829	425	13	the	the	DET
ap-1829	425	14	repository	repository	NOUN
ap-1829	425	15	is	be	AUX
ap-1829	425	16	being	be	AUX
ap-1829	425	17	bypassed	bypass	VERB
ap-1829	425	18	,	,	PUNCT
ap-1829	425	19	see	see	VERB
ap-1829	425	20	figure	figure	NOUN
ap-1829	425	21	9	9	NUM
ap-1829	425	22	;	;	PUNCT
ap-1829	425	23	(	(	PUNCT
ap-1829	425	24	3	3	NUM
ap-1829	425	25	.	.	PUNCT
ap-1829	425	26	)	)	PUNCT
ap-1829	426	1	the	the	DET
ap-1829	426	2	wetting	wet	VERB
ap-1829	426	3	front	front	NOUN
ap-1829	426	4	has	have	AUX
ap-1829	426	5	reached	reach	VERB
ap-1829	426	6	the	the	DET
ap-1829	426	7	repository	repository	NOUN
ap-1829	426	8	shield	shield	NOUN
ap-1829	426	9	,	,	PUNCT
ap-1829	426	10	steep	steep	ADJ
ap-1829	426	11	gradients	gradient	NOUN
ap-1829	426	12	appear	appear	VERB
ap-1829	426	13	at	at	ADP
ap-1829	426	14	the	the	DET
ap-1829	426	15	wetting	wet	VERB
ap-1829	426	16	front	front	ADJ
ap-1829	426	17	/	/	SYM
ap-1829	426	18	barrier	barrier	NOUN
ap-1829	426	19	interface	interface	NOUN
ap-1829	426	20	,	,	PUNCT
ap-1829	426	21	see	see	VERB
ap-1829	426	22	figure	figure	NOUN
ap-1829	426	23	10	10	NUM
ap-1829	426	24	.	.	PUNCT
ap-1829	427	1	the	the	DET
ap-1829	427	2	right	right	ADJ
ap-1829	427	3	hand	hand	NOUN
ap-1829	427	4	side	side	NOUN
ap-1829	427	5	preconditioner	preconditioner	NOUN
ap-1829	427	6	efficiency	efficiency	NOUN
ap-1829	427	7	was	be	AUX
ap-1829	427	8	evaluated	evaluate	VERB
ap-1829	427	9	for	for	ADP
ap-1829	427	10	each	each	DET
ap-1829	427	11	period	period	NOUN
ap-1829	427	12	,	,	PUNCT
ap-1829	427	13	for	for	ADP
ap-1829	427	14	a	a	DET
ap-1829	427	15	selected	select	VERB
ap-1829	427	16	time	time	NOUN
ap-1829	427	17	and	and	CCONJ
ap-1829	427	18	iteration	iteration	NOUN
ap-1829	427	19	level	level	NOUN
ap-1829	427	20	.	.	PUNCT
ap-1829	428	1	minimal	minimal	ADJ
ap-1829	428	2	and	and	CCONJ
ap-1829	428	3	maximal	maximal	ADJ
ap-1829	428	4	eigenvalues	eigenvalue	NOUN
ap-1829	428	5	were	be	AUX
ap-1829	428	6	evaluated	evaluate	VERB
ap-1829	428	7	for	for	ADP
ap-1829	428	8	the	the	DET
ap-1829	428	9	matrix	matrix	NOUN
ap-1829	428	10	at	at	ADP
ap-1829	428	11	×a	×a	PROPN
ap-1829	428	12	,	,	PUNCT
ap-1829	428	13	as	as	SCONJ
ap-1829	428	14	the	the	DET
ap-1829	428	15	problem	problem	NOUN
ap-1829	428	16	is	be	AUX
ap-1829	428	17	non	non	ADJ
ap-1829	428	18	-	-	ADJ
ap-1829	428	19	symmetric	symmetric	ADJ
ap-1829	428	20	,	,	PUNCT
ap-1829	428	21	and	and	CCONJ
ap-1829	428	22	thus	thus	ADV
ap-1829	428	23	a	a	DET
ap-1829	428	24	conjugate	conjugate	ADJ
ap-1829	428	25	gradient	gradient	ADJ
ap-1829	428	26	algorithm	algorithm	NOUN
ap-1829	428	27	for	for	ADP
ap-1829	428	28	normal	normal	ADJ
ap-1829	428	29	equations	equation	NOUN
ap-1829	428	30	was	be	AUX
ap-1829	428	31	applied	apply	VERB
ap-1829	428	32	.	.	PUNCT
ap-1829	429	1	maximal	maximal	ADJ
ap-1829	429	2	eigenvalues	eigenvalue	NOUN
ap-1829	429	3	were	be	AUX
ap-1829	429	4	evaluated	evaluate	VERB
ap-1829	429	5	by	by	ADP
ap-1829	429	6	the	the	DET
ap-1829	429	7	power	power	NOUN
ap-1829	429	8	method	method	NOUN
ap-1829	429	9	and	and	CCONJ
ap-1829	429	10	minimal	minimal	ADJ
ap-1829	429	11	eigenvalues	eigenvalue	NOUN
ap-1829	429	12	were	be	AUX
ap-1829	429	13	evaluated	evaluate	VERB
ap-1829	429	14	by	by	ADP
ap-1829	429	15	inverse	inverse	ADJ
ap-1829	429	16	iteration	iteration	NOUN
ap-1829	429	17	with	with	ADP
ap-1829	429	18	cholesky	cholesky	ADJ
ap-1829	429	19	decomposition	decomposition	NOUN
ap-1829	429	20	.	.	PUNCT
ap-1829	430	1	the	the	DET
ap-1829	430	2	results	result	NOUN
ap-1829	430	3	are	be	AUX
ap-1829	430	4	depicted	depict	VERB
ap-1829	430	5	in	in	ADP
ap-1829	430	6	table	table	NOUN
ap-1829	430	7	4	4	NUM
ap-1829	430	8	.	.	NOUN
ap-1829	430	9	5	5	NUM
ap-1829	430	10	.	.	PUNCT
ap-1829	431	1	conclusions	conclusion	NOUN
ap-1829	431	2	this	this	DET
ap-1829	431	3	paper	paper	NOUN
ap-1829	431	4	has	have	AUX
ap-1829	431	5	aimed	aim	VERB
ap-1829	431	6	to	to	PART
ap-1829	431	7	present	present	VERB
ap-1829	431	8	several	several	ADJ
ap-1829	431	9	new	new	ADJ
ap-1829	431	10	algorithms	algorithm	NOUN
ap-1829	431	11	that	that	PRON
ap-1829	431	12	were	be	AUX
ap-1829	431	13	implemented	implement	VERB
ap-1829	431	14	in	in	ADP
ap-1829	431	15	the	the	DET
ap-1829	431	16	drutes	drute	NOUN
ap-1829	431	17	opensource	opensource	PROPN
ap-1829	431	18	project	project	NOUN
ap-1829	432	1	[	[	X
ap-1829	432	2	1	1	X
ap-1829	432	3	]	]	PUNCT
ap-1829	432	4	–	–	PUNCT
ap-1829	432	5	a	a	DET
ap-1829	432	6	finite	finite	ADJ
ap-1829	432	7	element	element	NOUN
ap-1829	432	8	solver	solver	VERB
ap-1829	432	9	for	for	ADP
ap-1829	432	10	nonlinear	nonlinear	ADJ
ap-1829	432	11	coupled	couple	VERB
ap-1829	432	12	parabolic	parabolic	NOUN
ap-1829	432	13	problems	problem	NOUN
ap-1829	432	14	,	,	PUNCT
ap-1829	432	15	namely	namely	ADV
ap-1829	432	16	the	the	DET
ap-1829	432	17	richards	richard	NOUN
ap-1829	432	18	equation	equation	NOUN
ap-1829	432	19	with	with	ADP
ap-1829	432	20	the	the	DET
ap-1829	432	21	dual	dual	ADJ
ap-1829	432	22	porosity	porosity	NOUN
ap-1829	432	23	approach	approach	NOUN
ap-1829	432	24	,	,	PUNCT
ap-1829	432	25	in	in	ADP
ap-1829	432	26	order	order	NOUN
ap-1829	432	27	to	to	PART
ap-1829	432	28	improve	improve	VERB
ap-1829	432	29	the	the	DET
ap-1829	432	30	accuracy	accuracy	NOUN
ap-1829	432	31	and	and	CCONJ
ap-1829	432	32	efficiency	efficiency	NOUN
ap-1829	432	33	of	of	ADP
ap-1829	432	34	its	its	PRON
ap-1829	432	35	numerical	numerical	ADJ
ap-1829	432	36	treatment	treatment	NOUN
ap-1829	432	37	.	.	PUNCT
ap-1829	433	1	the	the	DET
ap-1829	433	2	mass	mass	ADJ
ap-1829	433	3	curve	curve	NOUN
ap-1829	433	4	zone	zone	NOUN
ap-1829	433	5	approach	approach	NOUN
ap-1829	433	6	,	,	PUNCT
ap-1829	433	7	an	an	DET
ap-1829	433	8	efficient	efficient	ADJ
ap-1829	433	9	and	and	CCONJ
ap-1829	433	10	accurate	accurate	ADJ
ap-1829	433	11	method	method	NOUN
ap-1829	433	12	for	for	ADP
ap-1829	433	13	the	the	DET
ap-1829	433	14	euler	euler	NOUN
ap-1829	433	15	time	time	NOUN
ap-1829	433	16	integration	integration	NOUN
ap-1829	433	17	method	method	NOUN
ap-1829	433	18	,	,	PUNCT
ap-1829	433	19	has	have	AUX
ap-1829	433	20	been	be	AUX
ap-1829	433	21	presented	present	VERB
ap-1829	433	22	and	and	CCONJ
ap-1829	433	23	tested	test	VERB
ap-1829	433	24	.	.	PUNCT
ap-1829	434	1	this	this	DET
ap-1829	434	2	method	method	NOUN
ap-1829	434	3	is	be	AUX
ap-1829	434	4	based	base	VERB
ap-1829	434	5	on	on	ADP
ap-1829	434	6	an	an	DET
ap-1829	434	7	automatic	automatic	ADJ
ap-1829	434	8	time	time	NOUN
ap-1829	434	9	step	step	NOUN
ap-1829	434	10	selection	selection	NOUN
ap-1829	434	11	.	.	PUNCT
ap-1829	435	1	the	the	DET
ap-1829	435	2	length	length	NOUN
ap-1829	435	3	of	of	ADP
ap-1829	435	4	the	the	DET
ap-1829	435	5	time	time	NOUN
ap-1829	435	6	step	step	NOUN
ap-1829	435	7	is	be	AUX
ap-1829	435	8	selected	select	VERB
ap-1829	435	9	in	in	ADP
ap-1829	435	10	such	such	DET
ap-1829	435	11	a	a	DET
ap-1829	435	12	way	way	NOUN
ap-1829	435	13	that	that	PRON
ap-1829	435	14	the	the	DET
ap-1829	435	15	error	error	NOUN
ap-1829	435	16	figure	figure	NOUN
ap-1829	435	17	10	10	NUM
ap-1829	435	18	.	.	PUNCT
ap-1829	436	1	wetting	wet	VERB
ap-1829	436	2	front	front	NOUN
ap-1829	436	3	has	have	AUX
ap-1829	436	4	reached	reach	VERB
ap-1829	436	5	the	the	DET
ap-1829	436	6	repository	repository	NOUN
ap-1829	436	7	shield	shield	NOUN
ap-1829	436	8	,	,	PUNCT
ap-1829	436	9	steep	steep	ADJ
ap-1829	436	10	gradients	gradient	NOUN
ap-1829	436	11	appears	appear	VERB
ap-1829	436	12	at	at	ADP
ap-1829	436	13	the	the	DET
ap-1829	436	14	wetting	wet	VERB
ap-1829	436	15	front	front	ADJ
ap-1829	436	16	/	/	SYM
ap-1829	436	17	barrier	barrier	NOUN
ap-1829	436	18	interface	interface	NOUN
ap-1829	436	19	.	.	PUNCT
ap-1829	437	1	of	of	ADP
ap-1829	437	2	the	the	DET
ap-1829	437	3	discrete	discrete	ADJ
ap-1829	437	4	approximation	approximation	NOUN
ap-1829	437	5	of	of	ADP
ap-1829	437	6	the	the	DET
ap-1829	437	7	time	time	NOUN
ap-1829	437	8	derivative	derivative	ADJ
ap-1829	437	9	term	term	NOUN
ap-1829	437	10	(	(	PUNCT
ap-1829	437	11	mass	mass	ADJ
ap-1829	437	12	term	term	NOUN
ap-1829	437	13	)	)	PUNCT
ap-1829	437	14	is	be	AUX
ap-1829	437	15	always	always	ADV
ap-1829	437	16	kept	keep	VERB
ap-1829	437	17	below	below	ADP
ap-1829	437	18	a	a	DET
ap-1829	437	19	certain	certain	ADJ
ap-1829	437	20	value	value	NOUN
ap-1829	437	21	.	.	PUNCT
ap-1829	438	1	a	a	DET
ap-1829	438	2	different	different	ADJ
ap-1829	438	3	problem	problem	NOUN
ap-1829	438	4	concerned	concern	VERB
ap-1829	438	5	the	the	DET
ap-1829	438	6	conditioning	conditioning	NOUN
ap-1829	438	7	of	of	ADP
ap-1829	438	8	the	the	DET
ap-1829	438	9	richards	richard	NOUN
ap-1829	438	10	equation	equation	NOUN
ap-1829	438	11	problem	problem	NOUN
ap-1829	438	12	.	.	PUNCT
ap-1829	439	1	it	it	PRON
ap-1829	439	2	is	be	AUX
ap-1829	439	3	well	well	ADV
ap-1829	439	4	known	know	VERB
ap-1829	439	5	that	that	SCONJ
ap-1829	439	6	finite	finite	PROPN
ap-1829	439	7	element	element	NOUN
ap-1829	439	8	approximation	approximation	NOUN
ap-1829	439	9	of	of	ADP
ap-1829	439	10	the	the	DET
ap-1829	439	11	richards	richard	NOUN
ap-1829	439	12	equation	equation	NOUN
ap-1829	439	13	forms	form	VERB
ap-1829	439	14	badly	badly	ADV
ap-1829	439	15	-	-	PUNCT
ap-1829	439	16	conditioned	condition	VERB
ap-1829	439	17	matrices	matrix	NOUN
ap-1829	439	18	.	.	PUNCT
ap-1829	440	1	a	a	DET
ap-1829	440	2	very	very	ADV
ap-1829	440	3	simple	simple	ADJ
ap-1829	440	4	and	and	CCONJ
ap-1829	440	5	efficient	efficient	ADJ
ap-1829	440	6	preconditioning	preconditioning	NOUN
ap-1829	440	7	method	method	NOUN
ap-1829	440	8	based	base	VERB
ap-1829	440	9	on	on	ADP
ap-1829	440	10	diagonal	diagonal	ADJ
ap-1829	440	11	scaling	scaling	NOUN
ap-1829	440	12	has	have	AUX
ap-1829	440	13	been	be	AUX
ap-1829	440	14	presented	present	VERB
ap-1829	440	15	.	.	PUNCT
ap-1829	441	1	then	then	ADV
ap-1829	441	2	the	the	DET
ap-1829	441	3	method	method	NOUN
ap-1829	441	4	of	of	ADP
ap-1829	441	5	preconditioning	preconditioning	NOUN
ap-1829	441	6	was	be	AUX
ap-1829	441	7	tested	test	VERB
ap-1829	441	8	on	on	ADP
ap-1829	441	9	a	a	DET
ap-1829	441	10	real	real	ADJ
ap-1829	441	11	problem	problem	NOUN
ap-1829	441	12	–	–	PUNCT
ap-1829	441	13	infiltration	infiltration	NOUN
ap-1829	441	14	into	into	ADP
ap-1829	441	15	a	a	DET
ap-1829	441	16	capillary	capillary	ADJ
ap-1829	441	17	barrier	barrier	NOUN
ap-1829	441	18	layer	layer	NOUN
ap-1829	441	19	that	that	PRON
ap-1829	441	20	was	be	AUX
ap-1829	441	21	used	use	VERB
ap-1829	441	22	as	as	ADP
ap-1829	441	23	a	a	DET
ap-1829	441	24	protective	protective	ADJ
ap-1829	441	25	shield	shield	NOUN
ap-1829	441	26	around	around	ADP
ap-1829	441	27	a	a	DET
ap-1829	441	28	waste	waste	NOUN
ap-1829	441	29	repository	repository	NOUN
ap-1829	441	30	.	.	PUNCT
ap-1829	442	1	the	the	DET
ap-1829	442	2	method	method	NOUN
ap-1829	442	3	presented	present	VERB
ap-1829	442	4	here	here	ADV
ap-1829	442	5	efficiently	efficiently	ADV
ap-1829	442	6	decreased	decrease	VERB
ap-1829	442	7	the	the	DET
ap-1829	442	8	condition	condition	NOUN
ap-1829	442	9	number	number	NOUN
ap-1829	442	10	of	of	ADP
ap-1829	442	11	the	the	DET
ap-1829	442	12	evaluated	evaluated	ADJ
ap-1829	442	13	problem	problem	NOUN
ap-1829	442	14	by	by	ADP
ap-1829	442	15	more	more	ADJ
ap-1829	442	16	than	than	ADP
ap-1829	442	17	13	13	NUM
ap-1829	442	18	orders	order	NOUN
ap-1829	442	19	of	of	ADP
ap-1829	442	20	magnitude	magnitude	NOUN
ap-1829	442	21	.	.	PUNCT
ap-1829	443	1	the	the	DET
ap-1829	443	2	best	good	ADJ
ap-1829	443	3	performance	performance	NOUN
ap-1829	443	4	was	be	AUX
ap-1829	443	5	observed	observe	VERB
ap-1829	443	6	for	for	ADP
ap-1829	443	7	the	the	DET
ap-1829	443	8	initial	initial	ADJ
ap-1829	443	9	time	time	NOUN
ap-1829	443	10	levels	level	NOUN
ap-1829	443	11	,	,	PUNCT
ap-1829	443	12	where	where	SCONJ
ap-1829	443	13	the	the	DET
ap-1829	443	14	condition	condition	NOUN
ap-1829	443	15	number	number	NOUN
ap-1829	443	16	of	of	ADP
ap-1829	443	17	the	the	DET
ap-1829	443	18	original	original	ADJ
ap-1829	443	19	matrix	matrix	NOUN
ap-1829	443	20	was	be	AUX
ap-1829	443	21	κ	κ	NOUN
ap-1829	443	22	=	=	SYM
ap-1829	443	23	1.43	1.43	NUM
ap-1829	443	24	·	·	SYM
ap-1829	443	25	1013	1013	NUM
ap-1829	443	26	,	,	PUNCT
ap-1829	443	27	while	while	SCONJ
ap-1829	443	28	after	after	ADP
ap-1829	443	29	preconditioning	precondition	VERB
ap-1829	443	30	κ	κ	X
ap-1829	443	31	=	=	SYM
ap-1829	443	32	1.00215	1.00215	NUM
ap-1829	443	33	,	,	PUNCT
ap-1829	443	34	and	and	CCONJ
ap-1829	443	35	thus	thus	ADV
ap-1829	443	36	the	the	DET
ap-1829	443	37	preconditioned	preconditioned	ADJ
ap-1829	443	38	matrix	matrix	NOUN
ap-1829	443	39	was	be	AUX
ap-1829	443	40	even	even	ADV
ap-1829	443	41	close	close	ADJ
ap-1829	443	42	to	to	ADP
ap-1829	443	43	an	an	DET
ap-1829	443	44	identity	identity	NOUN
ap-1829	443	45	problem	problem	NOUN
ap-1829	443	46	.	.	PUNCT
ap-1829	444	1	generally	generally	ADV
ap-1829	444	2	speaking	speak	VERB
ap-1829	444	3	,	,	PUNCT
ap-1829	444	4	all	all	DET
ap-1829	444	5	matrices	matrix	NOUN
ap-1829	444	6	that	that	PRON
ap-1829	444	7	appeared	appear	VERB
ap-1829	444	8	in	in	ADP
ap-1829	444	9	this	this	DET
ap-1829	444	10	simulation	simulation	NOUN
ap-1829	444	11	experiment	experiment	NOUN
ap-1829	444	12	had	have	VERB
ap-1829	444	13	a	a	DET
ap-1829	444	14	condition	condition	NOUN
ap-1829	444	15	number	number	NOUN
ap-1829	444	16	around	around	ADP
ap-1829	444	17	1013–1015	1013–1015	NUM
ap-1829	444	18	,	,	PUNCT
ap-1829	444	19	and	and	CCONJ
ap-1829	444	20	the	the	DET
ap-1829	444	21	proposed	propose	VERB
ap-1829	444	22	preconditioner	preconditioner	NOUN
ap-1829	444	23	decreased	decrease	VERB
ap-1829	444	24	the	the	DET
ap-1829	444	25	conditioning	conditioning	NOUN
ap-1829	444	26	to	to	ADP
ap-1829	444	27	values	value	NOUN
ap-1829	444	28	lower	low	ADJ
ap-1829	444	29	than	than	ADP
ap-1829	444	30	102–103	102–103	NUM
ap-1829	444	31	.	.	PUNCT
ap-1829	445	1	the	the	DET
ap-1829	445	2	efficiency	efficiency	NOUN
ap-1829	445	3	of	of	ADP
ap-1829	445	4	the	the	DET
ap-1829	445	5	proposed	propose	VERB
ap-1829	445	6	preconditioner	preconditioner	NOUN
ap-1829	445	7	is	be	AUX
ap-1829	445	8	highly	highly	ADV
ap-1829	445	9	dependent	dependent	ADJ
ap-1829	445	10	on	on	ADP
ap-1829	445	11	the	the	DET
ap-1829	445	12	selected	select	VERB
ap-1829	445	13	time	time	NOUN
ap-1829	445	14	step	step	NOUN
ap-1829	445	15	.	.	PUNCT
ap-1829	446	1	all	all	DET
ap-1829	446	2	simulated	simulate	VERB
ap-1829	446	3	cases	case	NOUN
ap-1829	446	4	demonstrate	demonstrate	VERB
ap-1829	446	5	great	great	ADJ
ap-1829	446	6	effectiveness	effectiveness	NOUN
ap-1829	446	7	of	of	ADP
ap-1829	446	8	the	the	DET
ap-1829	446	9	discussed	discuss	VERB
ap-1829	446	10	automated	automate	VERB
ap-1829	446	11	time	time	NOUN
ap-1829	446	12	step	step	NOUN
ap-1829	446	13	selection	selection	NOUN
ap-1829	446	14	method	method	NOUN
ap-1829	446	15	for	for	ADP
ap-1829	446	16	euler	euler	NOUN
ap-1829	446	17	time	time	NOUN
ap-1829	446	18	integration	integration	NOUN
ap-1829	446	19	,	,	PUNCT
ap-1829	446	20	and	and	CCONJ
ap-1829	446	21	for	for	ADP
ap-1829	446	22	the	the	DET
ap-1829	446	23	proposed	propose	VERB
ap-1829	446	24	matrix	matrix	NOUN
ap-1829	446	25	preconditioner	preconditioner	NOUN
ap-1829	446	26	.	.	PUNCT
ap-1829	447	1	generally	generally	ADV
ap-1829	447	2	speaking	speak	VERB
ap-1829	447	3	,	,	PUNCT
ap-1829	447	4	both	both	CCONJ
ap-1829	447	5	the	the	DET
ap-1829	447	6	design	design	NOUN
ap-1829	447	7	and	and	CCONJ
ap-1829	447	8	the	the	DET
ap-1829	447	9	implementation	implementation	NOUN
ap-1829	447	10	of	of	ADP
ap-1829	447	11	the	the	DET
ap-1829	447	12	preconditioner	preconditioner	NOUN
ap-1829	447	13	are	be	AUX
ap-1829	447	14	trivial	trivial	ADJ
ap-1829	447	15	,	,	PUNCT
ap-1829	447	16	and	and	CCONJ
ap-1829	447	17	it	it	PRON
ap-1829	447	18	is	be	AUX
ap-1829	447	19	therefore	therefore	ADV
ap-1829	447	20	a	a	DET
ap-1829	447	21	recommended	recommend	VERB
ap-1829	447	22	method	method	NOUN
ap-1829	447	23	for	for	ADP
ap-1829	447	24	conjugate	conjugate	ADJ
ap-1829	447	25	gradient	gradient	NOUN
ap-1829	447	26	based	base	VERB
ap-1829	447	27	finite	finite	ADJ
ap-1829	447	28	element	element	NOUN
ap-1829	447	29	solvers	solver	NOUN
ap-1829	447	30	of	of	ADP
ap-1829	447	31	transport	transport	NOUN
ap-1829	447	32	processes	process	NOUN
ap-1829	447	33	in	in	ADP
ap-1829	447	34	a	a	DET
ap-1829	447	35	porous	porous	ADJ
ap-1829	447	36	medium	medium	NOUN
ap-1829	447	37	.	.	PUNCT
ap-1829	448	1	acknowledgements	acknowledgement	NOUN
ap-1829	448	2	financial	financial	ADJ
ap-1829	448	3	support	support	NOUN
ap-1829	448	4	from	from	ADP
ap-1829	448	5	the	the	DET
ap-1829	448	6	czech	czech	PROPN
ap-1829	448	7	science	science	NOUN
ap-1829	448	8	foundation	foundation	PROPN
ap-1829	448	9	(	(	PUNCT
ap-1829	448	10	research	research	NOUN
ap-1829	448	11	project	project	NOUN
ap-1829	448	12	gacr	gacr	NOUN
ap-1829	448	13	13	13	NUM
ap-1829	448	14	-	-	SYM
ap-1829	448	15	11977p	11977p	NUM
ap-1829	448	16	)	)	PUNCT
ap-1829	448	17	and	and	CCONJ
ap-1829	448	18	from	from	ADP
ap-1829	448	19	the	the	DET
ap-1829	448	20	czech	czech	PROPN
ap-1829	448	21	ministry	ministry	PROPN
ap-1829	448	22	of	of	ADP
ap-1829	448	23	education	education	PROPN
ap-1829	448	24	,	,	PUNCT
ap-1829	448	25	youth	youth	NOUN
ap-1829	448	26	and	and	CCONJ
ap-1829	448	27	sports	sport	NOUN
ap-1829	448	28	(	(	PUNCT
ap-1829	448	29	project	project	NOUN
ap-1829	448	30	cost	cost	NOUN
ap-1829	448	31	cz	cz	NOUN
ap-1829	448	32	ld13068	ld13068	NOUN
ap-1829	448	33	)	)	PUNCT
ap-1829	448	34	is	be	AUX
ap-1829	448	35	gratefully	gratefully	ADV
ap-1829	448	36	acknowledged	acknowledge	VERB
ap-1829	448	37	.	.	PUNCT
ap-1829	449	1	references	reference	NOUN
ap-1829	449	2	[	[	X
ap-1829	449	3	1	1	NUM
ap-1829	449	4	]	]	PUNCT
ap-1829	449	5	m.	m.	NOUN
ap-1829	449	6	kuráž	kuráž	PROPN
ap-1829	449	7	,	,	PUNCT
ap-1829	449	8	p.	p.	PROPN
ap-1829	449	9	mayer	mayer	PROPN
ap-1829	449	10	:	:	PUNCT
ap-1829	449	11	drutes	drute	NOUN
ap-1829	449	12	–	–	PUNCT
ap-1829	449	13	finite	finite	PROPN
ap-1829	449	14	element	element	NOUN
ap-1829	449	15	solver	solver	VERB
ap-1829	449	16	for	for	ADP
ap-1829	449	17	nonlinear	nonlinear	ADJ
ap-1829	449	18	coupled	couple	VERB
ap-1829	449	19	convection	convection	NOUN
ap-1829	449	20	-	-	PUNCT
ap-1829	449	21	diffusion	diffusion	NOUN
ap-1829	449	22	-	-	PUNCT
ap-1829	449	23	reaction	reaction	NOUN
ap-1829	449	24	357	357	NUM
ap-1829	449	25	michal	michal	PROPN
ap-1829	449	26	kuráž	kuráž	PROPN
ap-1829	449	27	,	,	PUNCT
ap-1829	449	28	petr	petr	PROPN
ap-1829	449	29	mayer	mayer	PROPN
ap-1829	449	30	acta	acta	PROPN
ap-1829	449	31	polytechnica	polytechnica	PROPN
ap-1829	449	32	time	time	NOUN
ap-1829	450	1	no	no	DET
ap-1829	450	2	preconditioning	precondition	VERB
ap-1829	450	3	preconditioned	precondition	VERB
ap-1829	450	4	[	[	X
ap-1829	450	5	days	days	X
ap-1829	450	6	]	]	X
ap-1829	450	7	λmax	λmax	NOUN
ap-1829	450	8	λmin	λmin	NOUN
ap-1829	450	9	κ	κ	PROPN
ap-1829	450	10	λmax	λmax	PROPN
ap-1829	450	11	λmin	λmin	VERB
ap-1829	450	12	κ	κ	PROPN
ap-1829	450	13	1.0	1.0	NUM
ap-1829	450	14	2.547	2.547	NUM
ap-1829	450	15	·	·	PUNCT
ap-1829	450	16	1013	1013	NUM
ap-1829	450	17	1.7823	1.7823	NUM
ap-1829	450	18	1.43	1.43	NUM
ap-1829	450	19	·	·	PUNCT
ap-1829	450	20	1013	1013	NUM
ap-1829	450	21	1.0011	1.0011	NUM
ap-1829	450	22	0.9989	0.9989	NUM
ap-1829	450	23	1.00215	1.00215	NUM
ap-1829	450	24	15.0	15.0	NUM
ap-1829	450	25	9.286	9.286	NUM
ap-1829	450	26	·	·	PUNCT
ap-1829	450	27	105	105	NUM
ap-1829	450	28	2.499	2.499	NUM
ap-1829	450	29	·	·	PUNCT
ap-1829	450	30	10−9	10−9	NUM
ap-1829	450	31	3.72	3.72	NUM
ap-1829	450	32	·	·	SYM
ap-1829	450	33	1014	1014	NUM
ap-1829	450	34	12.1142	12.1142	NUM
ap-1829	450	35	0.03508	0.03508	NUM
ap-1829	450	36	345.335	345.335	NUM
ap-1829	450	37	120.0	120.0	NUM
ap-1829	450	38	9.112	9.112	NUM
ap-1829	450	39	·	·	PUNCT
ap-1829	450	40	105	105	NUM
ap-1829	450	41	1.391	1.391	NUM
ap-1829	450	42	·	·	SYM
ap-1829	450	43	10−9	10−9	NUM
ap-1829	450	44	6.55	6.55	NUM
ap-1829	450	45	·	·	PUNCT
ap-1829	450	46	1014	1014	NUM
ap-1829	450	47	12.7672	12.7672	NUM
ap-1829	450	48	0.02345	0.02345	NUM
ap-1829	450	49	544.338	544.338	NUM
ap-1829	450	50	table	table	NOUN
ap-1829	450	51	4	4	NUM
ap-1829	450	52	.	.	PUNCT
ap-1829	451	1	conditioning	conditioning	NOUN
ap-1829	451	2	improvements	improvement	NOUN
ap-1829	451	3	before	before	ADV
ap-1829	451	4	and	and	CCONJ
ap-1829	451	5	after	after	ADP
ap-1829	451	6	right	right	ADJ
ap-1829	451	7	hand	hand	NOUN
ap-1829	451	8	side	side	NOUN
ap-1829	451	9	diagonal	diagonal	ADJ
ap-1829	451	10	scaling	scaling	NOUN
ap-1829	451	11	.	.	PUNCT
ap-1829	452	1	problems	problem	NOUN
ap-1829	452	2	,	,	PUNCT
ap-1829	452	3	http://www.freecode.com/projects/drutes	http://www.freecode.com/projects/drutes	PROPN
ap-1829	452	4	,	,	PUNCT
ap-1829	452	5	www	www	X
ap-1829	452	6	[	[	X
ap-1829	452	7	2	2	NUM
ap-1829	452	8	]	]	X
ap-1829	452	9	l.a	l.a	PROPN
ap-1829	452	10	.	.	PROPN
ap-1829	452	11	richards	richards	PROPN
ap-1829	452	12	:	:	PUNCT
ap-1829	452	13	capillary	capillary	ADJ
ap-1829	452	14	conduction	conduction	NOUN
ap-1829	452	15	of	of	ADP
ap-1829	452	16	liquids	liquid	NOUN
ap-1829	452	17	through	through	ADP
ap-1829	452	18	porous	porous	ADJ
ap-1829	452	19	media	medium	NOUN
ap-1829	452	20	,	,	PUNCT
ap-1829	452	21	physics	physics	NOUN
ap-1829	452	22	i	i	PROPN
ap-1829	452	23	,	,	PUNCT
ap-1829	452	24	1	1	NUM
ap-1829	452	25	,	,	PUNCT
ap-1829	452	26	11	11	NUM
ap-1829	452	27	,	,	PUNCT
ap-1829	452	28	1931	1931	NUM
ap-1829	452	29	,	,	PUNCT
ap-1829	452	30	318	318	NUM
ap-1829	452	31	-	-	SYM
ap-1829	452	32	333	333	NUM
ap-1829	452	33	[	[	X
ap-1829	452	34	3	3	NUM
ap-1829	452	35	]	]	PUNCT
ap-1829	452	36	s.	s.	PROPN
ap-1829	452	37	p.	p.	PROPN
ap-1829	452	38	neuman	neuman	NOUN
ap-1829	452	39	,	,	PUNCT
ap-1829	452	40	p.	p.	NOUN
ap-1829	452	41	a.	a.	NOUN
ap-1829	452	42	witherspoon	witherspoon	PROPN
ap-1829	452	43	:	:	PUNCT
ap-1829	452	44	finite	finite	PROPN
ap-1829	452	45	element	element	NOUN
ap-1829	452	46	method	method	NOUN
ap-1829	452	47	analyzing	analyze	VERB
ap-1829	452	48	steady	steady	ADJ
ap-1829	452	49	seepage	seepage	NOUN
ap-1829	452	50	with	with	ADP
ap-1829	452	51	a	a	DET
ap-1829	452	52	free	free	ADJ
ap-1829	452	53	surface	surface	NOUN
ap-1829	452	54	,	,	PUNCT
ap-1829	452	55	water	water	NOUN
ap-1829	452	56	resources	resource	NOUN
ap-1829	452	57	research	research	NOUN
ap-1829	452	58	,	,	PUNCT
ap-1829	452	59	6	6	NUM
ap-1829	452	60	,	,	PUNCT
ap-1829	452	61	3	3	NUM
ap-1829	452	62	,	,	PUNCT
ap-1829	452	63	1970	1970	NUM
ap-1829	452	64	,	,	PUNCT
ap-1829	452	65	889	889	NUM
ap-1829	452	66	-	-	SYM
ap-1829	452	67	897	897	NUM
ap-1829	453	1	[	[	X
ap-1829	453	2	4	4	NUM
ap-1829	453	3	]	]	PUNCT
ap-1829	453	4	h.	h.	PROPN
ap-1829	453	5	w.	w.	PROPN
ap-1829	453	6	alt	alt	PROPN
ap-1829	453	7	,	,	PUNCT
ap-1829	453	8	s.	s.	PROPN
ap-1829	453	9	luckhaus	luckhaus	PROPN
ap-1829	453	10	:	:	PUNCT
ap-1829	453	11	quasilinear	quasilinear	VERB
ap-1829	453	12	elliptic	elliptic	ADJ
ap-1829	453	13	-	-	PUNCT
ap-1829	453	14	parabolic	parabolic	NOUN
ap-1829	453	15	differential	differential	ADJ
ap-1829	453	16	equations	equation	NOUN
ap-1829	453	17	,	,	PUNCT
ap-1829	453	18	mathematische	mathematische	NOUN
ap-1829	453	19	zeitschrift	zeitschrift	NOUN
ap-1829	453	20	,	,	PUNCT
ap-1829	453	21	183	183	NUM
ap-1829	453	22	,	,	PUNCT
ap-1829	453	23	3	3	NUM
ap-1829	453	24	,	,	PUNCT
ap-1829	453	25	1983	1983	NUM
ap-1829	453	26	,	,	PUNCT
ap-1829	453	27	311	311	NUM
ap-1829	453	28	-	-	SYM
ap-1829	453	29	341	341	NUM
ap-1829	453	30	[	[	SYM
ap-1829	453	31	5	5	NUM
ap-1829	453	32	]	]	PUNCT
ap-1829	453	33	m.	m.	NOUN
ap-1829	453	34	a.	a.	PROPN
ap-1829	453	35	celia	celia	PROPN
ap-1829	453	36	,	,	PUNCT
ap-1829	453	37	e.	e.	PROPN
ap-1829	453	38	t.	t.	PROPN
ap-1829	453	39	bouloutas	bouloutas	PROPN
ap-1829	453	40	,	,	PUNCT
ap-1829	453	41	r.	r.	PROPN
ap-1829	453	42	l.	l.	PROPN
ap-1829	453	43	zarba	zarba	PROPN
ap-1829	453	44	:	:	PUNCT
ap-1829	453	45	a	a	DET
ap-1829	453	46	general	general	ADJ
ap-1829	453	47	mass	mass	ADJ
ap-1829	453	48	-	-	PUNCT
ap-1829	453	49	conservative	conservative	ADJ
ap-1829	453	50	numerical	numerical	ADJ
ap-1829	453	51	solution	solution	NOUN
ap-1829	453	52	for	for	ADP
ap-1829	453	53	the	the	DET
ap-1829	453	54	unsaturated	unsaturated	ADJ
ap-1829	453	55	flow	flow	NOUN
ap-1829	453	56	equation	equation	NOUN
ap-1829	453	57	,	,	PUNCT
ap-1829	453	58	water	water	NOUN
ap-1829	453	59	resources	resource	NOUN
ap-1829	453	60	research	research	NOUN
ap-1829	453	61	,	,	PUNCT
ap-1829	453	62	26	26	NUM
ap-1829	453	63	,	,	PUNCT
ap-1829	453	64	7	7	NUM
ap-1829	453	65	,	,	PUNCT
ap-1829	453	66	1990	1990	NUM
ap-1829	453	67	,	,	PUNCT
ap-1829	453	68	1483	1483	NUM
ap-1829	453	69	-	-	SYM
ap-1829	453	70	1496	1496	NUM
ap-1829	453	71	[	[	X
ap-1829	453	72	6	6	NUM
ap-1829	453	73	]	]	PUNCT
ap-1829	453	74	j.	j.	PROPN
ap-1829	453	75	kačur	kačur	PROPN
ap-1829	453	76	:	:	PUNCT
ap-1829	453	77	solution	solution	NOUN
ap-1829	453	78	of	of	ADP
ap-1829	453	79	nonlinear	nonlinear	ADJ
ap-1829	453	80	and	and	CCONJ
ap-1829	453	81	degenerate	degenerate	ADJ
ap-1829	453	82	convection	convection	NOUN
ap-1829	453	83	-	-	PUNCT
ap-1829	453	84	diffusion	diffusion	NOUN
ap-1829	453	85	problems	problem	NOUN
ap-1829	453	86	,	,	PUNCT
ap-1829	453	87	nonlinear	nonlinear	ADJ
ap-1829	453	88	analysis	analysis	NOUN
ap-1829	453	89	,	,	PUNCT
ap-1829	453	90	47	47	NUM
ap-1829	453	91	,	,	PUNCT
ap-1829	453	92	1	1	NUM
ap-1829	453	93	,	,	PUNCT
ap-1829	453	94	2001	2001	NUM
ap-1829	453	95	,	,	PUNCT
ap-1829	453	96	123	123	NUM
ap-1829	453	97	-	-	SYM
ap-1829	453	98	134	134	NUM
ap-1829	454	1	[	[	X
ap-1829	454	2	7	7	NUM
ap-1829	454	3	]	]	X
ap-1829	454	4	c.e	c.e	PROPN
ap-1829	454	5	.	.	PROPN
ap-1829	454	6	kees	kees	PROPN
ap-1829	454	7	,	,	PUNCT
ap-1829	454	8	m.w	m.w	PROPN
ap-1829	454	9	.	.	PROPN
ap-1829	454	10	farthing	farthing	PROPN
ap-1829	454	11	,	,	PUNCT
ap-1829	454	12	c.n	c.n	PROPN
ap-1829	454	13	.	.	PROPN
ap-1829	454	14	dawson	dawson	PROPN
ap-1829	454	15	:	:	PUNCT
ap-1829	454	16	locally	locally	ADV
ap-1829	454	17	conservative	conservative	ADJ
ap-1829	454	18	,	,	PUNCT
ap-1829	454	19	stabilized	stabilize	VERB
ap-1829	454	20	finite	finite	ADJ
ap-1829	454	21	element	element	NOUN
ap-1829	454	22	methods	method	NOUN
ap-1829	454	23	for	for	ADP
ap-1829	454	24	variably	variably	ADV
ap-1829	454	25	saturated	saturate	VERB
ap-1829	454	26	flow	flow	NOUN
ap-1829	454	27	,	,	PUNCT
ap-1829	454	28	comput	comput	NOUN
ap-1829	454	29	.	.	PUNCT
ap-1829	455	1	methods	method	NOUN
ap-1829	455	2	appl	appl	PROPN
ap-1829	455	3	.	.	PROPN
ap-1829	455	4	mech	mech	PROPN
ap-1829	455	5	.	.	PUNCT
ap-1829	456	1	engrg	engrg	PROPN
ap-1829	456	2	.	.	PROPN
ap-1829	456	3	,	,	PUNCT
ap-1829	456	4	197	197	NUM
ap-1829	456	5	,	,	PUNCT
ap-1829	456	6	51	51	NUM
ap-1829	456	7	,	,	PUNCT
ap-1829	456	8	4610–4625	4610–4625	NUM
ap-1829	456	9	,	,	PUNCT
ap-1829	456	10	2008	2008	NUM
ap-1829	457	1	[	[	X
ap-1829	457	2	8	8	NUM
ap-1829	457	3	]	]	X
ap-1829	457	4	p.	p.	NOUN
ap-1829	457	5	šolín	šolín	PROPN
ap-1829	457	6	,	,	PUNCT
ap-1829	457	7	m.	m.	NOUN
ap-1829	457	8	kuráž	kuráž	PROPN
ap-1829	457	9	:	:	PUNCT
ap-1829	457	10	solving	solve	VERB
ap-1829	457	11	the	the	DET
ap-1829	457	12	nonstationary	nonstationary	ADJ
ap-1829	457	13	richards	richard	NOUN
ap-1829	457	14	equation	equation	NOUN
ap-1829	457	15	with	with	ADP
ap-1829	457	16	adaptive	adaptive	ADJ
ap-1829	457	17	hp	hp	NOUN
ap-1829	457	18	-	-	PUNCT
ap-1829	457	19	fem	fem	NOUN
ap-1829	457	20	,	,	PUNCT
ap-1829	457	21	advances	advance	NOUN
ap-1829	457	22	in	in	ADP
ap-1829	457	23	water	water	NOUN
ap-1829	457	24	resources	resource	NOUN
ap-1829	457	25	,	,	PUNCT
ap-1829	457	26	34	34	NUM
ap-1829	457	27	,	,	PUNCT
ap-1829	457	28	9	9	NUM
ap-1829	457	29	,	,	PUNCT
ap-1829	457	30	2011	2011	NUM
ap-1829	457	31	,	,	PUNCT
ap-1829	457	32	1062	1062	NUM
ap-1829	457	33	-	-	SYM
ap-1829	457	34	1081	1081	NUM
ap-1829	457	35	[	[	X
ap-1829	457	36	9	9	NUM
ap-1829	457	37	]	]	PUNCT
ap-1829	457	38	m.	m.	NOUN
ap-1829	457	39	kuráž	kuráž	PROPN
ap-1829	457	40	,	,	PUNCT
ap-1829	457	41	p.	p.	PROPN
ap-1829	457	42	mayer	mayer	PROPN
ap-1829	457	43	,	,	PUNCT
ap-1829	457	44	m	m	PROPN
ap-1829	457	45	lepš	lepš	PROPN
ap-1829	457	46	,	,	PUNCT
ap-1829	457	47	d.	d.	PROPN
ap-1829	457	48	trpkošová	trpkošová	PROPN
ap-1829	457	49	:	:	PUNCT
ap-1829	457	50	an	an	DET
ap-1829	457	51	adaptive	adaptive	ADJ
ap-1829	457	52	time	time	NOUN
ap-1829	457	53	discretization	discretization	NOUN
ap-1829	457	54	of	of	ADP
ap-1829	457	55	the	the	DET
ap-1829	457	56	classical	classical	NOUN
ap-1829	457	57	and	and	CCONJ
ap-1829	457	58	the	the	DET
ap-1829	457	59	dual	dual	ADJ
ap-1829	457	60	porosity	porosity	NOUN
ap-1829	457	61	model	model	NOUN
ap-1829	457	62	of	of	ADP
ap-1829	457	63	richards	richard	NOUN
ap-1829	457	64	’	'	PUNCT
ap-1829	457	65	equation	equation	NOUN
ap-1829	457	66	,	,	PUNCT
ap-1829	457	67	journal	journal	NOUN
ap-1829	457	68	of	of	ADP
ap-1829	457	69	computational	computational	ADJ
ap-1829	457	70	and	and	CCONJ
ap-1829	457	71	applied	applied	ADJ
ap-1829	457	72	mathematics	mathematic	NOUN
ap-1829	457	73	,	,	PUNCT
ap-1829	457	74	233	233	NUM
ap-1829	457	75	,	,	PUNCT
ap-1829	457	76	12	12	NUM
ap-1829	457	77	,	,	PUNCT
ap-1829	457	78	2010	2010	NUM
ap-1829	457	79	,	,	PUNCT
ap-1829	457	80	3167	3167	NUM
ap-1829	457	81	-	-	SYM
ap-1829	457	82	3177	3177	NUM
ap-1829	457	83	[	[	SYM
ap-1829	457	84	10	10	NUM
ap-1829	457	85	]	]	PUNCT
ap-1829	457	86	m.	m.	NOUN
ap-1829	457	87	kuráž	kuráž	PROPN
ap-1829	457	88	,	,	PUNCT
ap-1829	457	89	p.	p.	PROPN
ap-1829	457	90	mayer	mayer	PROPN
ap-1829	457	91	,	,	PUNCT
ap-1829	457	92	v.	v.	PROPN
ap-1829	457	93	havlíček	havlíček	PROPN
ap-1829	457	94	,	,	PUNCT
ap-1829	457	95	p.	p.	PROPN
ap-1829	457	96	pech	pech	PROPN
ap-1829	457	97	,	,	PUNCT
ap-1829	457	98	j.	j.	PROPN
ap-1829	457	99	pavlásek	pavlásek	PROPN
ap-1829	457	100	:	:	PUNCT
ap-1829	457	101	dual	dual	ADJ
ap-1829	457	102	permeability	permeability	NOUN
ap-1829	457	103	variably	variably	ADV
ap-1829	457	104	saturated	saturate	VERB
ap-1829	457	105	flow	flow	NOUN
ap-1829	457	106	and	and	CCONJ
ap-1829	457	107	contaminant	contaminant	NOUN
ap-1829	457	108	transport	transport	NOUN
ap-1829	457	109	modeling	modeling	NOUN
ap-1829	457	110	of	of	ADP
ap-1829	457	111	a	a	DET
ap-1829	457	112	nuclear	nuclear	ADJ
ap-1829	457	113	waste	waste	NOUN
ap-1829	457	114	repository	repository	NOUN
ap-1829	457	115	with	with	ADP
ap-1829	457	116	capillary	capillary	ADJ
ap-1829	457	117	barrier	barrier	NOUN
ap-1829	457	118	protection	protection	NOUN
ap-1829	457	119	,	,	PUNCT
ap-1829	457	120	applied	apply	VERB
ap-1829	457	121	mathematics	mathematic	NOUN
ap-1829	457	122	and	and	CCONJ
ap-1829	457	123	computation	computation	NOUN
ap-1829	457	124	,	,	PUNCT
ap-1829	457	125	219	219	NUM
ap-1829	457	126	,	,	PUNCT
ap-1829	457	127	13	13	NUM
ap-1829	457	128	,	,	PUNCT
ap-1829	457	129	2013	2013	NUM
ap-1829	457	130	,	,	PUNCT
ap-1829	457	131	7127	7127	NUM
ap-1829	457	132	-	-	SYM
ap-1829	457	133	7138	7138	NUM
ap-1829	458	1	[	[	X
ap-1829	458	2	11	11	NUM
ap-1829	458	3	]	]	X
ap-1829	458	4	h.	h.	PROPN
ap-1829	458	5	h.	h.	PROPN
ap-1829	458	6	gerke	gerke	PROPN
ap-1829	458	7	,	,	PUNCT
ap-1829	458	8	m.	m.	NOUN
ap-1829	458	9	t.	t.	PROPN
ap-1829	458	10	h.	h.	PROPN
ap-1829	458	11	van	van	PROPN
ap-1829	458	12	genuchten	genuchten	NOUN
ap-1829	458	13	:	:	PUNCT
ap-1829	458	14	a	a	DET
ap-1829	458	15	dual	dual	ADJ
ap-1829	458	16	-	-	PUNCT
ap-1829	458	17	porosity	porosity	NOUN
ap-1829	458	18	model	model	NOUN
ap-1829	458	19	for	for	ADP
ap-1829	458	20	simulating	simulate	VERB
ap-1829	458	21	the	the	DET
ap-1829	458	22	preferential	preferential	ADJ
ap-1829	458	23	movement	movement	NOUN
ap-1829	458	24	of	of	ADP
ap-1829	458	25	water	water	NOUN
ap-1829	458	26	and	and	CCONJ
ap-1829	458	27	solutes	solute	NOUN
ap-1829	458	28	in	in	ADP
ap-1829	458	29	structured	structured	ADJ
ap-1829	458	30	porous	porous	ADJ
ap-1829	458	31	media	medium	NOUN
ap-1829	458	32	,	,	PUNCT
ap-1829	458	33	water	water	NOUN
ap-1829	458	34	resources	resource	NOUN
ap-1829	458	35	research	research	NOUN
ap-1829	458	36	,	,	PUNCT
ap-1829	458	37	29	29	NUM
ap-1829	458	38	,	,	PUNCT
ap-1829	458	39	2	2	NUM
ap-1829	458	40	,	,	PUNCT
ap-1829	458	41	1993	1993	NUM
ap-1829	458	42	,	,	PUNCT
ap-1829	458	43	305	305	NUM
ap-1829	458	44	-	-	SYM
ap-1829	458	45	319	319	NUM
ap-1829	459	1	[	[	X
ap-1829	459	2	12	12	NUM
ap-1829	459	3	]	]	PUNCT
ap-1829	459	4	m.	m.	NOUN
ap-1829	459	5	t.	t.	PROPN
ap-1829	459	6	h.	h.	PROPN
ap-1829	459	7	van	van	PROPN
ap-1829	459	8	genuchten	genuchten	NOUN
ap-1829	459	9	:	:	PUNCT
ap-1829	459	10	a	a	DET
ap-1829	459	11	closed	close	VERB
ap-1829	459	12	-	-	PUNCT
ap-1829	459	13	form	form	NOUN
ap-1829	459	14	equation	equation	NOUN
ap-1829	459	15	for	for	ADP
ap-1829	459	16	predicting	predict	VERB
ap-1829	459	17	the	the	DET
ap-1829	459	18	hydraulic	hydraulic	ADJ
ap-1829	459	19	conductivity	conductivity	NOUN
ap-1829	459	20	of	of	ADP
ap-1829	459	21	unsaturated	unsaturated	ADJ
ap-1829	459	22	soils	soil	NOUN
ap-1829	459	23	,	,	PUNCT
ap-1829	459	24	journal	journal	NOUN
ap-1829	459	25	of	of	ADP
ap-1829	459	26	soil	soil	NOUN
ap-1829	459	27	science	science	NOUN
ap-1829	459	28	,	,	PUNCT
ap-1829	459	29	44	44	NUM
ap-1829	459	30	,	,	PUNCT
ap-1829	459	31	5	5	NUM
ap-1829	459	32	,	,	PUNCT
ap-1829	459	33	1980	1980	NUM
ap-1829	459	34	,	,	PUNCT
ap-1829	459	35	892	892	NUM
ap-1829	459	36	-	-	SYM
ap-1829	459	37	898	898	NUM
ap-1829	460	1	[	[	X
ap-1829	460	2	13	13	NUM
ap-1829	460	3	]	]	X
ap-1829	460	4	y.	y.	PROPN
ap-1829	460	5	mualem	mualem	PROPN
ap-1829	460	6	:	:	PUNCT
ap-1829	460	7	a	a	DET
ap-1829	460	8	new	new	ADJ
ap-1829	460	9	model	model	NOUN
ap-1829	460	10	for	for	ADP
ap-1829	460	11	predicting	predict	VERB
ap-1829	460	12	the	the	DET
ap-1829	460	13	hydraulic	hydraulic	ADJ
ap-1829	460	14	conductivity	conductivity	NOUN
ap-1829	460	15	of	of	ADP
ap-1829	460	16	unsaturated	unsaturated	ADJ
ap-1829	460	17	porous	porous	ADJ
ap-1829	460	18	media	medium	NOUN
ap-1829	460	19	,	,	PUNCT
ap-1829	460	20	water	water	NOUN
ap-1829	460	21	resources	resource	NOUN
ap-1829	460	22	research	research	NOUN
ap-1829	460	23	,	,	PUNCT
ap-1829	460	24	12	12	NUM
ap-1829	460	25	,	,	PUNCT
ap-1829	460	26	3	3	NUM
ap-1829	460	27	,	,	PUNCT
ap-1829	460	28	1976	1976	NUM
ap-1829	460	29	,	,	PUNCT
ap-1829	460	30	513	513	NUM
ap-1829	460	31	-	-	SYM
ap-1829	460	32	522	522	NUM
ap-1829	460	33	[	[	X
ap-1829	460	34	14	14	NUM
ap-1829	460	35	]	]	X
ap-1829	460	36	d.	d.	PROPN
ap-1829	460	37	kavetski	kavetski	PROPN
ap-1829	460	38	,	,	PUNCT
ap-1829	460	39	p.	p.	NOUN
ap-1829	460	40	binning	binning	NOUN
ap-1829	460	41	,	,	PUNCT
ap-1829	460	42	s.w	s.w	PROPN
ap-1829	460	43	.	.	PROPN
ap-1829	460	44	sloan	sloan	PROPN
ap-1829	460	45	:	:	PUNCT
ap-1829	461	1	adaptive	adaptive	ADJ
ap-1829	461	2	time	time	NOUN
ap-1829	461	3	stepping	step	VERB
ap-1829	461	4	and	and	CCONJ
ap-1829	461	5	error	error	NOUN
ap-1829	461	6	control	control	NOUN
ap-1829	461	7	in	in	ADP
ap-1829	461	8	a	a	DET
ap-1829	461	9	mass	mass	ADJ
ap-1829	461	10	conservative	conservative	ADJ
ap-1829	461	11	numerical	numerical	ADJ
ap-1829	461	12	solution	solution	NOUN
ap-1829	461	13	of	of	ADP
ap-1829	461	14	the	the	DET
ap-1829	461	15	mixedform	mixedform	NOUN
ap-1829	461	16	of	of	ADP
ap-1829	461	17	richards	richard	NOUN
ap-1829	461	18	’	'	PUNCT
ap-1829	461	19	equation	equation	NOUN
ap-1829	461	20	,	,	PUNCT
ap-1829	461	21	advances	advance	NOUN
ap-1829	461	22	in	in	ADP
ap-1829	461	23	water	water	NOUN
ap-1829	461	24	resources	resource	NOUN
ap-1829	461	25	.	.	PUNCT
ap-1829	462	1	24	24	NUM
ap-1829	462	2	,	,	PUNCT
ap-1829	462	3	2001	2001	NUM
ap-1829	462	4	,	,	PUNCT
ap-1829	462	5	595	595	NUM
ap-1829	462	6	-	-	SYM
ap-1829	462	7	605	605	NUM
ap-1829	463	1	[	[	SYM
ap-1829	463	2	15	15	NUM
ap-1829	463	3	]	]	X
ap-1829	463	4	m.d	m.d	PROPN
ap-1829	463	5	.	.	PROPN
ap-1829	463	6	tocci	tocci	PROPN
ap-1829	463	7	,	,	PUNCT
ap-1829	463	8	c.	c.	PROPN
ap-1829	463	9	t.	t.	PROPN
ap-1829	463	10	kelley	kelley	PROPN
ap-1829	463	11	,	,	PUNCT
ap-1829	463	12	c.	c.	PROPN
ap-1829	463	13	t.	t.	PROPN
ap-1829	463	14	miller	miller	PROPN
ap-1829	463	15	:	:	PUNCT
ap-1829	463	16	accurate	accurate	ADJ
ap-1829	463	17	and	and	CCONJ
ap-1829	463	18	economical	economical	ADJ
ap-1829	463	19	solution	solution	NOUN
ap-1829	463	20	of	of	ADP
ap-1829	463	21	the	the	DET
ap-1829	463	22	pressure	pressure	NOUN
ap-1829	463	23	head	head	NOUN
ap-1829	463	24	form	form	NOUN
ap-1829	463	25	of	of	ADP
ap-1829	463	26	the	the	DET
ap-1829	463	27	richards	richard	NOUN
ap-1829	463	28	equation	equation	NOUN
ap-1829	463	29	by	by	ADP
ap-1829	463	30	the	the	DET
ap-1829	463	31	method	method	NOUN
ap-1829	463	32	of	of	ADP
ap-1829	463	33	lines	line	NOUN
ap-1829	463	34	,	,	PUNCT
ap-1829	463	35	advances	advance	NOUN
ap-1829	463	36	in	in	ADP
ap-1829	463	37	water	water	NOUN
ap-1829	463	38	resources	resource	NOUN
ap-1829	463	39	,	,	PUNCT
ap-1829	463	40	20	20	NUM
ap-1829	463	41	,	,	PUNCT
ap-1829	463	42	1997	1997	NUM
ap-1829	463	43	,	,	PUNCT
ap-1829	463	44	1	1	NUM
ap-1829	463	45	-	-	SYM
ap-1829	463	46	14	14	NUM
ap-1829	464	1	[	[	X
ap-1829	464	2	16	16	NUM
ap-1829	464	3	]	]	X
ap-1829	464	4	c.	c.	PROPN
ap-1829	464	5	t.	t.	PROPN
ap-1829	464	6	miller	miller	PROPN
ap-1829	464	7	,	,	PUNCT
ap-1829	464	8	c.	c.	PROPN
ap-1829	464	9	abhishek	abhishek	PROPN
ap-1829	464	10	,	,	PUNCT
ap-1829	464	11	m.	m.	PROPN
ap-1829	464	12	w.	w.	PROPN
ap-1829	464	13	farthing	farthing	PROPN
ap-1829	464	14	:	:	PUNCT
ap-1829	464	15	a	a	DET
ap-1829	464	16	spatially	spatially	ADV
ap-1829	464	17	and	and	CCONJ
ap-1829	464	18	temporally	temporally	ADV
ap-1829	464	19	adaptive	adaptive	ADJ
ap-1829	464	20	solution	solution	NOUN
ap-1829	464	21	of	of	ADP
ap-1829	464	22	richards	richard	NOUN
ap-1829	464	23	’	'	PUNCT
ap-1829	464	24	equation	equation	NOUN
ap-1829	464	25	,	,	PUNCT
ap-1829	464	26	advances	advance	NOUN
ap-1829	464	27	in	in	ADP
ap-1829	464	28	water	water	NOUN
ap-1829	464	29	resources	resource	NOUN
ap-1829	464	30	,	,	PUNCT
ap-1829	464	31	29	29	NUM
ap-1829	464	32	,	,	PUNCT
ap-1829	464	33	2006	2006	NUM
ap-1829	464	34	,	,	PUNCT
ap-1829	464	35	525	525	NUM
ap-1829	464	36	-	-	SYM
ap-1829	464	37	545	545	NUM
ap-1829	464	38	[	[	X
ap-1829	464	39	17	17	NUM
ap-1829	464	40	]	]	X
ap-1829	464	41	w.	w.	PROPN
ap-1829	464	42	r.	r.	PROPN
ap-1829	464	43	gardner	gardner	PROPN
ap-1829	464	44	:	:	PUNCT
ap-1829	464	45	some	some	DET
ap-1829	464	46	steady	steady	ADJ
ap-1829	464	47	state	state	NOUN
ap-1829	464	48	solutions	solution	NOUN
ap-1829	464	49	of	of	ADP
ap-1829	464	50	the	the	DET
ap-1829	464	51	unsaturated	unsaturated	ADJ
ap-1829	464	52	moisture	moisture	NOUN
ap-1829	464	53	flow	flow	NOUN
ap-1829	464	54	equation	equation	NOUN
ap-1829	464	55	with	with	ADP
ap-1829	464	56	application	application	NOUN
ap-1829	464	57	to	to	ADP
ap-1829	464	58	evaporation	evaporation	NOUN
ap-1829	464	59	from	from	ADP
ap-1829	464	60	a	a	DET
ap-1829	464	61	water	water	NOUN
ap-1829	464	62	table	table	NOUN
ap-1829	464	63	,	,	PUNCT
ap-1829	464	64	soil	soil	NOUN
ap-1829	464	65	science	science	NOUN
ap-1829	464	66	,	,	PUNCT
ap-1829	464	67	85	85	NUM
ap-1829	464	68	,	,	PUNCT
ap-1829	464	69	1958	1958	NUM
ap-1829	464	70	,	,	PUNCT
ap-1829	464	71	228	228	NUM
ap-1829	464	72	-	-	SYM
ap-1829	464	73	232	232	NUM
ap-1829	465	1	[	[	X
ap-1829	465	2	18	18	NUM
ap-1829	465	3	]	]	PUNCT
ap-1829	465	4	k.	k.	PROPN
ap-1829	465	5	noborio	noborio	PROPN
ap-1829	465	6	,	,	PUNCT
ap-1829	465	7	k.j	k.j	PROPN
ap-1829	465	8	.	.	PROPN
ap-1829	466	1	mcinnes	mcinnes	PROPN
ap-1829	466	2	,	,	PUNCT
ap-1829	466	3	j.l	j.l	PROPN
ap-1829	466	4	.	.	PROPN
ap-1829	466	5	heilman	heilman	PROPN
ap-1829	466	6	:	:	PUNCT
ap-1829	466	7	two	two	NUM
ap-1829	466	8	-	-	PUNCT
ap-1829	466	9	dimensional	dimensional	ADJ
ap-1829	466	10	model	model	NOUN
ap-1829	466	11	for	for	ADP
ap-1829	466	12	water	water	NOUN
ap-1829	466	13	,	,	PUNCT
ap-1829	466	14	heat	heat	NOUN
ap-1829	466	15	,	,	PUNCT
ap-1829	466	16	and	and	CCONJ
ap-1829	466	17	solute	solute	VERB
ap-1829	466	18	transport	transport	NOUN
ap-1829	466	19	in	in	ADP
ap-1829	466	20	furrow	furrow	NOUN
ap-1829	466	21	-	-	PUNCT
ap-1829	466	22	irrigated	irrigate	VERB
ap-1829	466	23	soil	soil	NOUN
ap-1829	466	24	:	:	PUNCT
ap-1829	466	25	i.	i.	PROPN
ap-1829	466	26	theory	theory	PROPN
ap-1829	466	27	,	,	PUNCT
ap-1829	466	28	soil	soil	NOUN
ap-1829	466	29	science	science	NOUN
ap-1829	466	30	society	society	PROPN
ap-1829	466	31	of	of	ADP
ap-1829	466	32	america	america	PROPN
ap-1829	466	33	journal	journal	PROPN
ap-1829	466	34	,	,	PUNCT
ap-1829	466	35	60	60	NUM
ap-1829	466	36	,	,	PUNCT
ap-1829	466	37	4	4	NUM
ap-1829	466	38	,	,	PUNCT
ap-1829	466	39	1996	1996	NUM
ap-1829	466	40	,	,	PUNCT
ap-1829	466	41	1001–1009	1001–1009	NUM
ap-1829	466	42	[	[	SYM
ap-1829	466	43	19	19	NUM
ap-1829	466	44	]	]	X
ap-1829	466	45	e.	e.	PROPN
ap-1829	466	46	rank	rank	PROPN
ap-1829	466	47	,	,	PUNCT
ap-1829	466	48	c.	c.	PROPN
ap-1829	466	49	katz	katz	PROPN
ap-1829	466	50	,	,	PUNCT
ap-1829	466	51	h.	h.	PROPN
ap-1829	466	52	werner	werner	PROPN
ap-1829	466	53	:	:	PUNCT
ap-1829	466	54	on	on	ADP
ap-1829	466	55	the	the	DET
ap-1829	466	56	importance	importance	NOUN
ap-1829	466	57	of	of	ADP
ap-1829	466	58	the	the	DET
ap-1829	466	59	discrete	discrete	ADJ
ap-1829	466	60	maximum	maximum	ADJ
ap-1829	466	61	principle	principle	NOUN
ap-1829	466	62	in	in	ADP
ap-1829	466	63	transient	transient	ADJ
ap-1829	466	64	analysis	analysis	NOUN
ap-1829	466	65	using	use	VERB
ap-1829	466	66	finite	finite	ADJ
ap-1829	466	67	element	element	NOUN
ap-1829	466	68	methods	method	NOUN
ap-1829	466	69	,	,	PUNCT
ap-1829	466	70	international	international	ADJ
ap-1829	466	71	journal	journal	NOUN
ap-1829	466	72	for	for	ADP
ap-1829	466	73	numerical	numerical	ADJ
ap-1829	466	74	methods	method	NOUN
ap-1829	466	75	in	in	ADP
ap-1829	466	76	engineering	engineering	NOUN
ap-1829	466	77	,	,	PUNCT
ap-1829	466	78	19	19	NUM
ap-1829	466	79	,	,	PUNCT
ap-1829	466	80	1983	1983	NUM
ap-1829	466	81	,	,	PUNCT
ap-1829	466	82	1771–1782	1771–1782	NUM
ap-1829	467	1	[	[	X
ap-1829	467	2	20	20	NUM
ap-1829	467	3	]	]	PUNCT
ap-1829	467	4	g.	g.	PROPN
ap-1829	467	5	pini	pini	PROPN
ap-1829	467	6	,	,	PUNCT
ap-1829	467	7	g.	g.	PROPN
ap-1829	467	8	gambolati	gambolati	PROPN
ap-1829	467	9	:	:	PUNCT
ap-1829	467	10	is	be	AUX
ap-1829	467	11	simple	simple	ADJ
ap-1829	467	12	diagonal	diagonal	ADJ
ap-1829	467	13	scaling	scale	VERB
ap-1829	467	14	the	the	DET
ap-1829	467	15	best	good	ADJ
ap-1829	467	16	preconditioner	preconditioner	NOUN
ap-1829	467	17	for	for	ADP
ap-1829	467	18	conjugate	conjugate	ADJ
ap-1829	467	19	gradients	gradient	NOUN
ap-1829	467	20	on	on	ADP
ap-1829	467	21	supercomputers	supercomputer	NOUN
ap-1829	467	22	?	?	PUNCT
ap-1829	467	23	,	,	PUNCT
ap-1829	467	24	advances	advance	NOUN
ap-1829	467	25	in	in	ADP
ap-1829	467	26	water	water	NOUN
ap-1829	467	27	resources	resource	NOUN
ap-1829	467	28	,	,	PUNCT
ap-1829	467	29	13	13	NUM
ap-1829	467	30	,	,	PUNCT
ap-1829	467	31	1990	1990	NUM
ap-1829	467	32	,	,	PUNCT
ap-1829	467	33	147	147	NUM
ap-1829	467	34	-	-	SYM
ap-1829	467	35	153	153	NUM
ap-1829	468	1	[	[	X
ap-1829	468	2	21	21	NUM
ap-1829	468	3	]	]	PUNCT
ap-1829	468	4	x.	x.	NOUN
ap-1829	468	5	xu	xu	PROPN
ap-1829	468	6	,	,	PUNCT
ap-1829	468	7	n.	n.	PROPN
ap-1829	468	8	qin	qin	PROPN
ap-1829	468	9	,	,	PUNCT
ap-1829	468	10	b.e	b.e	PROPN
ap-1829	468	11	.	.	PROPN
ap-1829	468	12	richards	richards	PROPN
ap-1829	468	13	:	:	PUNCT
ap-1829	468	14	alpha	alpha	NOUN
ap-1829	468	15	-	-	PUNCT
ap-1829	468	16	gmres	gmres	PROPN
ap-1829	468	17	:	:	PUNCT
ap-1829	468	18	a	a	DET
ap-1829	468	19	new	new	ADJ
ap-1829	468	20	parallelizable	parallelizable	ADJ
ap-1829	468	21	iterative	iterative	NOUN
ap-1829	468	22	solver	solver	ADV
ap-1829	468	23	for	for	ADP
ap-1829	468	24	large	large	ADJ
ap-1829	468	25	sparse	sparse	ADJ
ap-1829	468	26	non	non	ADJ
ap-1829	468	27	-	-	ADJ
ap-1829	468	28	symmetric	symmetric	ADJ
ap-1829	468	29	linear	linear	PROPN
ap-1829	468	30	systems	system	NOUN
ap-1829	468	31	arising	arise	VERB
ap-1829	468	32	from	from	ADP
ap-1829	468	33	cfd	cfd	NOUN
ap-1829	468	34	,	,	PUNCT
ap-1829	468	35	international	international	ADJ
ap-1829	468	36	journal	journal	NOUN
ap-1829	468	37	for	for	ADP
ap-1829	468	38	numerical	numerical	ADJ
ap-1829	468	39	methods	method	NOUN
ap-1829	468	40	in	in	ADP
ap-1829	468	41	fluids	fluid	NOUN
ap-1829	468	42	,	,	PUNCT
ap-1829	468	43	15	15	NUM
ap-1829	468	44	,	,	PUNCT
ap-1829	468	45	1992	1992	NUM
ap-1829	468	46	,	,	PUNCT
ap-1829	468	47	613	613	NUM
ap-1829	468	48	-	-	SYM
ap-1829	468	49	623	623	NUM
ap-1829	469	1	[	[	X
ap-1829	469	2	22	22	NUM
ap-1829	469	3	]	]	PUNCT
ap-1829	469	4	a.	a.	NOUN
ap-1829	469	5	greenbaum	greenbaum	PROPN
ap-1829	469	6	,	,	PUNCT
ap-1829	469	7	v.	v.	ADP
ap-1829	469	8	pták	pták	ADJ
ap-1829	469	9	,	,	PUNCT
ap-1829	469	10	z.	z.	PROPN
ap-1829	469	11	strakoš	strakoš	VERB
ap-1829	469	12	:	:	PUNCT
ap-1829	469	13	any	any	DET
ap-1829	469	14	nonincreasing	nonincrease	VERB
ap-1829	469	15	convergence	convergence	NOUN
ap-1829	469	16	curve	curve	NOUN
ap-1829	469	17	is	be	AUX
ap-1829	469	18	possible	possible	ADJ
ap-1829	469	19	for	for	ADP
ap-1829	469	20	gmres	gmre	NOUN
ap-1829	469	21	,	,	PUNCT
ap-1829	469	22	siam	siam	ADJ
ap-1829	469	23	journal	journal	NOUN
ap-1829	469	24	on	on	ADP
ap-1829	469	25	matrix	matrix	NOUN
ap-1829	469	26	analysis	analysis	NOUN
ap-1829	469	27	and	and	CCONJ
ap-1829	469	28	applications	application	NOUN
ap-1829	469	29	,	,	PUNCT
ap-1829	469	30	17	17	NUM
ap-1829	469	31	,	,	PUNCT
ap-1829	469	32	1996	1996	NUM
ap-1829	469	33	,	,	PUNCT
ap-1829	469	34	465	465	NUM
ap-1829	469	35	-	-	SYM
ap-1829	469	36	469	469	NUM
ap-1829	469	37	[	[	X
ap-1829	469	38	23	23	NUM
ap-1829	469	39	]	]	PUNCT
ap-1829	469	40	m.	m.	NOUN
ap-1829	469	41	benzi	benzi	PROPN
ap-1829	469	42	:	:	PUNCT
ap-1829	469	43	preconditioning	precondition	VERB
ap-1829	469	44	techniques	technique	NOUN
ap-1829	469	45	for	for	ADP
ap-1829	469	46	large	large	ADJ
ap-1829	469	47	linear	linear	ADJ
ap-1829	469	48	systems	system	NOUN
ap-1829	469	49	:	:	PUNCT
ap-1829	469	50	a	a	DET
ap-1829	469	51	survey	survey	NOUN
ap-1829	469	52	,	,	PUNCT
ap-1829	469	53	journal	journal	NOUN
ap-1829	469	54	of	of	ADP
ap-1829	469	55	computational	computational	ADJ
ap-1829	469	56	physics	physics	NOUN
ap-1829	469	57	,	,	PUNCT
ap-1829	469	58	182	182	NUM
ap-1829	469	59	,	,	PUNCT
ap-1829	469	60	2002	2002	NUM
ap-1829	469	61	,	,	PUNCT
ap-1829	469	62	418	418	NUM
ap-1829	469	63	-	-	SYM
ap-1829	469	64	477	477	NUM
ap-1829	470	1	[	[	X
ap-1829	470	2	24	24	NUM
ap-1829	470	3	]	]	PUNCT
ap-1829	470	4	m.	m.	NOUN
ap-1829	470	5	kuráž	kuráž	PROPN
ap-1829	470	6	:	:	PUNCT
ap-1829	470	7	numerical	numerical	ADJ
ap-1829	470	8	solution	solution	NOUN
ap-1829	470	9	of	of	ADP
ap-1829	470	10	the	the	DET
ap-1829	470	11	flow	flow	NOUN
ap-1829	470	12	and	and	CCONJ
ap-1829	470	13	transport	transport	NOUN
ap-1829	470	14	equations	equation	NOUN
ap-1829	470	15	in	in	ADP
ap-1829	470	16	a	a	DET
ap-1829	470	17	porous	porous	ADJ
ap-1829	470	18	medium	medium	NOUN
ap-1829	470	19	with	with	ADP
ap-1829	470	20	the	the	DET
ap-1829	470	21	dual	dual	ADJ
ap-1829	470	22	permeability	permeability	NOUN
ap-1829	470	23	conceptual	conceptual	ADJ
ap-1829	470	24	approach	approach	NOUN
ap-1829	470	25	,	,	PUNCT
ap-1829	470	26	verbum	verbum	NOUN
ap-1829	470	27	publishing	publishing	NOUN
ap-1829	470	28	,	,	PUNCT
ap-1829	470	29	zlín	zlín	NOUN
ap-1829	470	30	,	,	PUNCT
ap-1829	470	31	2011	2011	NUM
ap-1829	470	32	358	358	NUM
ap-1829	470	33	http://www.freecode.com/projects/drutes	http://www.freecode.com/projects/drutes	PROPN
ap-1829	470	34	acta	acta	VERB
ap-1829	470	35	polytechnica	polytechnica	PROPN
ap-1829	470	36	53(4):347–358	53(4):347–358	PROPN
ap-1829	470	37	,	,	PUNCT
ap-1829	470	38	2013	2013	NUM
ap-1829	470	39	1	1	NUM
ap-1829	470	40	introduction	introduction	NOUN
ap-1829	470	41	2	2	NUM
ap-1829	470	42	mathematical	mathematical	ADJ
ap-1829	470	43	model	model	NOUN
ap-1829	470	44	2.1	2.1	NUM
ap-1829	470	45	strong	strong	ADJ
ap-1829	470	46	and	and	CCONJ
ap-1829	470	47	weak	weak	ADJ
ap-1829	470	48	formulations	formulation	NOUN
ap-1829	470	49	3	3	NUM
ap-1829	470	50	time	time	NOUN
ap-1829	470	51	step	step	NOUN
ap-1829	470	52	adaptivity	adaptivity	NOUN
ap-1829	470	53	3.1	3.1	NUM
ap-1829	470	54	case	case	NOUN
ap-1829	470	55	study	study	NOUN
ap-1829	470	56	3.2	3.2	NUM
ap-1829	470	57	results	result	NOUN
ap-1829	470	58	and	and	CCONJ
ap-1829	470	59	conclusions	conclusion	NOUN
ap-1829	470	60	4	4	NUM
ap-1829	470	61	preconditioner	preconditioner	NOUN
ap-1829	470	62	4.1	4.1	NUM
ap-1829	470	63	on	on	ADP
ap-1829	470	64	selecting	select	VERB
ap-1829	470	65	an	an	DET
ap-1829	470	66	algorithm	algorithm	NOUN
ap-1829	470	67	for	for	ADP
ap-1829	470	68	solving	solve	VERB
ap-1829	470	69	the	the	DET
ap-1829	470	70	systems	system	NOUN
ap-1829	470	71	of	of	ADP
ap-1829	470	72	linear	linear	PROPN
ap-1829	470	73	equations	equation	NOUN
ap-1829	470	74	4.2	4.2	NUM
ap-1829	470	75	theoretical	theoretical	ADJ
ap-1829	470	76	case	case	NOUN
ap-1829	470	77	study	study	NOUN
ap-1829	470	78	4.2.1	4.2.1	NUM
ap-1829	470	79	conditioning	conditioning	NOUN
ap-1829	470	80	improvements	improvement	NOUN
ap-1829	470	81	4.3	4.3	NUM
ap-1829	470	82	practical	practical	ADJ
ap-1829	470	83	case	case	NOUN
ap-1829	470	84	study	study	NOUN
ap-1829	470	85	4.4	4.4	NUM
ap-1829	470	86	numerical	numerical	ADJ
ap-1829	470	87	properties	property	NOUN
ap-1829	470	88	4.4.1	4.4.1	NUM
ap-1829	470	89	conditioning	conditioning	NOUN
ap-1829	470	90	improvements	improvement	NOUN
ap-1829	470	91	5	5	NUM
ap-1829	470	92	conclusions	conclusion	NOUN
ap-1829	470	93	acknowledgements	acknowledgement	NOUN
ap-1829	470	94	references	reference	NOUN