id	sid	tid	token	lemma	pos
app01-4621	1	1	acta	acta	PROPN
app01-4621	1	2	polytechnica	polytechnica	PROPN
app01-4621	1	3	ctu	ctu	PROPN
app01-4621	1	4	proceedings	proceeding	NOUN
app01-4621	1	5	doi:10.14311	doi:10.14311	PROPN
app01-4621	1	6	/	/	SYM
app01-4621	1	7	app.2017.13.0029	app.2017.13.0029	PROPN
app01-4621	1	8	acta	acta	PROPN
app01-4621	1	9	polytechnica	polytechnica	PROPN
app01-4621	1	10	ctu	ctu	PROPN
app01-4621	1	11	proceedings	proceeding	NOUN
app01-4621	1	12	13:29–34	13:29–34	NUM
app01-4621	1	13	,	,	PUNCT
app01-4621	1	14	2017	2017	NUM
app01-4621	1	15	©	©	PROPN
app01-4621	1	16	czech	czech	PROPN
app01-4621	1	17	technical	technical	PROPN
app01-4621	1	18	university	university	PROPN
app01-4621	1	19	in	in	ADP
app01-4621	1	20	prague	prague	PROPN
app01-4621	1	21	,	,	PUNCT
app01-4621	1	22	2017	2017	NUM
app01-4621	1	23	available	available	ADJ
app01-4621	1	24	online	online	ADV
app01-4621	1	25	at	at	ADP
app01-4621	1	26	http://ojs.cvut.cz/ojs/index.php/app	http://ojs.cvut.cz/ojs/index.php/app	NOUN
app01-4621	1	27	synthesized	synthesize	VERB
app01-4621	1	28	enrichment	enrichment	NOUN
app01-4621	1	29	functions	function	NOUN
app01-4621	1	30	for	for	ADP
app01-4621	1	31	extended	extended	ADJ
app01-4621	1	32	finite	finite	ADJ
app01-4621	1	33	element	element	NOUN
app01-4621	1	34	analyses	analysis	NOUN
app01-4621	1	35	with	with	ADP
app01-4621	1	36	fully	fully	ADV
app01-4621	1	37	resolved	resolve	VERB
app01-4621	1	38	microstructure	microstructure	ADJ
app01-4621	1	39	martin	martin	NOUN
app01-4621	1	40	doškářa,∗	doškářa,∗	NOUN
app01-4621	1	41	,	,	PUNCT
app01-4621	1	42	jan	jan	PROPN
app01-4621	1	43	nováka	nováka	PROPN
app01-4621	1	44	,	,	PUNCT
app01-4621	1	45	jan	jan	PROPN
app01-4621	1	46	zemana	zemana	PROPN
app01-4621	1	47	,	,	PUNCT
app01-4621	1	48	b	b	PROPN
app01-4621	1	49	a	a	DET
app01-4621	1	50	faculty	faculty	NOUN
app01-4621	1	51	of	of	ADP
app01-4621	1	52	civil	civil	ADJ
app01-4621	1	53	engineering	engineering	NOUN
app01-4621	1	54	,	,	PUNCT
app01-4621	1	55	czech	czech	PROPN
app01-4621	1	56	technical	technical	PROPN
app01-4621	1	57	university	university	PROPN
app01-4621	1	58	in	in	ADP
app01-4621	1	59	prague	prague	PROPN
app01-4621	1	60	,	,	PUNCT
app01-4621	1	61	thákurova	thákurova	PROPN
app01-4621	1	62	7/2077	7/2077	PROPN
app01-4621	1	63	,	,	PUNCT
app01-4621	1	64	166	166	NUM
app01-4621	1	65	29	29	NUM
app01-4621	1	66	prague	prague	NOUN
app01-4621	1	67	6	6	NUM
app01-4621	1	68	,	,	PUNCT
app01-4621	1	69	czech	czech	PROPN
app01-4621	1	70	republic	republic	PROPN
app01-4621	1	71	b	b	PROPN
app01-4621	1	72	the	the	DET
app01-4621	1	73	institute	institute	PROPN
app01-4621	1	74	of	of	ADP
app01-4621	1	75	information	information	NOUN
app01-4621	1	76	theory	theory	NOUN
app01-4621	1	77	and	and	CCONJ
app01-4621	1	78	automation	automation	NOUN
app01-4621	1	79	,	,	PUNCT
app01-4621	1	80	academy	academy	NOUN
app01-4621	1	81	of	of	ADP
app01-4621	1	82	sciences	sciences	PROPN
app01-4621	1	83	of	of	ADP
app01-4621	1	84	the	the	DET
app01-4621	1	85	czech	czech	PROPN
app01-4621	1	86	republic	republic	NOUN
app01-4621	1	87	,	,	PUNCT
app01-4621	1	88	pod	pod	PROPN
app01-4621	1	89	vodárenskou	vodárenskou	PROPN
app01-4621	1	90	věží	věží	VERB
app01-4621	1	91	4	4	NUM
app01-4621	1	92	,	,	PUNCT
app01-4621	1	93	182	182	NUM
app01-4621	1	94	08	08	NUM
app01-4621	1	95	prague	prague	NOUN
app01-4621	1	96	8	8	NUM
app01-4621	1	97	,	,	PUNCT
app01-4621	1	98	czech	czech	PROPN
app01-4621	1	99	republic	republic	NOUN
app01-4621	1	100	∗	∗	NOUN
app01-4621	1	101	corresponding	correspond	VERB
app01-4621	1	102	author	author	NOUN
app01-4621	1	103	:	:	PUNCT
app01-4621	1	104	martin.doskar@fsv.cvut.cz	martin.doskar@fsv.cvut.cz	NOUN
app01-4621	1	105	abstract	abstract	NOUN
app01-4621	1	106	.	.	PUNCT
app01-4621	2	1	inspired	inspire	VERB
app01-4621	2	2	by	by	ADP
app01-4621	2	3	the	the	DET
app01-4621	2	4	first	first	ADJ
app01-4621	2	5	order	order	NOUN
app01-4621	2	6	numerical	numerical	ADJ
app01-4621	2	7	homogenization	homogenization	NOUN
app01-4621	2	8	,	,	PUNCT
app01-4621	2	9	we	we	PRON
app01-4621	2	10	present	present	VERB
app01-4621	2	11	a	a	DET
app01-4621	2	12	method	method	NOUN
app01-4621	2	13	for	for	ADP
app01-4621	2	14	extracting	extract	VERB
app01-4621	2	15	continuous	continuous	ADJ
app01-4621	2	16	fluctuation	fluctuation	NOUN
app01-4621	2	17	fields	field	NOUN
app01-4621	2	18	from	from	ADP
app01-4621	2	19	the	the	DET
app01-4621	2	20	wang	wang	PROPN
app01-4621	2	21	tile	tile	NOUN
app01-4621	2	22	based	base	VERB
app01-4621	2	23	compression	compression	NOUN
app01-4621	2	24	of	of	ADP
app01-4621	2	25	a	a	DET
app01-4621	2	26	material	material	NOUN
app01-4621	2	27	microstructure	microstructure	NOUN
app01-4621	2	28	.	.	PUNCT
app01-4621	3	1	the	the	DET
app01-4621	3	2	fluctuation	fluctuation	NOUN
app01-4621	3	3	fields	field	NOUN
app01-4621	3	4	are	be	AUX
app01-4621	3	5	then	then	ADV
app01-4621	3	6	used	use	VERB
app01-4621	3	7	as	as	ADP
app01-4621	3	8	enrichment	enrichment	NOUN
app01-4621	3	9	basis	basis	NOUN
app01-4621	3	10	in	in	ADP
app01-4621	3	11	extended	extended	ADJ
app01-4621	3	12	finite	finite	ADJ
app01-4621	3	13	element	element	NOUN
app01-4621	3	14	method	method	NOUN
app01-4621	3	15	(	(	PUNCT
app01-4621	3	16	xfem	xfem	X
app01-4621	3	17	)	)	PUNCT
app01-4621	3	18	to	to	PART
app01-4621	3	19	reduce	reduce	VERB
app01-4621	3	20	number	number	NOUN
app01-4621	3	21	of	of	ADP
app01-4621	3	22	unknowns	unknown	NOUN
app01-4621	3	23	in	in	ADP
app01-4621	3	24	problems	problem	NOUN
app01-4621	3	25	with	with	ADP
app01-4621	3	26	fully	fully	ADV
app01-4621	3	27	resolved	resolve	VERB
app01-4621	3	28	microstructural	microstructural	ADJ
app01-4621	3	29	geometry	geometry	NOUN
app01-4621	3	30	synthesized	synthesize	VERB
app01-4621	3	31	by	by	ADP
app01-4621	3	32	means	mean	NOUN
app01-4621	3	33	of	of	ADP
app01-4621	3	34	the	the	DET
app01-4621	3	35	tiling	tile	VERB
app01-4621	3	36	concept	concept	NOUN
app01-4621	3	37	.	.	PUNCT
app01-4621	4	1	in	in	ADP
app01-4621	4	2	addition	addition	NOUN
app01-4621	4	3	,	,	PUNCT
app01-4621	4	4	the	the	DET
app01-4621	4	5	xfem	xfem	PROPN
app01-4621	4	6	basis	basis	NOUN
app01-4621	4	7	functions	function	NOUN
app01-4621	4	8	are	be	AUX
app01-4621	4	9	taken	take	VERB
app01-4621	4	10	as	as	ADP
app01-4621	4	11	reduced	reduce	VERB
app01-4621	4	12	modes	mode	NOUN
app01-4621	4	13	of	of	ADP
app01-4621	4	14	a	a	DET
app01-4621	4	15	detailed	detailed	ADJ
app01-4621	4	16	discretization	discretization	NOUN
app01-4621	4	17	in	in	ADP
app01-4621	4	18	order	order	NOUN
app01-4621	4	19	to	to	PART
app01-4621	4	20	circumvent	circumvent	VERB
app01-4621	4	21	the	the	DET
app01-4621	4	22	need	need	NOUN
app01-4621	4	23	for	for	ADP
app01-4621	4	24	non	non	ADJ
app01-4621	4	25	-	-	ADJ
app01-4621	4	26	standard	standard	ADJ
app01-4621	4	27	numerical	numerical	ADJ
app01-4621	4	28	quadratures	quadrature	NOUN
app01-4621	4	29	.	.	PUNCT
app01-4621	5	1	the	the	DET
app01-4621	5	2	methodology	methodology	NOUN
app01-4621	5	3	is	be	AUX
app01-4621	5	4	illustrated	illustrate	VERB
app01-4621	5	5	with	with	ADP
app01-4621	5	6	a	a	DET
app01-4621	5	7	scalar	scalar	ADJ
app01-4621	5	8	steady	steady	ADJ
app01-4621	5	9	-	-	PUNCT
app01-4621	5	10	state	state	NOUN
app01-4621	5	11	problem	problem	NOUN
app01-4621	5	12	.	.	PUNCT
app01-4621	6	1	keywords	keyword	NOUN
app01-4621	6	2	:	:	PUNCT
app01-4621	6	3	wang	wang	PROPN
app01-4621	6	4	tiling	tiling	NOUN
app01-4621	6	5	,	,	PUNCT
app01-4621	6	6	microstructure	microstructure	ADJ
app01-4621	6	7	synthesis	synthesis	NOUN
app01-4621	6	8	,	,	PUNCT
app01-4621	6	9	microstructure	microstructure	NOUN
app01-4621	6	10	-	-	PUNCT
app01-4621	6	11	informed	inform	VERB
app01-4621	6	12	enrichment	enrichment	NOUN
app01-4621	6	13	functions	function	NOUN
app01-4621	6	14	,	,	PUNCT
app01-4621	6	15	extended	extend	VERB
app01-4621	6	16	finite	finite	ADJ
app01-4621	6	17	element	element	NOUN
app01-4621	6	18	method	method	NOUN
app01-4621	6	19	.	.	PUNCT
app01-4621	7	1	1	1	X
app01-4621	7	2	.	.	X
app01-4621	7	3	introduction	introduction	NOUN
app01-4621	7	4	all	all	DET
app01-4621	7	5	materials	material	NOUN
app01-4621	7	6	exhibit	exhibit	VERB
app01-4621	7	7	heterogeneous	heterogeneous	ADJ
app01-4621	7	8	microstructure	microstructure	NOUN
app01-4621	7	9	at	at	ADP
app01-4621	7	10	certain	certain	ADJ
app01-4621	7	11	level	level	NOUN
app01-4621	7	12	of	of	ADP
app01-4621	7	13	detail	detail	NOUN
app01-4621	7	14	.	.	PUNCT
app01-4621	8	1	besides	besides	SCONJ
app01-4621	8	2	the	the	DET
app01-4621	8	3	physical	physical	ADJ
app01-4621	8	4	properties	property	NOUN
app01-4621	8	5	of	of	ADP
app01-4621	8	6	microstructural	microstructural	ADJ
app01-4621	8	7	constituents	constituent	NOUN
app01-4621	8	8	,	,	PUNCT
app01-4621	8	9	the	the	DET
app01-4621	8	10	overall	overall	ADJ
app01-4621	8	11	response	response	NOUN
app01-4621	8	12	is	be	AUX
app01-4621	8	13	also	also	ADV
app01-4621	8	14	dictated	dictate	VERB
app01-4621	8	15	by	by	ADP
app01-4621	8	16	their	their	PRON
app01-4621	8	17	spatial	spatial	ADJ
app01-4621	8	18	arrangement	arrangement	NOUN
app01-4621	8	19	.	.	PUNCT
app01-4621	9	1	with	with	ADP
app01-4621	9	2	the	the	DET
app01-4621	9	3	advance	advance	NOUN
app01-4621	9	4	of	of	ADP
app01-4621	9	5	numerical	numerical	ADJ
app01-4621	9	6	methods	method	NOUN
app01-4621	9	7	and	and	CCONJ
app01-4621	9	8	computational	computational	ADJ
app01-4621	9	9	power	power	NOUN
app01-4621	9	10	,	,	PUNCT
app01-4621	9	11	there	there	PRON
app01-4621	9	12	is	be	VERB
app01-4621	9	13	an	an	DET
app01-4621	9	14	emphasis	emphasis	NOUN
app01-4621	9	15	on	on	ADP
app01-4621	9	16	devising	devise	VERB
app01-4621	9	17	approaches	approach	NOUN
app01-4621	9	18	that	that	PRON
app01-4621	9	19	take	take	VERB
app01-4621	9	20	the	the	DET
app01-4621	9	21	microstructural	microstructural	ADJ
app01-4621	9	22	characteristics	characteristic	NOUN
app01-4621	9	23	into	into	ADP
app01-4621	9	24	account	account	NOUN
app01-4621	9	25	and	and	CCONJ
app01-4621	9	26	propagate	propagate	VERB
app01-4621	9	27	knowledge	knowledge	NOUN
app01-4621	9	28	of	of	ADP
app01-4621	9	29	material	material	ADJ
app01-4621	9	30	composition	composition	NOUN
app01-4621	9	31	into	into	ADP
app01-4621	9	32	upper	upper	ADJ
app01-4621	9	33	-	-	PUNCT
app01-4621	9	34	scale	scale	NOUN
app01-4621	9	35	models	model	NOUN
app01-4621	9	36	.	.	PUNCT
app01-4621	10	1	in	in	ADP
app01-4621	10	2	our	our	PRON
app01-4621	10	3	contribution	contribution	NOUN
app01-4621	10	4	,	,	PUNCT
app01-4621	10	5	we	we	PRON
app01-4621	10	6	focus	focus	VERB
app01-4621	10	7	on	on	ADP
app01-4621	10	8	problems	problem	NOUN
app01-4621	10	9	in	in	ADP
app01-4621	10	10	which	which	PRON
app01-4621	10	11	the	the	DET
app01-4621	10	12	underlying	underlie	VERB
app01-4621	10	13	microstructural	microstructural	ADJ
app01-4621	10	14	geometry	geometry	NOUN
app01-4621	10	15	is	be	AUX
app01-4621	10	16	explicitly	explicitly	ADV
app01-4621	10	17	known	know	VERB
app01-4621	10	18	.	.	PUNCT
app01-4621	11	1	we	we	PRON
app01-4621	11	2	consider	consider	VERB
app01-4621	11	3	problems	problem	NOUN
app01-4621	11	4	where	where	SCONJ
app01-4621	11	5	the	the	DET
app01-4621	11	6	characteristic	characteristic	ADJ
app01-4621	11	7	length	length	NOUN
app01-4621	11	8	of	of	ADP
app01-4621	11	9	the	the	DET
app01-4621	11	10	microstructure	microstructure	NOUN
app01-4621	11	11	is	be	AUX
app01-4621	11	12	comparable	comparable	ADJ
app01-4621	11	13	to	to	ADP
app01-4621	11	14	the	the	DET
app01-4621	11	15	dimension	dimension	NOUN
app01-4621	11	16	of	of	ADP
app01-4621	11	17	an	an	DET
app01-4621	11	18	upper	upper	ADJ
app01-4621	11	19	-	-	PUNCT
app01-4621	11	20	scale	scale	NOUN
app01-4621	11	21	model	model	NOUN
app01-4621	11	22	;	;	PUNCT
app01-4621	11	23	hence	hence	ADV
app01-4621	11	24	,	,	PUNCT
app01-4621	11	25	the	the	DET
app01-4621	11	26	nested	nested	ADJ
app01-4621	11	27	numerical	numerical	ADJ
app01-4621	11	28	homogenization	homogenization	NOUN
app01-4621	11	29	,	,	PUNCT
app01-4621	11	30	such	such	ADJ
app01-4621	11	31	as	as	ADP
app01-4621	11	32	the	the	DET
app01-4621	11	33	fe2	fe2	PROPN
app01-4621	11	34	method	method	NOUN
app01-4621	11	35	[	[	X
app01-4621	11	36	1	1	NUM
app01-4621	11	37	]	]	PUNCT
app01-4621	11	38	,	,	PUNCT
app01-4621	11	39	is	be	AUX
app01-4621	11	40	not	not	PART
app01-4621	11	41	applicable	applicable	ADJ
app01-4621	11	42	because	because	SCONJ
app01-4621	11	43	the	the	DET
app01-4621	11	44	underlying	underlying	ADJ
app01-4621	11	45	assumption	assumption	NOUN
app01-4621	11	46	of	of	ADP
app01-4621	11	47	the	the	DET
app01-4621	11	48	separation	separation	NOUN
app01-4621	11	49	of	of	ADP
app01-4621	11	50	scales	scale	NOUN
app01-4621	11	51	is	be	AUX
app01-4621	11	52	violated	violate	VERB
app01-4621	11	53	[	[	PUNCT
app01-4621	11	54	2	2	NUM
app01-4621	11	55	,	,	PUNCT
app01-4621	11	56	and	and	CCONJ
app01-4621	11	57	references	reference	NOUN
app01-4621	11	58	therein	therein	ADV
app01-4621	11	59	]	]	PUNCT
app01-4621	11	60	.	.	PUNCT
app01-4621	12	1	this	this	DET
app01-4621	12	2	work	work	NOUN
app01-4621	12	3	supplements	supplement	NOUN
app01-4621	12	4	our	our	PRON
app01-4621	12	5	previous	previous	ADJ
app01-4621	12	6	results	result	NOUN
app01-4621	12	7	regarding	regard	VERB
app01-4621	12	8	efficient	efficient	ADJ
app01-4621	12	9	modelling	modelling	NOUN
app01-4621	12	10	of	of	ADP
app01-4621	12	11	materials	material	NOUN
app01-4621	12	12	with	with	ADP
app01-4621	12	13	stochastic	stochastic	ADJ
app01-4621	12	14	heterogeneous	heterogeneous	ADJ
app01-4621	12	15	microstructure	microstructure	NOUN
app01-4621	12	16	,	,	PUNCT
app01-4621	12	17	e.g.	e.g.	ADV
app01-4621	12	18	,	,	PUNCT
app01-4621	12	19	[	[	X
app01-4621	12	20	3	3	NUM
app01-4621	12	21	,	,	PUNCT
app01-4621	12	22	4	4	NUM
app01-4621	12	23	]	]	PUNCT
app01-4621	12	24	.	.	PUNCT
app01-4621	13	1	the	the	DET
app01-4621	13	2	microstructural	microstructural	ADJ
app01-4621	13	3	geometry	geometry	NOUN
app01-4621	13	4	of	of	ADP
app01-4621	13	5	a	a	DET
app01-4621	13	6	macro	macro	ADJ
app01-4621	13	7	-	-	NOUN
app01-4621	13	8	scale	scale	NOUN
app01-4621	13	9	model	model	NOUN
app01-4621	13	10	—	—	PUNCT
app01-4621	13	11	as	as	ADV
app01-4621	13	12	well	well	ADV
app01-4621	13	13	as	as	ADP
app01-4621	13	14	its	its	PRON
app01-4621	13	15	finite	finite	ADJ
app01-4621	13	16	element	element	NOUN
app01-4621	13	17	discretization	discretization	NOUN
app01-4621	13	18	—	—	PUNCT
app01-4621	13	19	is	be	AUX
app01-4621	13	20	synthesized	synthesize	VERB
app01-4621	13	21	using	use	VERB
app01-4621	13	22	the	the	DET
app01-4621	13	23	wang	wang	NOUN
app01-4621	13	24	tiling	tile	VERB
app01-4621	13	25	concept	concept	NOUN
app01-4621	13	26	,	,	PUNCT
app01-4621	13	27	recalled	recall	VERB
app01-4621	13	28	in	in	ADP
app01-4621	13	29	section	section	NOUN
app01-4621	13	30	2	2	NUM
app01-4621	13	31	.	.	PUNCT
app01-4621	14	1	here	here	ADV
app01-4621	14	2	,	,	PUNCT
app01-4621	14	3	we	we	PRON
app01-4621	14	4	present	present	VERB
app01-4621	14	5	a	a	DET
app01-4621	14	6	method	method	NOUN
app01-4621	14	7	to	to	PART
app01-4621	14	8	extract	extract	VERB
app01-4621	14	9	dominant	dominant	ADJ
app01-4621	14	10	responses	response	NOUN
app01-4621	14	11	of	of	ADP
app01-4621	14	12	a	a	DET
app01-4621	14	13	compressed	compressed	ADJ
app01-4621	14	14	microstructure	microstructure	NOUN
app01-4621	14	15	to	to	ADP
app01-4621	14	16	prescribed	prescribe	VERB
app01-4621	14	17	macroscopic	macroscopic	ADJ
app01-4621	14	18	loading	loading	NOUN
app01-4621	14	19	.	.	PUNCT
app01-4621	15	1	we	we	PRON
app01-4621	15	2	reuse	reuse	VERB
app01-4621	15	3	the	the	DET
app01-4621	15	4	extracted	extract	VERB
app01-4621	15	5	responses	response	NOUN
app01-4621	15	6	to	to	PART
app01-4621	15	7	synthesize	synthesize	VERB
app01-4621	15	8	a	a	DET
app01-4621	15	9	microstructure	microstructure	NOUN
app01-4621	15	10	-	-	PUNCT
app01-4621	15	11	informed	inform	VERB
app01-4621	15	12	enrichment	enrichment	NOUN
app01-4621	15	13	basis	basis	NOUN
app01-4621	15	14	in	in	ADP
app01-4621	15	15	order	order	NOUN
app01-4621	15	16	to	to	PART
app01-4621	15	17	accelerate	accelerate	VERB
app01-4621	15	18	the	the	DET
app01-4621	15	19	upper	upper	ADJ
app01-4621	15	20	scale	scale	NOUN
app01-4621	15	21	calculations	calculation	NOUN
app01-4621	15	22	.	.	PUNCT
app01-4621	16	1	the	the	DET
app01-4621	16	2	numerical	numerical	ADJ
app01-4621	16	3	scheme	scheme	NOUN
app01-4621	16	4	,	,	PUNCT
app01-4621	16	5	outlined	outline	VERB
app01-4621	16	6	in	in	ADP
app01-4621	16	7	section	section	NOUN
app01-4621	16	8	4	4	NUM
app01-4621	16	9	,	,	PUNCT
app01-4621	16	10	combines	combine	VERB
app01-4621	16	11	extended	extend	VERB
app01-4621	16	12	finite	finite	ADJ
app01-4621	16	13	element	element	NOUN
app01-4621	16	14	framework	framework	NOUN
app01-4621	16	15	(	(	PUNCT
app01-4621	16	16	xfem	xfem	X
app01-4621	16	17	)	)	PUNCT
app01-4621	17	1	[	[	X
app01-4621	17	2	5	5	NUM
app01-4621	17	3	,	,	PUNCT
app01-4621	17	4	6	6	NUM
app01-4621	17	5	,	,	PUNCT
app01-4621	17	6	and	and	CCONJ
app01-4621	17	7	references	reference	NOUN
app01-4621	17	8	therein	therein	ADV
app01-4621	17	9	]	]	PUNCT
app01-4621	17	10	,	,	PUNCT
app01-4621	17	11	used	use	VERB
app01-4621	17	12	for	for	ADP
app01-4621	17	13	definition	definition	NOUN
app01-4621	17	14	of	of	ADP
app01-4621	17	15	local	local	ADJ
app01-4621	17	16	basis	basis	NOUN
app01-4621	17	17	functions	function	NOUN
app01-4621	17	18	,	,	PUNCT
app01-4621	17	19	with	with	ADP
app01-4621	17	20	the	the	DET
app01-4621	17	21	reduced	reduce	VERB
app01-4621	17	22	order	order	NOUN
app01-4621	17	23	modelling	model	VERB
app01-4621	17	24	approach	approach	NOUN
app01-4621	17	25	[	[	X
app01-4621	17	26	7	7	NUM
app01-4621	17	27	]	]	PUNCT
app01-4621	17	28	,	,	PUNCT
app01-4621	17	29	allowing	allow	VERB
app01-4621	17	30	for	for	ADP
app01-4621	17	31	utilization	utilization	NOUN
app01-4621	17	32	of	of	ADP
app01-4621	17	33	standard	standard	ADJ
app01-4621	17	34	finite	finite	ADJ
app01-4621	17	35	element	element	NOUN
app01-4621	17	36	procedures	procedure	NOUN
app01-4621	17	37	.	.	PUNCT
app01-4621	18	1	finally	finally	ADV
app01-4621	18	2	,	,	PUNCT
app01-4621	18	3	section	section	NOUN
app01-4621	18	4	5	5	NUM
app01-4621	18	5	illustrates	illustrate	VERB
app01-4621	18	6	the	the	DET
app01-4621	18	7	methodology	methodology	NOUN
app01-4621	18	8	with	with	ADP
app01-4621	18	9	a	a	DET
app01-4621	18	10	two	two	NUM
app01-4621	18	11	-	-	PUNCT
app01-4621	18	12	dimensional	dimensional	ADJ
app01-4621	18	13	problem	problem	NOUN
app01-4621	18	14	of	of	ADP
app01-4621	18	15	steady	steady	ADJ
app01-4621	18	16	-	-	PUNCT
app01-4621	18	17	state	state	NOUN
app01-4621	18	18	thermal	thermal	ADJ
app01-4621	18	19	conduction	conduction	NOUN
app01-4621	18	20	in	in	ADP
app01-4621	18	21	an	an	DET
app01-4621	18	22	l	l	NOUN
app01-4621	18	23	-	-	ADJ
app01-4621	18	24	shaped	shape	VERB
app01-4621	18	25	domain	domain	NOUN
app01-4621	18	26	.	.	PUNCT
app01-4621	19	1	2	2	X
app01-4621	19	2	.	.	X
app01-4621	19	3	wang	wang	PROPN
app01-4621	19	4	tiling	tile	VERB
app01-4621	19	5	concept	concept	NOUN
app01-4621	19	6	microstructure	microstructure	NOUN
app01-4621	19	7	of	of	ADP
app01-4621	19	8	random	random	ADJ
app01-4621	19	9	heterogeneous	heterogeneous	ADJ
app01-4621	19	10	materials	material	NOUN
app01-4621	19	11	is	be	AUX
app01-4621	19	12	usually	usually	ADV
app01-4621	19	13	represented	represent	VERB
app01-4621	19	14	by	by	ADP
app01-4621	19	15	means	mean	NOUN
app01-4621	19	16	of	of	ADP
app01-4621	19	17	a	a	DET
app01-4621	19	18	periodic	periodic	ADJ
app01-4621	19	19	finitesize	finitesize	NOUN
app01-4621	19	20	model	model	NOUN
app01-4621	19	21	—	—	PUNCT
app01-4621	19	22	appearing	appear	VERB
app01-4621	19	23	in	in	ADP
app01-4621	19	24	the	the	DET
app01-4621	19	25	literature	literature	NOUN
app01-4621	19	26	under	under	ADP
app01-4621	19	27	various	various	ADJ
app01-4621	19	28	names	name	NOUN
app01-4621	19	29	such	such	ADJ
app01-4621	19	30	as	as	ADP
app01-4621	19	31	statistically	statistically	ADV
app01-4621	19	32	optimal	optimal	ADJ
app01-4621	19	33	representative	representative	ADJ
app01-4621	19	34	unit	unit	NOUN
app01-4621	19	35	cell	cell	NOUN
app01-4621	19	36	,	,	PUNCT
app01-4621	19	37	statistically	statistically	ADV
app01-4621	19	38	similar	similar	ADJ
app01-4621	19	39	representative	representative	ADJ
app01-4621	19	40	volume	volume	NOUN
app01-4621	19	41	element	element	NOUN
app01-4621	19	42	,	,	PUNCT
app01-4621	19	43	or	or	CCONJ
app01-4621	19	44	statistically	statistically	ADV
app01-4621	19	45	equivalent	equivalent	ADJ
app01-4621	19	46	periodic	periodic	ADJ
app01-4621	19	47	unit	unit	NOUN
app01-4621	19	48	cell	cell	NOUN
app01-4621	19	49	(	(	PUNCT
app01-4621	19	50	sepuc)—that	sepuc)—that	PRON
app01-4621	19	51	resembles	resemble	VERB
app01-4621	19	52	the	the	DET
app01-4621	19	53	material	material	NOUN
app01-4621	19	54	in	in	ADP
app01-4621	19	55	terms	term	NOUN
app01-4621	19	56	of	of	ADP
app01-4621	19	57	various	various	ADJ
app01-4621	19	58	spatial	spatial	ADJ
app01-4621	19	59	statistics	statistic	NOUN
app01-4621	19	60	.	.	PUNCT
app01-4621	20	1	this	this	DET
app01-4621	20	2	setting	setting	NOUN
app01-4621	20	3	is	be	AUX
app01-4621	20	4	particularly	particularly	ADV
app01-4621	20	5	suitable	suitable	ADJ
app01-4621	20	6	for	for	ADP
app01-4621	20	7	the	the	DET
app01-4621	20	8	family	family	NOUN
app01-4621	20	9	of	of	ADP
app01-4621	20	10	fe2	fe2	PROPN
app01-4621	20	11	simulations	simulation	NOUN
app01-4621	20	12	,	,	PUNCT
app01-4621	20	13	e.g.	e.g.	ADV
app01-4621	20	14	,	,	PUNCT
app01-4621	20	15	[	[	X
app01-4621	20	16	1	1	NUM
app01-4621	20	17	]	]	PUNCT
app01-4621	20	18	,	,	PUNCT
app01-4621	20	19	in	in	ADP
app01-4621	20	20	which	which	PRON
app01-4621	20	21	it	it	PRON
app01-4621	20	22	is	be	AUX
app01-4621	20	23	often	often	ADV
app01-4621	20	24	accompanied	accompany	VERB
app01-4621	20	25	with	with	ADP
app01-4621	20	26	periodic	periodic	ADJ
app01-4621	20	27	boundary	boundary	ADJ
app01-4621	20	28	conditions	condition	NOUN
app01-4621	20	29	imposed	impose	VERB
app01-4621	20	30	at	at	ADP
app01-4621	20	31	the	the	DET
app01-4621	20	32	micro	micro	ADJ
app01-4621	20	33	-	-	NOUN
app01-4621	20	34	scale	scale	ADJ
app01-4621	20	35	level	level	NOUN
app01-4621	20	36	.	.	PUNCT
app01-4621	21	1	however	however	ADV
app01-4621	21	2	,	,	PUNCT
app01-4621	21	3	when	when	SCONJ
app01-4621	21	4	used	use	VERB
app01-4621	21	5	for	for	ADP
app01-4621	21	6	microstructure	microstructure	ADJ
app01-4621	21	7	synthesis	synthesis	NOUN
app01-4621	21	8	,	,	PUNCT
app01-4621	21	9	this	this	DET
app01-4621	21	10	representation	representation	NOUN
app01-4621	21	11	introduces	introduce	VERB
app01-4621	21	12	unrealistic	unrealistic	ADJ
app01-4621	21	13	,	,	PUNCT
app01-4621	21	14	spurious	spurious	ADJ
app01-4621	21	15	periodic	periodic	ADJ
app01-4621	21	16	correlations	correlation	NOUN
app01-4621	21	17	.	.	PUNCT
app01-4621	22	1	the	the	DET
app01-4621	22	2	formalism	formalism	NOUN
app01-4621	22	3	of	of	ADP
app01-4621	22	4	wang	wang	PROPN
app01-4621	22	5	tiles	tile	NOUN
app01-4621	22	6	represents	represent	VERB
app01-4621	22	7	a	a	DET
app01-4621	22	8	compromise	compromise	NOUN
app01-4621	22	9	between	between	ADP
app01-4621	22	10	the	the	DET
app01-4621	22	11	amount	amount	NOUN
app01-4621	22	12	of	of	ADP
app01-4621	22	13	induced	induced	ADJ
app01-4621	22	14	correlation	correlation	NOUN
app01-4621	22	15	and	and	CCONJ
app01-4621	22	16	complexity	complexity	NOUN
app01-4621	22	17	of	of	ADP
app01-4621	22	18	a	a	DET
app01-4621	22	19	microstructure	microstructure	ADJ
app01-4621	22	20	representation	representation	NOUN
app01-4621	22	21	.	.	PUNCT
app01-4621	23	1	instead	instead	ADV
app01-4621	23	2	of	of	ADP
app01-4621	23	3	a	a	DET
app01-4621	23	4	single	single	ADJ
app01-4621	23	5	cell	cell	NOUN
app01-4621	23	6	,	,	PUNCT
app01-4621	23	7	microstructural	microstructural	ADJ
app01-4621	23	8	information	information	NOUN
app01-4621	23	9	is	be	AUX
app01-4621	23	10	compressed	compress	VERB
app01-4621	23	11	into	into	ADP
app01-4621	23	12	a	a	DET
app01-4621	23	13	set	set	NOUN
app01-4621	23	14	of	of	ADP
app01-4621	23	15	equi	equi	NOUN
app01-4621	23	16	-	-	PUNCT
app01-4621	23	17	sized	sized	ADJ
app01-4621	23	18	wang	wang	PROPN
app01-4621	23	19	tiles	tile	NOUN
app01-4621	23	20	with	with	ADP
app01-4621	23	21	pre	pre	ADJ
app01-4621	23	22	-	-	ADJ
app01-4621	23	23	defined	define	VERB
app01-4621	23	24	requirements	requirement	NOUN
app01-4621	23	25	on	on	ADP
app01-4621	23	26	mutual	mutual	ADJ
app01-4621	23	27	compatibility	compatibility	NOUN
app01-4621	23	28	.	.	PUNCT
app01-4621	24	1	in	in	ADP
app01-4621	24	2	the	the	DET
app01-4621	24	3	abstract	abstract	ADJ
app01-4621	24	4	setting	setting	NOUN
app01-4621	24	5	,	,	PUNCT
app01-4621	24	6	the	the	DET
app01-4621	24	7	compatibility	compatibility	NOUN
app01-4621	24	8	constraints	constraint	NOUN
app01-4621	24	9	are	be	AUX
app01-4621	24	10	represented	represent	VERB
app01-4621	24	11	by	by	ADP
app01-4621	24	12	codes	code	NOUN
app01-4621	24	13	assigned	assign	VERB
app01-4621	24	14	to	to	ADP
app01-4621	24	15	tile	tile	NOUN
app01-4621	24	16	edges	edge	NOUN
app01-4621	24	17	,	,	PUNCT
app01-4621	24	18	illustrated	illustrate	VERB
app01-4621	24	19	with	with	ADP
app01-4621	24	20	distinct	distinct	ADJ
app01-4621	24	21	colours	colour	NOUN
app01-4621	24	22	in	in	ADP
app01-4621	24	23	figure	figure	NOUN
app01-4621	24	24	1	1	NUM
app01-4621	24	25	.	.	PUNCT
app01-4621	25	1	a	a	DET
app01-4621	25	2	realization	realization	NOUN
app01-4621	25	3	of	of	ADP
app01-4621	25	4	the	the	DET
app01-4621	25	5	compressed	compress	VERB
app01-4621	25	6	microstructure	microstructure	NOUN
app01-4621	25	7	is	be	AUX
app01-4621	25	8	then	then	ADV
app01-4621	25	9	synthesized	synthesize	VERB
app01-4621	25	10	following	follow	VERB
app01-4621	25	11	a	a	DET
app01-4621	25	12	simple	simple	ADJ
app01-4621	25	13	stochastic	stochastic	ADJ
app01-4621	25	14	algorithm	algorithm	NOUN
app01-4621	25	15	:	:	PUNCT
app01-4621	25	16	an	an	DET
app01-4621	25	17	empty	empty	ADJ
app01-4621	25	18	grid	grid	NOUN
app01-4621	25	19	of	of	ADP
app01-4621	25	20	29	29	NUM
app01-4621	25	21	http://dx.doi.org/10.14311/app.2017.13.0029	http://dx.doi.org/10.14311/app.2017.13.0029	PROPN
app01-4621	25	22	http://ojs.cvut.cz/ojs/index.php/app	http://ojs.cvut.cz/ojs/index.php/app	PROPN
app01-4621	25	23	m.	m.	PROPN
app01-4621	25	24	doškář	doškář	PROPN
app01-4621	25	25	,	,	PUNCT
app01-4621	25	26	j.	j.	PROPN
app01-4621	25	27	novák	novák	PROPN
app01-4621	25	28	,	,	PUNCT
app01-4621	25	29	j.	j.	PROPN
app01-4621	25	30	zeman	zeman	PROPN
app01-4621	25	31	acta	acta	PROPN
app01-4621	25	32	polytechnica	polytechnica	PROPN
app01-4621	25	33	ctu	ctu	PROPN
app01-4621	25	34	proceedings	proceeding	NOUN
app01-4621	25	35	a	a	DET
app01-4621	25	36	desired	desire	VERB
app01-4621	25	37	size	size	NOUN
app01-4621	25	38	is	be	AUX
app01-4621	25	39	sequentially	sequentially	ADV
app01-4621	25	40	filled	fill	VERB
app01-4621	25	41	with	with	ADP
app01-4621	25	42	instances	instance	NOUN
app01-4621	25	43	of	of	ADP
app01-4621	25	44	wang	wang	PROPN
app01-4621	25	45	tiles	tile	VERB
app01-4621	25	46	such	such	ADJ
app01-4621	25	47	that	that	SCONJ
app01-4621	25	48	the	the	DET
app01-4621	25	49	adjacent	adjacent	ADJ
app01-4621	25	50	tile	tile	NOUN
app01-4621	25	51	edges	edge	NOUN
app01-4621	25	52	are	be	AUX
app01-4621	25	53	compatible	compatible	ADJ
app01-4621	25	54	.	.	PUNCT
app01-4621	26	1	at	at	ADP
app01-4621	26	2	each	each	DET
app01-4621	26	3	position	position	NOUN
app01-4621	26	4	,	,	PUNCT
app01-4621	26	5	a	a	DET
app01-4621	26	6	tile	tile	NOUN
app01-4621	26	7	is	be	AUX
app01-4621	26	8	randomly	randomly	ADV
app01-4621	26	9	chosen	choose	VERB
app01-4621	26	10	from	from	ADP
app01-4621	26	11	a	a	DET
app01-4621	26	12	subset	subset	NOUN
app01-4621	26	13	of	of	ADP
app01-4621	26	14	tiles	tile	NOUN
app01-4621	26	15	compliant	compliant	ADJ
app01-4621	26	16	with	with	ADP
app01-4621	26	17	previously	previously	ADV
app01-4621	26	18	placed	place	VERB
app01-4621	26	19	tiles	tile	NOUN
app01-4621	26	20	;	;	PUNCT
app01-4621	26	21	hence	hence	ADV
app01-4621	26	22	,	,	PUNCT
app01-4621	26	23	the	the	DET
app01-4621	26	24	algorithm	algorithm	NOUN
app01-4621	26	25	generates	generate	VERB
app01-4621	26	26	stochastic	stochastic	ADJ
app01-4621	26	27	realizations	realization	NOUN
app01-4621	26	28	,	,	PUNCT
app01-4621	26	29	providing	provide	VERB
app01-4621	26	30	that	that	SCONJ
app01-4621	26	31	set	set	NOUN
app01-4621	26	32	of	of	ADP
app01-4621	26	33	tiles	tile	NOUN
app01-4621	26	34	is	be	AUX
app01-4621	26	35	rich	rich	ADJ
app01-4621	26	36	enough	enough	ADV
app01-4621	26	37	such	such	ADJ
app01-4621	26	38	that	that	DET
app01-4621	26	39	multiple	multiple	ADJ
app01-4621	26	40	tiles	tile	NOUN
app01-4621	26	41	are	be	AUX
app01-4621	26	42	admissible	admissible	ADJ
app01-4621	26	43	at	at	ADP
app01-4621	26	44	each	each	DET
app01-4621	26	45	assembly	assembly	NOUN
app01-4621	26	46	step	step	NOUN
app01-4621	26	47	;	;	PUNCT
app01-4621	26	48	see	see	VERB
app01-4621	26	49	figure	figure	NOUN
app01-4621	26	50	1	1	NUM
app01-4621	26	51	for	for	ADP
app01-4621	26	52	an	an	DET
app01-4621	26	53	illustration	illustration	NOUN
app01-4621	26	54	.	.	PUNCT
app01-4621	27	1	figure	figure	NOUN
app01-4621	27	2	1	1	NUM
app01-4621	27	3	.	.	PUNCT
app01-4621	28	1	the	the	DET
app01-4621	28	2	compressed	compress	VERB
app01-4621	28	3	microstructural	microstructural	ADJ
app01-4621	28	4	geometry	geometry	NOUN
app01-4621	28	5	represented	represent	VERB
app01-4621	28	6	with	with	ADP
app01-4621	28	7	the	the	DET
app01-4621	28	8	set	set	NOUN
app01-4621	28	9	of	of	ADP
app01-4621	28	10	wang	wang	PROPN
app01-4621	28	11	tiles	tiles	PROPN
app01-4621	28	12	(	(	PUNCT
app01-4621	28	13	top	top	NOUN
app01-4621	28	14	)	)	PUNCT
app01-4621	28	15	and	and	CCONJ
app01-4621	28	16	an	an	DET
app01-4621	28	17	illustration	illustration	NOUN
app01-4621	28	18	of	of	ADP
app01-4621	28	19	a	a	DET
app01-4621	28	20	step	step	NOUN
app01-4621	28	21	in	in	ADP
app01-4621	28	22	the	the	DET
app01-4621	28	23	tiling	tile	VERB
app01-4621	28	24	algorithm	algorithm	NOUN
app01-4621	28	25	with	with	ADP
app01-4621	28	26	partially	partially	ADV
app01-4621	28	27	assembled	assemble	VERB
app01-4621	28	28	microstructure	microstructure	NOUN
app01-4621	28	29	(	(	PUNCT
app01-4621	28	30	bottom	bottom	NOUN
app01-4621	28	31	)	)	PUNCT
app01-4621	28	32	.	.	PUNCT
app01-4621	29	1	procedures	procedure	NOUN
app01-4621	29	2	designed	design	VERB
app01-4621	29	3	to	to	PART
app01-4621	29	4	compress	compress	VERB
app01-4621	29	5	a	a	DET
app01-4621	29	6	given	give	VERB
app01-4621	29	7	microstructure	microstructure	NOUN
app01-4621	29	8	into	into	ADP
app01-4621	29	9	a	a	DET
app01-4621	29	10	sepuc	sepuc	NOUN
app01-4621	29	11	can	can	AUX
app01-4621	29	12	be	be	AUX
app01-4621	29	13	straightforwardly	straightforwardly	ADV
app01-4621	29	14	extended	extend	VERB
app01-4621	29	15	to	to	PART
app01-4621	29	16	take	take	VERB
app01-4621	29	17	into	into	ADP
app01-4621	29	18	account	account	NOUN
app01-4621	29	19	generalized	generalized	ADJ
app01-4621	29	20	periodicity	periodicity	NOUN
app01-4621	29	21	occurring	occur	VERB
app01-4621	29	22	in	in	ADP
app01-4621	29	23	the	the	DET
app01-4621	29	24	tiling	tile	VERB
app01-4621	29	25	concept	concept	NOUN
app01-4621	29	26	,	,	PUNCT
app01-4621	29	27	e.g.	e.g.	ADV
app01-4621	29	28	,	,	PUNCT
app01-4621	29	29	the	the	DET
app01-4621	29	30	standard	standard	ADJ
app01-4621	29	31	optimization	optimization	NOUN
app01-4621	29	32	procedure	procedure	NOUN
app01-4621	29	33	based	base	VERB
app01-4621	29	34	on	on	ADP
app01-4621	29	35	minimizing	minimize	VERB
app01-4621	29	36	discrepancy	discrepancy	NOUN
app01-4621	29	37	in	in	ADP
app01-4621	29	38	the	the	DET
app01-4621	29	39	two	two	NUM
app01-4621	29	40	-	-	PUNCT
app01-4621	29	41	point	point	NOUN
app01-4621	29	42	probability	probability	NOUN
app01-4621	29	43	function	function	NOUN
app01-4621	29	44	was	be	AUX
app01-4621	29	45	used	use	VERB
app01-4621	29	46	in	in	ADP
app01-4621	29	47	[	[	X
app01-4621	29	48	3	3	NUM
app01-4621	29	49	]	]	PUNCT
app01-4621	29	50	.	.	PUNCT
app01-4621	30	1	we	we	PRON
app01-4621	30	2	also	also	ADV
app01-4621	30	3	adapted	adapt	VERB
app01-4621	30	4	a	a	DET
app01-4621	30	5	sample	sample	NOUN
app01-4621	30	6	-	-	PUNCT
app01-4621	30	7	based	base	VERB
app01-4621	30	8	approach	approach	NOUN
app01-4621	30	9	originated	originate	VERB
app01-4621	30	10	in	in	ADP
app01-4621	30	11	computer	computer	NOUN
app01-4621	30	12	graphics	graphic	NOUN
app01-4621	30	13	in	in	ADP
app01-4621	30	14	order	order	NOUN
app01-4621	30	15	to	to	PART
app01-4621	30	16	address	address	VERB
app01-4621	30	17	the	the	DET
app01-4621	30	18	high	high	ADJ
app01-4621	30	19	computational	computational	ADJ
app01-4621	30	20	cost	cost	NOUN
app01-4621	30	21	of	of	ADP
app01-4621	30	22	the	the	DET
app01-4621	30	23	optimization	optimization	NOUN
app01-4621	30	24	-	-	PUNCT
app01-4621	30	25	based	base	VERB
app01-4621	30	26	design	design	NOUN
app01-4621	30	27	[	[	X
app01-4621	30	28	4	4	NUM
app01-4621	30	29	]	]	PUNCT
app01-4621	30	30	.	.	PUNCT
app01-4621	31	1	currently	currently	ADV
app01-4621	31	2	,	,	PUNCT
app01-4621	31	3	a	a	DET
app01-4621	31	4	variety	variety	NOUN
app01-4621	31	5	of	of	ADP
app01-4621	31	6	material	material	NOUN
app01-4621	31	7	microstructures	microstructure	NOUN
app01-4621	31	8	,	,	PUNCT
app01-4621	31	9	ranging	range	VERB
app01-4621	31	10	from	from	ADP
app01-4621	31	11	particulate	particulate	NOUN
app01-4621	31	12	media	medium	NOUN
app01-4621	31	13	to	to	ADP
app01-4621	31	14	complex	complex	ADJ
app01-4621	31	15	foam	foam	NOUN
app01-4621	31	16	-	-	PUNCT
app01-4621	31	17	like	like	ADJ
app01-4621	31	18	microstructures	microstructure	NOUN
app01-4621	31	19	,	,	PUNCT
app01-4621	31	20	can	can	AUX
app01-4621	31	21	be	be	AUX
app01-4621	31	22	represented	represent	VERB
app01-4621	31	23	with	with	ADP
app01-4621	31	24	the	the	DET
app01-4621	31	25	framework	framework	NOUN
app01-4621	31	26	of	of	ADP
app01-4621	31	27	wang	wang	PROPN
app01-4621	31	28	tiling	tile	VERB
app01-4621	31	29	.	.	PUNCT
app01-4621	32	1	individual	individual	ADJ
app01-4621	32	2	realizations	realization	NOUN
app01-4621	32	3	of	of	ADP
app01-4621	32	4	the	the	DET
app01-4621	32	5	microstructure	microstructure	NOUN
app01-4621	32	6	are	be	AUX
app01-4621	32	7	then	then	ADV
app01-4621	32	8	generated	generate	VERB
app01-4621	32	9	in	in	ADP
app01-4621	32	10	linear	linear	ADJ
app01-4621	32	11	time	time	NOUN
app01-4621	32	12	with	with	ADP
app01-4621	32	13	respect	respect	NOUN
app01-4621	32	14	to	to	ADP
app01-4621	32	15	the	the	DET
app01-4621	32	16	required	require	VERB
app01-4621	32	17	sample	sample	NOUN
app01-4621	32	18	size	size	NOUN
app01-4621	32	19	,	,	PUNCT
app01-4621	32	20	which	which	PRON
app01-4621	32	21	makes	make	VERB
app01-4621	32	22	the	the	DET
app01-4621	32	23	tiling	tile	VERB
app01-4621	32	24	concept	concept	NOUN
app01-4621	32	25	appealing	appeal	VERB
app01-4621	32	26	for	for	ADP
app01-4621	32	27	applications	application	NOUN
app01-4621	32	28	where	where	SCONJ
app01-4621	32	29	multiple	multiple	ADJ
app01-4621	32	30	microstructure	microstructure	ADJ
app01-4621	32	31	samples	sample	NOUN
app01-4621	32	32	are	be	AUX
app01-4621	32	33	required	require	VERB
app01-4621	32	34	,	,	PUNCT
app01-4621	32	35	e.g.	e.g.	ADV
app01-4621	32	36	,	,	PUNCT
app01-4621	32	37	investigation	investigation	NOUN
app01-4621	32	38	of	of	ADP
app01-4621	32	39	the	the	DET
app01-4621	32	40	rve	rve	PROPN
app01-4621	32	41	size	size	NOUN
app01-4621	32	42	[	[	X
app01-4621	32	43	8	8	NUM
app01-4621	32	44	]	]	PUNCT
app01-4621	32	45	.	.	PUNCT
app01-4621	33	1	3	3	X
app01-4621	33	2	.	.	NUM
app01-4621	33	3	synthesized	synthesize	VERB
app01-4621	33	4	enrichments	enrichment	NOUN
app01-4621	33	5	fields	field	VERB
app01-4621	33	6	the	the	DET
app01-4621	33	7	idea	idea	NOUN
app01-4621	33	8	of	of	ADP
app01-4621	33	9	compressing	compress	VERB
app01-4621	33	10	fluctuation	fluctuation	NOUN
app01-4621	33	11	fields	field	NOUN
app01-4621	33	12	using	use	VERB
app01-4621	33	13	the	the	DET
app01-4621	33	14	wang	wang	NOUN
app01-4621	33	15	tiling	tile	VERB
app01-4621	33	16	concept	concept	NOUN
app01-4621	33	17	has	have	AUX
app01-4621	33	18	been	be	AUX
app01-4621	33	19	introduced	introduce	VERB
app01-4621	33	20	in	in	ADP
app01-4621	33	21	novák	novák	NOUN
app01-4621	33	22	et	et	PROPN
app01-4621	33	23	al	al	PROPN
app01-4621	33	24	.	.	PUNCT
app01-4621	34	1	[	[	X
app01-4621	34	2	9	9	NUM
app01-4621	34	3	]	]	PUNCT
app01-4621	34	4	,	,	PUNCT
app01-4621	34	5	where	where	SCONJ
app01-4621	34	6	the	the	DET
app01-4621	34	7	microstructural	microstructural	ADJ
app01-4621	34	8	geometry	geometry	NOUN
app01-4621	34	9	of	of	ADP
app01-4621	34	10	individual	individual	ADJ
app01-4621	34	11	tiles	tile	NOUN
app01-4621	34	12	was	be	AUX
app01-4621	34	13	optimized	optimize	VERB
app01-4621	34	14	with	with	ADP
app01-4621	34	15	respect	respect	NOUN
app01-4621	34	16	to	to	ADP
app01-4621	34	17	(	(	PUNCT
app01-4621	34	18	i	i	NOUN
app01-4621	34	19	)	)	PUNCT
app01-4621	34	20	meeting	meet	VERB
app01-4621	34	21	prescribed	prescribe	VERB
app01-4621	34	22	spatial	spatial	ADJ
app01-4621	34	23	statistics	statistic	NOUN
app01-4621	34	24	and	and	CCONJ
app01-4621	34	25	(	(	PUNCT
app01-4621	34	26	ii	ii	NOUN
app01-4621	34	27	)	)	PUNCT
app01-4621	34	28	minimizing	minimize	VERB
app01-4621	34	29	traction	traction	ADJ
app01-4621	34	30	discrepancies	discrepancy	NOUN
app01-4621	34	31	among	among	ADP
app01-4621	34	32	congruent	congruent	ADJ
app01-4621	34	33	edges	edge	NOUN
app01-4621	34	34	in	in	ADP
app01-4621	34	35	an	an	DET
app01-4621	34	36	auxiliary	auxiliary	ADJ
app01-4621	34	37	tiling	tiling	NOUN
app01-4621	34	38	.	.	PUNCT
app01-4621	35	1	however	however	ADV
app01-4621	35	2	,	,	PUNCT
app01-4621	35	3	the	the	DET
app01-4621	35	4	resulting	result	VERB
app01-4621	35	5	synthesized	synthesize	VERB
app01-4621	35	6	stress	stress	NOUN
app01-4621	35	7	fields	field	NOUN
app01-4621	35	8	exhibited	exhibit	VERB
app01-4621	35	9	unavoidable	unavoidable	ADJ
app01-4621	35	10	discontinuities	discontinuity	NOUN
app01-4621	35	11	and	and	CCONJ
app01-4621	35	12	the	the	DET
app01-4621	35	13	objective	objective	ADJ
app01-4621	35	14	function	function	NOUN
app01-4621	35	15	required	require	VERB
app01-4621	35	16	careful	careful	ADJ
app01-4621	35	17	tuning	tuning	NOUN
app01-4621	35	18	of	of	ADP
app01-4621	35	19	weight	weight	NOUN
app01-4621	35	20	parameters	parameter	NOUN
app01-4621	35	21	because	because	SCONJ
app01-4621	35	22	the	the	DET
app01-4621	35	23	two	two	NUM
app01-4621	35	24	requirements	requirement	NOUN
app01-4621	35	25	turned	turn	VERB
app01-4621	35	26	to	to	PART
app01-4621	35	27	be	be	AUX
app01-4621	35	28	hard	hard	ADJ
app01-4621	35	29	to	to	PART
app01-4621	35	30	achieve	achieve	VERB
app01-4621	35	31	simultaneously	simultaneously	ADV
app01-4621	35	32	.	.	PUNCT
app01-4621	36	1	in	in	ADP
app01-4621	36	2	contrast	contrast	NOUN
app01-4621	36	3	,	,	PUNCT
app01-4621	36	4	the	the	DET
app01-4621	36	5	present	present	ADJ
app01-4621	36	6	method	method	NOUN
app01-4621	36	7	generates	generate	VERB
app01-4621	36	8	continuous	continuous	ADJ
app01-4621	36	9	fields	field	NOUN
app01-4621	36	10	of	of	ADP
app01-4621	36	11	the	the	DET
app01-4621	36	12	primal	primal	ADJ
app01-4621	36	13	unknowns	unknown	NOUN
app01-4621	36	14	for	for	ADP
app01-4621	36	15	any	any	DET
app01-4621	36	16	existing	exist	VERB
app01-4621	36	17	microstructure	microstructure	ADJ
app01-4621	36	18	compression	compression	NOUN
app01-4621	36	19	.	.	PUNCT
app01-4621	37	1	we	we	PRON
app01-4621	37	2	illustrate	illustrate	VERB
app01-4621	37	3	the	the	DET
app01-4621	37	4	methodology	methodology	NOUN
app01-4621	37	5	with	with	ADP
app01-4621	37	6	the	the	DET
app01-4621	37	7	steady	steady	ADJ
app01-4621	37	8	-	-	PUNCT
app01-4621	37	9	state	state	NOUN
app01-4621	37	10	heat	heat	NOUN
app01-4621	37	11	conduction	conduction	NOUN
app01-4621	37	12	problem	problem	NOUN
app01-4621	37	13	,	,	PUNCT
app01-4621	37	14	governed	govern	VERB
app01-4621	37	15	by	by	ADP
app01-4621	37	16	∇	∇	X
app01-4621	37	17	·	·	PUNCT
app01-4621	37	18	(	(	PUNCT
app01-4621	37	19	−k(x	−k(x	PROPN
app01-4621	37	20	)	)	PUNCT
app01-4621	37	21	·	·	PUNCT
app01-4621	37	22	∇θ(x	∇θ(x	NOUN
app01-4621	37	23	)	)	PUNCT
app01-4621	37	24	)	)	PUNCT
app01-4621	38	1	=	=	SYM
app01-4621	38	2	0	0	PUNCT
app01-4621	38	3	,	,	PUNCT
app01-4621	38	4	x	x	PUNCT
app01-4621	38	5	∈	∈	PROPN
app01-4621	38	6	ω	ω	NUM
app01-4621	38	7	,	,	PUNCT
app01-4621	38	8	(	(	PUNCT
app01-4621	38	9	1	1	X
app01-4621	38	10	)	)	PUNCT
app01-4621	38	11	where	where	SCONJ
app01-4621	38	12	θ	θ	PROPN
app01-4621	38	13	denotes	denote	VERB
app01-4621	38	14	the	the	DET
app01-4621	38	15	unknown	unknown	ADJ
app01-4621	38	16	temperature	temperature	NOUN
app01-4621	38	17	field	field	NOUN
app01-4621	38	18	,	,	PUNCT
app01-4621	38	19	k	k	PROPN
app01-4621	38	20	is	be	AUX
app01-4621	38	21	a	a	DET
app01-4621	38	22	local	local	ADJ
app01-4621	38	23	heat	heat	NOUN
app01-4621	38	24	conductivity	conductivity	NOUN
app01-4621	38	25	tensor	tensor	NOUN
app01-4621	38	26	and	and	CCONJ
app01-4621	38	27	no	no	DET
app01-4621	38	28	heat	heat	NOUN
app01-4621	38	29	sources	source	NOUN
app01-4621	38	30	are	be	AUX
app01-4621	38	31	considered	consider	VERB
app01-4621	38	32	.	.	PUNCT
app01-4621	39	1	first	first	ADV
app01-4621	39	2	,	,	PUNCT
app01-4621	39	3	we	we	PRON
app01-4621	39	4	assume	assume	VERB
app01-4621	39	5	the	the	DET
app01-4621	39	6	decomposition	decomposition	NOUN
app01-4621	39	7	of	of	ADP
app01-4621	39	8	θ	θ	PROPN
app01-4621	39	9	into	into	ADP
app01-4621	39	10	a	a	DET
app01-4621	39	11	fluctuation	fluctuation	NOUN
app01-4621	39	12	part	part	NOUN
app01-4621	39	13	θ̃	θ̃	PROPN
app01-4621	39	14	,	,	PUNCT
app01-4621	39	15	caused	cause	VERB
app01-4621	39	16	by	by	ADP
app01-4621	39	17	the	the	DET
app01-4621	39	18	presence	presence	NOUN
app01-4621	39	19	of	of	ADP
app01-4621	39	20	heterogeneities	heterogeneity	NOUN
app01-4621	39	21	,	,	PUNCT
app01-4621	39	22	and	and	CCONJ
app01-4621	39	23	a	a	DET
app01-4621	39	24	macroscopic	macroscopic	ADJ
app01-4621	39	25	part	part	NOUN
app01-4621	39	26	controlled	control	VERB
app01-4621	39	27	with	with	ADP
app01-4621	39	28	a	a	DET
app01-4621	39	29	macroscopic	macroscopic	ADJ
app01-4621	39	30	temperature	temperature	NOUN
app01-4621	39	31	gradient	gradient	NOUN
app01-4621	39	32	h	h	NOUN
app01-4621	39	33	,	,	PUNCT
app01-4621	39	34	θ(x	θ(x	PROPN
app01-4621	39	35	)	)	PUNCT
app01-4621	39	36	=	=	SYM
app01-4621	39	37	θ̃(x	θ̃(x	NOUN
app01-4621	39	38	)	)	PUNCT
app01-4621	40	1	+	+	NUM
app01-4621	40	2	h	h	NOUN
app01-4621	40	3	·	·	PUNCT
app01-4621	40	4	x	x	SYM
app01-4621	40	5	,	,	PUNCT
app01-4621	40	6	∀x	∀x	X
app01-4621	40	7	∈	∈	PROPN
app01-4621	40	8	t(i),∀t(i	t(i),∀t(i	NOUN
app01-4621	40	9	)	)	PUNCT
app01-4621	41	1	∈	∈	PROPN
app01-4621	41	2	s	s	PROPN
app01-4621	41	3	,	,	PUNCT
app01-4621	41	4	(	(	PUNCT
app01-4621	41	5	2	2	X
app01-4621	41	6	)	)	PUNCT
app01-4621	41	7	where	where	SCONJ
app01-4621	41	8	t(i	t(i	NOUN
app01-4621	41	9	)	)	PUNCT
app01-4621	41	10	denotes	denote	VERB
app01-4621	41	11	the	the	DET
app01-4621	41	12	domain	domain	NOUN
app01-4621	41	13	of	of	ADP
app01-4621	41	14	the	the	DET
app01-4621	41	15	i	i	PROPN
app01-4621	41	16	-	-	PUNCT
app01-4621	41	17	th	th	X
app01-4621	41	18	tile	tile	NOUN
app01-4621	41	19	and	and	CCONJ
app01-4621	41	20	s	s	NOUN
app01-4621	41	21	=	=	NOUN
app01-4621	41	22	{	{	PUNCT
app01-4621	41	23	t(i	t(i	PROPN
app01-4621	41	24	)	)	PUNCT
app01-4621	41	25	,	,	PUNCT
app01-4621	41	26	i	i	PRON
app01-4621	41	27	=	=	NOUN
app01-4621	41	28	1	1	X
app01-4621	41	29	.	.	PUNCT
app01-4621	41	30	.	.	PUNCT
app01-4621	41	31	.	.	PUNCT
app01-4621	42	1	nt	not	PART
app01-4621	42	2	}	}	PUNCT
app01-4621	42	3	represent	represent	VERB
app01-4621	42	4	the	the	DET
app01-4621	42	5	set	set	NOUN
app01-4621	42	6	of	of	ADP
app01-4621	42	7	nt	not	PART
app01-4621	42	8	available	available	ADJ
app01-4621	42	9	tiles	tile	NOUN
app01-4621	42	10	.	.	PUNCT
app01-4621	43	1	without	without	ADP
app01-4621	43	2	loss	loss	NOUN
app01-4621	43	3	of	of	ADP
app01-4621	43	4	generality	generality	NOUN
app01-4621	43	5	,	,	PUNCT
app01-4621	43	6	each	each	DET
app01-4621	43	7	tile	tile	NOUN
app01-4621	43	8	is	be	AUX
app01-4621	43	9	assumed	assume	VERB
app01-4621	43	10	centred	centre	VERB
app01-4621	43	11	,	,	PUNCT
app01-4621	43	12	i.e.	i.e.	X
app01-4621	43	13	,	,	PUNCT
app01-4621	43	14	t(i	t(i	NUM
app01-4621	43	15	)	)	PUNCT
app01-4621	44	1	=	=	PUNCT
app01-4621	45	1	[	[	X
app01-4621	45	2	−α	−α	NOUN
app01-4621	45	3	,	,	PUNCT
app01-4621	45	4	α]2	α]2	PROPN
app01-4621	45	5	,	,	PUNCT
app01-4621	45	6	where	where	SCONJ
app01-4621	45	7	2α	2α	NOUN
app01-4621	45	8	is	be	AUX
app01-4621	45	9	the	the	DET
app01-4621	45	10	size	size	NOUN
app01-4621	45	11	of	of	ADP
app01-4621	45	12	the	the	DET
app01-4621	45	13	tile	tile	NOUN
app01-4621	45	14	edge	edge	NOUN
app01-4621	45	15	.	.	PUNCT
app01-4621	46	1	in	in	ADP
app01-4621	46	2	order	order	NOUN
app01-4621	46	3	to	to	PART
app01-4621	46	4	enforce	enforce	VERB
app01-4621	46	5	continuity	continuity	NOUN
app01-4621	46	6	of	of	ADP
app01-4621	46	7	the	the	DET
app01-4621	46	8	extracted	extract	VERB
app01-4621	46	9	fields	field	NOUN
app01-4621	46	10	,	,	PUNCT
app01-4621	46	11	all	all	DET
app01-4621	46	12	tiles	tile	NOUN
app01-4621	46	13	are	be	AUX
app01-4621	46	14	loaded	load	VERB
app01-4621	46	15	with	with	ADP
app01-4621	46	16	the	the	DET
app01-4621	46	17	prescribed	prescribed	ADJ
app01-4621	46	18	macroscopic	macroscopic	ADJ
app01-4621	46	19	gradient	gradient	NOUN
app01-4621	46	20	h	h	NOUN
app01-4621	46	21	and	and	CCONJ
app01-4621	46	22	solved	solve	VERB
app01-4621	46	23	simultaneously	simultaneously	ADV
app01-4621	46	24	.	.	PUNCT
app01-4621	47	1	providing	provide	VERB
app01-4621	47	2	that	that	SCONJ
app01-4621	47	3	the	the	DET
app01-4621	47	4	tile	tile	NOUN
app01-4621	47	5	geometries	geometry	NOUN
app01-4621	47	6	are	be	AUX
app01-4621	47	7	discretized	discretize	VERB
app01-4621	47	8	with	with	ADP
app01-4621	47	9	a	a	DET
app01-4621	47	10	compatible	compatible	ADJ
app01-4621	47	11	triangulation	triangulation	NOUN
app01-4621	47	12	—	—	PUNCT
app01-4621	47	13	meaning	mean	VERB
app01-4621	47	14	that	that	SCONJ
app01-4621	47	15	discretization	discretization	NOUN
app01-4621	47	16	of	of	ADP
app01-4621	47	17	the	the	DET
app01-4621	47	18	corresponding	correspond	VERB
app01-4621	47	19	tile	tile	NOUN
app01-4621	47	20	edges	edge	NOUN
app01-4621	47	21	is	be	AUX
app01-4621	47	22	the	the	DET
app01-4621	47	23	same	same	ADJ
app01-4621	47	24	across	across	ADP
app01-4621	47	25	all	all	DET
app01-4621	47	26	tiles	tile	NOUN
app01-4621	47	27	—	—	PUNCT
app01-4621	47	28	the	the	DET
app01-4621	47	29	continuity	continuity	NOUN
app01-4621	47	30	is	be	AUX
app01-4621	47	31	ensured	ensure	VERB
app01-4621	47	32	by	by	ADP
app01-4621	47	33	associating	associate	VERB
app01-4621	47	34	the	the	DET
app01-4621	47	35	corresponding	corresponding	ADJ
app01-4621	47	36	edge	edge	NOUN
app01-4621	47	37	unknowns	unknown	NOUN
app01-4621	47	38	during	during	ADP
app01-4621	47	39	the	the	DET
app01-4621	47	40	localization	localization	NOUN
app01-4621	47	41	of	of	ADP
app01-4621	47	42	an	an	DET
app01-4621	47	43	element	element	ADJ
app01-4621	47	44	contribution	contribution	NOUN
app01-4621	47	45	into	into	ADP
app01-4621	47	46	the	the	DET
app01-4621	47	47	conductivity	conductivity	NOUN
app01-4621	47	48	matrix	matrix	NOUN
app01-4621	47	49	of	of	ADP
app01-4621	47	50	the	the	DET
app01-4621	47	51	whole	whole	ADJ
app01-4621	47	52	set	set	NOUN
app01-4621	47	53	.	.	PUNCT
app01-4621	48	1	the	the	DET
app01-4621	48	2	resulting	result	VERB
app01-4621	48	3	system	system	NOUN
app01-4621	48	4	takes	take	VERB
app01-4621	48	5	the	the	DET
app01-4621	48	6	standard	standard	ADJ
app01-4621	48	7	form	form	NOUN
app01-4621	48	8	ks	ks	NOUN
app01-4621	48	9	θ̃	θ̃	NOUN
app01-4621	48	10	=	=	PUNCT
app01-4621	49	1	f	f	PROPN
app01-4621	49	2	(	(	PUNCT
app01-4621	49	3	h	h	NOUN
app01-4621	49	4	)	)	PUNCT
app01-4621	49	5	,	,	PUNCT
app01-4621	49	6	(	(	PUNCT
app01-4621	49	7	3	3	X
app01-4621	49	8	)	)	PUNCT
app01-4621	49	9	where	where	SCONJ
app01-4621	49	10	ks	k	NOUN
app01-4621	49	11	=	=	SYM
app01-4621	49	12	at(i)∈s	at(i)∈s	PROPN
app01-4621	49	13	kt(i	kt(i	PUNCT
app01-4621	49	14	)	)	PUNCT
app01-4621	49	15	is	be	AUX
app01-4621	49	16	the	the	DET
app01-4621	49	17	conductivity	conductivity	NOUN
app01-4621	49	18	matrix	matrix	NOUN
app01-4621	49	19	and	and	CCONJ
app01-4621	49	20	f	f	PROPN
app01-4621	49	21	(	(	PUNCT
app01-4621	49	22	h	h	NOUN
app01-4621	49	23	)	)	PUNCT
app01-4621	49	24	is	be	AUX
app01-4621	49	25	a	a	DET
app01-4621	49	26	h	h	NOUN
app01-4621	49	27	-	-	PUNCT
app01-4621	49	28	dependent	dependent	ADJ
app01-4621	49	29	loading	loading	NOUN
app01-4621	49	30	vector	vector	NOUN
app01-4621	49	31	arising	arise	VERB
app01-4621	49	32	from	from	ADP
app01-4621	49	33	the	the	DET
app01-4621	49	34	weak	weak	ADJ
app01-4621	49	35	form	form	NOUN
app01-4621	49	36	after	after	ADP
app01-4621	49	37	plugging	plug	VERB
app01-4621	49	38	eq	eq	NOUN
app01-4621	49	39	.	.	PUNCT
app01-4621	50	1	(	(	PUNCT
app01-4621	50	2	2	2	NUM
app01-4621	50	3	)	)	PUNCT
app01-4621	50	4	into	into	ADP
app01-4621	50	5	eq	eq	NOUN
app01-4621	50	6	.	.	PUNCT
app01-4621	51	1	(	(	PUNCT
app01-4621	51	2	1	1	NUM
app01-4621	51	3	)	)	PUNCT
app01-4621	51	4	.	.	PUNCT
app01-4621	52	1	ks	ks	PROPN
app01-4621	52	2	has	have	VERB
app01-4621	52	3	block	block	NOUN
app01-4621	52	4	-	-	PUNCT
app01-4621	52	5	diagonal	diagonal	ADJ
app01-4621	52	6	structure	structure	NOUN
app01-4621	52	7	similar	similar	ADJ
app01-4621	52	8	to	to	ADP
app01-4621	52	9	primal	primal	ADJ
app01-4621	52	10	domain	domain	NOUN
app01-4621	52	11	decomposition	decomposition	NOUN
app01-4621	52	12	approaches	approach	NOUN
app01-4621	52	13	.	.	PUNCT
app01-4621	53	1	in	in	ADP
app01-4621	53	2	addition	addition	NOUN
app01-4621	53	3	,	,	PUNCT
app01-4621	53	4	two	two	NUM
app01-4621	53	5	types	type	NOUN
app01-4621	53	6	of	of	ADP
app01-4621	53	7	constraints	constraint	NOUN
app01-4621	53	8	are	be	AUX
app01-4621	53	9	imposed	impose	VERB
app01-4621	53	10	on	on	ADP
app01-4621	53	11	the	the	DET
app01-4621	53	12	set	set	NOUN
app01-4621	53	13	system	system	NOUN
app01-4621	53	14	.	.	PUNCT
app01-4621	54	1	first	first	ADV
app01-4621	54	2	,	,	PUNCT
app01-4621	54	3	we	we	PRON
app01-4621	54	4	eliminate	eliminate	VERB
app01-4621	54	5	zero	zero	NUM
app01-4621	54	6	-	-	PUNCT
app01-4621	54	7	energy	energy	NOUN
app01-4621	54	8	modes	mode	NOUN
app01-4621	54	9	of	of	ADP
app01-4621	54	10	ks	ks	PROPN
app01-4621	54	11	by	by	ADP
app01-4621	54	12	requirement	requirement	NOUN
app01-4621	54	13	1	1	NUM
app01-4621	54	14	|s|	|s|	PROPN
app01-4621	54	15	∫	∫	PROPN
app01-4621	54	16	s	s	PART
app01-4621	54	17	θ̃(x	θ̃(x	PROPN
app01-4621	54	18	)	)	PUNCT
app01-4621	54	19	dx	dx	PROPN
app01-4621	55	1	=	=	SYM
app01-4621	55	2	0	0	PROPN
app01-4621	55	3	.	.	PUNCT
app01-4621	56	1	(	(	PUNCT
app01-4621	56	2	4	4	X
app01-4621	56	3	)	)	PUNCT
app01-4621	56	4	the	the	DET
app01-4621	56	5	second	second	ADJ
app01-4621	56	6	constraint	constraint	NOUN
app01-4621	56	7	prevents	prevent	VERB
app01-4621	56	8	the	the	DET
app01-4621	56	9	fluctuation	fluctuation	NOUN
app01-4621	56	10	field	field	NOUN
app01-4621	56	11	θ̃	θ̃	NOUN
app01-4621	56	12	from	from	ADP
app01-4621	56	13	compensating	compensate	VERB
app01-4621	56	14	for	for	ADP
app01-4621	56	15	the	the	DET
app01-4621	56	16	loading	loading	NOUN
app01-4621	56	17	induced	induce	VERB
app01-4621	56	18	through	through	ADP
app01-4621	56	19	h	h	NOUN
app01-4621	56	20	.	.	PUNCT
app01-4621	57	1	30	30	NUM
app01-4621	57	2	vol	vol	NOUN
app01-4621	57	3	.	.	PUNCT
app01-4621	58	1	13/2017	13/2017	NUM
app01-4621	58	2	synthesized	synthesize	VERB
app01-4621	58	3	microstructure	microstructure	NOUN
app01-4621	58	4	-	-	PUNCT
app01-4621	58	5	informed	inform	VERB
app01-4621	58	6	enrichments	enrichment	NOUN
app01-4621	58	7	for	for	ADP
app01-4621	58	8	xfem	xfem	PROPN
app01-4621	58	9	analyses	analysis	NOUN
app01-4621	58	10	inspired	inspire	VERB
app01-4621	58	11	in	in	ADP
app01-4621	58	12	numerical	numerical	ADJ
app01-4621	58	13	homogenization	homogenization	NOUN
app01-4621	58	14	,	,	PUNCT
app01-4621	58	15	e.g.	e.g.	ADV
app01-4621	58	16	[	[	X
app01-4621	58	17	2	2	NUM
app01-4621	58	18	]	]	PUNCT
app01-4621	58	19	,	,	PUNCT
app01-4621	58	20	we	we	PRON
app01-4621	58	21	introduce	introduce	VERB
app01-4621	58	22	the	the	DET
app01-4621	58	23	second	second	ADJ
app01-4621	58	24	constraint	constraint	NOUN
app01-4621	58	25	enforcing	enforce	VERB
app01-4621	58	26	1	1	NUM
app01-4621	58	27	|ω|	|ω|	NUM
app01-4621	58	28	∫	∫	PROPN
app01-4621	58	29	ω	ω	PROPN
app01-4621	58	30	∇θ̃(x	∇θ̃(x	PROPN
app01-4621	58	31	)	)	PUNCT
app01-4621	58	32	dx	dx	PROPN
app01-4621	59	1	=	=	SYM
app01-4621	59	2	0	0	NUM
app01-4621	59	3	(	(	PUNCT
app01-4621	59	4	5	5	NUM
app01-4621	59	5	)	)	PUNCT
app01-4621	59	6	in	in	ADP
app01-4621	59	7	a	a	DET
app01-4621	59	8	chosen	choose	VERB
app01-4621	59	9	domain	domain	NOUN
app01-4621	59	10	ω	ω	X
app01-4621	59	11	loaded	load	VERB
app01-4621	59	12	analogously	analogously	ADV
app01-4621	59	13	to	to	ADP
app01-4621	59	14	eq	eq	PROPN
app01-4621	59	15	.	.	PUNCT
app01-4621	59	16	(	(	PUNCT
app01-4621	59	17	2	2	NUM
app01-4621	59	18	)	)	PUNCT
app01-4621	59	19	.	.	PUNCT
app01-4621	60	1	using	use	VERB
app01-4621	60	2	green	green	PROPN
app01-4621	60	3	’s	’s	PART
app01-4621	60	4	first	first	ADJ
app01-4621	60	5	identity	identity	NOUN
app01-4621	60	6	,	,	PUNCT
app01-4621	60	7	eq	eq	NOUN
app01-4621	60	8	.	.	PUNCT
app01-4621	61	1	(	(	PUNCT
app01-4621	61	2	5	5	X
app01-4621	61	3	)	)	PUNCT
app01-4621	61	4	can	can	AUX
app01-4621	61	5	be	be	AUX
app01-4621	61	6	recast	recast	VERB
app01-4621	61	7	into	into	ADP
app01-4621	61	8	a	a	DET
app01-4621	61	9	boundary	boundary	ADJ
app01-4621	61	10	integral∫	integral∫	NOUN
app01-4621	61	11	∂ω	∂ω	ADJ
app01-4621	61	12	θ̃(x)n(x	θ̃(x)n(x	X
app01-4621	61	13	)	)	PUNCT
app01-4621	61	14	ds	ds	NOUN
app01-4621	61	15	=	=	SYM
app01-4621	61	16	0	0	NUM
app01-4621	61	17	,	,	PUNCT
app01-4621	61	18	(	(	PUNCT
app01-4621	61	19	6	6	NUM
app01-4621	61	20	)	)	PUNCT
app01-4621	61	21	where	where	SCONJ
app01-4621	61	22	n(x	n(x	NOUN
app01-4621	61	23	)	)	PUNCT
app01-4621	61	24	denotes	denote	VERB
app01-4621	61	25	the	the	DET
app01-4621	61	26	outer	outer	ADJ
app01-4621	61	27	normal	normal	ADJ
app01-4621	61	28	of	of	ADP
app01-4621	61	29	the	the	DET
app01-4621	61	30	boundary	boundary	NOUN
app01-4621	61	31	.	.	PUNCT
app01-4621	62	1	in	in	ADP
app01-4621	62	2	particular	particular	ADJ
app01-4621	62	3	,	,	PUNCT
app01-4621	62	4	we	we	PRON
app01-4621	62	5	consider	consider	VERB
app01-4621	62	6	three	three	NUM
app01-4621	62	7	mutually	mutually	ADV
app01-4621	62	8	exclusive	exclusive	ADJ
app01-4621	62	9	types	type	NOUN
app01-4621	62	10	of	of	ADP
app01-4621	62	11	the	the	DET
app01-4621	62	12	second	second	ADJ
app01-4621	62	13	constraint	constraint	NOUN
app01-4621	62	14	:	:	PUNCT
app01-4621	62	15	(	(	PUNCT
app01-4621	62	16	k	k	X
app01-4621	62	17	)	)	PUNCT
app01-4621	62	18	the	the	DET
app01-4621	62	19	first	first	ADJ
app01-4621	62	20	type	type	NOUN
app01-4621	62	21	prescribes	prescribe	VERB
app01-4621	62	22	zero	zero	NUM
app01-4621	62	23	temperature	temperature	NOUN
app01-4621	62	24	fluctuations	fluctuation	NOUN
app01-4621	62	25	at	at	ADP
app01-4621	62	26	tile	tile	NOUN
app01-4621	62	27	boundaries	boundary	NOUN
app01-4621	62	28	,	,	PUNCT
app01-4621	62	29	θ̃|∂t(i	θ̃|∂t(i	NOUN
app01-4621	62	30	)	)	PUNCT
app01-4621	62	31	=	=	SYM
app01-4621	62	32	0	0	NUM
app01-4621	62	33	,	,	PUNCT
app01-4621	62	34	∀i	∀i	NOUN
app01-4621	62	35	=	=	SYM
app01-4621	62	36	1	1	NUM
app01-4621	62	37	.	.	PUNCT
app01-4621	62	38	.	.	PUNCT
app01-4621	62	39	.	.	PUNCT
app01-4621	63	1	nt	not	PART
app01-4621	63	2	,	,	PUNCT
app01-4621	63	3	(	(	PUNCT
app01-4621	63	4	7	7	X
app01-4621	63	5	)	)	PUNCT
app01-4621	63	6	where	where	SCONJ
app01-4621	63	7	∂t(i	∂t(i	PROPN
app01-4621	63	8	)	)	PUNCT
app01-4621	63	9	stands	stand	VERB
app01-4621	63	10	for	for	ADP
app01-4621	63	11	the	the	DET
app01-4621	63	12	boundary	boundary	NOUN
app01-4621	63	13	of	of	ADP
app01-4621	63	14	the	the	DET
app01-4621	63	15	i	i	PROPN
app01-4621	63	16	-	-	PUNCT
app01-4621	63	17	th	th	VERB
app01-4621	63	18	tile	tile	NOUN
app01-4621	63	19	.	.	PUNCT
app01-4621	64	1	(	(	PUNCT
app01-4621	64	2	p	p	X
app01-4621	64	3	)	)	PUNCT
app01-4621	64	4	in	in	ADP
app01-4621	64	5	the	the	DET
app01-4621	64	6	second	second	ADJ
app01-4621	64	7	type	type	NOUN
app01-4621	64	8	,	,	PUNCT
app01-4621	64	9	the	the	DET
app01-4621	64	10	requirement	requirement	NOUN
app01-4621	64	11	(	(	PUNCT
app01-4621	64	12	6	6	NUM
app01-4621	64	13	)	)	PUNCT
app01-4621	64	14	is	be	AUX
app01-4621	64	15	posed	pose	VERB
app01-4621	64	16	tile	tile	NOUN
app01-4621	64	17	-	-	PUNCT
app01-4621	64	18	wise	wise	ADJ
app01-4621	64	19	,	,	PUNCT
app01-4621	64	20	i.e.	i.e.	X
app01-4621	64	21	,∫	,∫	PUNCT
app01-4621	64	22	∂t(i	∂t(i	NUM
app01-4621	64	23	)	)	PUNCT
app01-4621	64	24	θ̃(x)n(x	θ̃(x)n(x	X
app01-4621	64	25	)	)	PUNCT
app01-4621	64	26	ds	ds	NOUN
app01-4621	64	27	=	=	SYM
app01-4621	64	28	0	0	NUM
app01-4621	64	29	,	,	PUNCT
app01-4621	64	30	∀i	∀i	NOUN
app01-4621	64	31	=	=	SYM
app01-4621	64	32	1	1	NUM
app01-4621	64	33	.	.	PUNCT
app01-4621	64	34	.	.	PUNCT
app01-4621	64	35	.	.	PUNCT
app01-4621	65	1	nt	nt	INTJ
app01-4621	65	2	.	.	PUNCT
app01-4621	66	1	(	(	PUNCT
app01-4621	66	2	8)	8)	NUM
app01-4621	66	3	(	(	PUNCT
app01-4621	66	4	s	s	NOUN
app01-4621	66	5	)	)	PUNCT
app01-4621	66	6	the	the	DET
app01-4621	66	7	last	last	ADJ
app01-4621	66	8	type	type	NOUN
app01-4621	66	9	imposes	impose	VERB
app01-4621	66	10	eq	eq	ADJ
app01-4621	66	11	.	.	PUNCT
app01-4621	67	1	(	(	PUNCT
app01-4621	67	2	6	6	NUM
app01-4621	67	3	)	)	PUNCT
app01-4621	67	4	over	over	ADP
app01-4621	67	5	the	the	DET
app01-4621	67	6	whole	whole	NOUN
app01-4621	67	7	set,∫	set,∫	PROPN
app01-4621	67	8	∂s	∂s	PROPN
app01-4621	68	1	θ̃(x)n(x	θ̃(x)n(x	X
app01-4621	68	2	)	)	PUNCT
app01-4621	68	3	ds	ds	NOUN
app01-4621	68	4	=	=	SYM
app01-4621	68	5	0	0	NUM
app01-4621	68	6	,	,	PUNCT
app01-4621	68	7	(	(	PUNCT
app01-4621	68	8	9	9	NUM
app01-4621	68	9	)	)	PUNCT
app01-4621	69	1	where	where	SCONJ
app01-4621	69	2	∂s	∂s	PROPN
app01-4621	69	3	=	=	PUNCT
app01-4621	69	4	{	{	PUNCT
app01-4621	69	5	∂t(i	∂t(i	PROPN
app01-4621	69	6	)	)	PUNCT
app01-4621	69	7	,	,	PUNCT
app01-4621	69	8	i	i	PRON
app01-4621	69	9	=	=	NOUN
app01-4621	69	10	1	1	X
app01-4621	69	11	.	.	PUNCT
app01-4621	69	12	.	.	PUNCT
app01-4621	69	13	.	.	PUNCT
app01-4621	70	1	nt	not	PART
app01-4621	70	2	}	}	PUNCT
app01-4621	70	3	.	.	PUNCT
app01-4621	71	1	note	note	VERB
app01-4621	71	2	that	that	SCONJ
app01-4621	71	3	(	(	PUNCT
app01-4621	71	4	k	k	X
app01-4621	71	5	)	)	PUNCT
app01-4621	71	6	corresponds	correspond	VERB
app01-4621	71	7	directly	directly	ADV
app01-4621	71	8	to	to	PART
app01-4621	71	9	kinematic	kinematic	VERB
app01-4621	71	10	uniform	uniform	ADJ
app01-4621	71	11	boundary	boundary	ADJ
app01-4621	71	12	conditions	condition	NOUN
app01-4621	71	13	used	use	VERB
app01-4621	71	14	in	in	ADP
app01-4621	71	15	numerical	numerical	ADJ
app01-4621	71	16	homogenization	homogenization	NOUN
app01-4621	71	17	,	,	PUNCT
app01-4621	71	18	while	while	SCONJ
app01-4621	71	19	(	(	PUNCT
app01-4621	71	20	p	p	NOUN
app01-4621	71	21	)	)	PUNCT
app01-4621	71	22	and	and	CCONJ
app01-4621	71	23	(	(	PUNCT
app01-4621	71	24	s	s	X
app01-4621	71	25	)	)	PUNCT
app01-4621	71	26	mimic	mimic	ADJ
app01-4621	71	27	periodic	periodic	ADJ
app01-4621	71	28	and	and	CCONJ
app01-4621	71	29	statically	statically	ADV
app01-4621	71	30	uniform	uniform	ADJ
app01-4621	71	31	boundary	boundary	ADJ
app01-4621	71	32	conditions	condition	NOUN
app01-4621	71	33	,	,	PUNCT
app01-4621	71	34	respectively	respectively	ADV
app01-4621	71	35	.	.	PUNCT
app01-4621	72	1	instead	instead	ADV
app01-4621	72	2	of	of	ADP
app01-4621	72	3	eq	eq	NOUN
app01-4621	72	4	.	.	PUNCT
app01-4621	73	1	(	(	PUNCT
app01-4621	73	2	3	3	NUM
app01-4621	73	3	)	)	PUNCT
app01-4621	73	4	,	,	PUNCT
app01-4621	73	5	the	the	DET
app01-4621	73	6	final	final	ADJ
app01-4621	73	7	fluctuations	fluctuation	NOUN
app01-4621	73	8	θ̃	θ̃	NOUN
app01-4621	73	9	follows	follow	VERB
app01-4621	73	10	from	from	ADP
app01-4621	73	11	ks	ks	PROPN
app01-4621	73	12	ct	ct	PROPN
app01-4621	74	1	i	i	PRON
app01-4621	74	2	ct	ct	PROPN
app01-4621	74	3	ii	ii	PROPN
app01-4621	74	4	ci	ci	PROPN
app01-4621	74	5	0	0	NUM
app01-4621	74	6	0	0	NUM
app01-4621	74	7	cii	cii	PROPN
app01-4621	74	8	0	0	NUM
app01-4621	74	9	0	0	NUM
app01-4621	74	10			NOUN
app01-4621	74	11	θ̃	θ̃	NOUN
app01-4621	74	12	λi	λi	ADP
app01-4621	74	13	λii	λii	NOUN
app01-4621	74	14			NOUN
app01-4621	74	15	=	=	SYM
app01-4621	74	16	f(h	f(h	NUM
app01-4621	74	17	)	)	PUNCT
app01-4621	74	18	0	0	NUM
app01-4621	74	19	0	0	NUM
app01-4621	75	1			NOUN
app01-4621	75	2	,	,	PUNCT
app01-4621	75	3	(	(	PUNCT
app01-4621	75	4	10	10	NUM
app01-4621	75	5	)	)	PUNCT
app01-4621	75	6	where	where	SCONJ
app01-4621	75	7	ci	ci	NOUN
app01-4621	75	8	and	and	CCONJ
app01-4621	75	9	cii	cii	PROPN
app01-4621	75	10	matrices	matrix	NOUN
app01-4621	75	11	represent	represent	VERB
app01-4621	75	12	the	the	DET
app01-4621	75	13	discretized	discretized	ADJ
app01-4621	75	14	versions	version	NOUN
app01-4621	75	15	of	of	ADP
app01-4621	75	16	eq	eq	PROPN
app01-4621	75	17	.	.	PUNCT
app01-4621	76	1	(	(	PUNCT
app01-4621	76	2	4	4	NUM
app01-4621	76	3	)	)	PUNCT
app01-4621	76	4	and	and	CCONJ
app01-4621	76	5	one	one	NUM
app01-4621	76	6	of	of	ADP
app01-4621	76	7	eqs	eqs	PROPN
app01-4621	76	8	.	.	PUNCT
app01-4621	77	1	(	(	PUNCT
app01-4621	77	2	7	7	NUM
app01-4621	77	3	)	)	PUNCT
app01-4621	77	4	,	,	PUNCT
app01-4621	77	5	(	(	PUNCT
app01-4621	77	6	8)	8)	NUM
app01-4621	77	7	,	,	PUNCT
app01-4621	77	8	or	or	CCONJ
app01-4621	77	9	(	(	PUNCT
app01-4621	77	10	9	9	NUM
app01-4621	77	11	)	)	PUNCT
app01-4621	77	12	,	,	PUNCT
app01-4621	77	13	respectively	respectively	ADV
app01-4621	77	14	,	,	PUNCT
app01-4621	77	15	and	and	CCONJ
app01-4621	77	16	λ•	λ•	ADJ
app01-4621	77	17	stands	stand	VERB
app01-4621	77	18	for	for	ADP
app01-4621	77	19	the	the	DET
app01-4621	77	20	corresponding	correspond	VERB
app01-4621	77	21	vector	vector	NOUN
app01-4621	77	22	of	of	ADP
app01-4621	77	23	lagrange	lagrange	NOUN
app01-4621	77	24	multipliers	multiplier	NOUN
app01-4621	77	25	.	.	PUNCT
app01-4621	78	1	while	while	SCONJ
app01-4621	78	2	cii	cii	PROPN
app01-4621	78	3	straightforwardly	straightforwardly	ADV
app01-4621	78	4	eliminates	eliminate	VERB
app01-4621	78	5	edge	edge	NOUN
app01-4621	78	6	unknowns	unknown	NOUN
app01-4621	78	7	for	for	ADP
app01-4621	78	8	the	the	DET
app01-4621	78	9	constraint	constraint	NOUN
app01-4621	78	10	type	type	NOUN
app01-4621	78	11	(	(	PUNCT
app01-4621	78	12	k	k	NOUN
app01-4621	78	13	)	)	PUNCT
app01-4621	78	14	,	,	PUNCT
app01-4621	78	15	constructing	construct	VERB
app01-4621	78	16	contributions	contribution	NOUN
app01-4621	78	17	of	of	ADP
app01-4621	78	18	individual	individual	ADJ
app01-4621	78	19	tile	tile	NOUN
app01-4621	78	20	separately	separately	ADV
app01-4621	78	21	and	and	CCONJ
app01-4621	78	22	localizing	localize	VERB
app01-4621	78	23	them	they	PRON
app01-4621	78	24	into	into	ADP
app01-4621	78	25	cii	cii	PROPN
app01-4621	78	26	leads	lead	VERB
app01-4621	78	27	to	to	ADP
app01-4621	78	28	an	an	DET
app01-4621	78	29	ill	ill	ADV
app01-4621	78	30	-	-	PUNCT
app01-4621	78	31	posed	pose	VERB
app01-4621	78	32	problem	problem	NOUN
app01-4621	78	33	for	for	ADP
app01-4621	78	34	types	type	NOUN
app01-4621	78	35	(	(	PUNCT
app01-4621	78	36	p	p	NOUN
app01-4621	78	37	)	)	PUNCT
app01-4621	78	38	and	and	CCONJ
app01-4621	78	39	(	(	PUNCT
app01-4621	78	40	s	s	X
app01-4621	78	41	)	)	PUNCT
app01-4621	78	42	from	from	ADP
app01-4621	78	43	eq	eq	ADP
app01-4621	78	44	.	.	PUNCT
app01-4621	79	1	(	(	PUNCT
app01-4621	79	2	6	6	NUM
app01-4621	79	3	)	)	PUNCT
app01-4621	79	4	,	,	PUNCT
app01-4621	79	5	it	it	PRON
app01-4621	79	6	clearly	clearly	ADV
app01-4621	79	7	follows	follow	VERB
app01-4621	79	8	that	that	SCONJ
app01-4621	79	9	if	if	SCONJ
app01-4621	79	10	two	two	NUM
app01-4621	79	11	opposite	opposite	ADJ
app01-4621	79	12	sides	side	NOUN
app01-4621	79	13	of	of	ADP
app01-4621	79	14	a	a	DET
app01-4621	79	15	tile	tile	NOUN
app01-4621	79	16	are	be	AUX
app01-4621	79	17	required	require	VERB
app01-4621	79	18	to	to	PART
app01-4621	79	19	be	be	AUX
app01-4621	79	20	compatible	compatible	ADJ
app01-4621	79	21	—	—	PUNCT
app01-4621	79	22	hence	hence	ADV
app01-4621	79	23	they	they	PRON
app01-4621	79	24	feature	feature	VERB
app01-4621	79	25	the	the	DET
app01-4621	79	26	same	same	ADJ
app01-4621	79	27	trace	trace	NOUN
app01-4621	79	28	of	of	ADP
app01-4621	79	29	θ̃—the	θ̃—the	DET
app01-4621	79	30	corresponding	corresponding	ADJ
app01-4621	79	31	component	component	NOUN
app01-4621	79	32	of	of	ADP
app01-4621	79	33	∇θ̃	∇θ̃	PROPN
app01-4621	79	34	average	average	ADJ
app01-4621	79	35	vanishes	vanish	VERB
app01-4621	79	36	and	and	CCONJ
app01-4621	79	37	so	so	ADV
app01-4621	79	38	does	do	VERB
app01-4621	79	39	the	the	DET
app01-4621	79	40	tile	tile	NOUN
app01-4621	79	41	contribution	contribution	NOUN
app01-4621	79	42	to	to	ADP
app01-4621	79	43	the	the	DET
app01-4621	79	44	relevant	relevant	ADJ
app01-4621	79	45	row	row	NOUN
app01-4621	79	46	in	in	ADP
app01-4621	79	47	cii	cii	PROPN
app01-4621	79	48	.	.	PUNCT
app01-4621	80	1	in	in	ADP
app01-4621	80	2	addition	addition	NOUN
app01-4621	80	3	,	,	PUNCT
app01-4621	80	4	the	the	DET
app01-4621	80	5	ill	ill	ADJ
app01-4621	80	6	-	-	PUNCT
app01-4621	80	7	posedness	posedness	NOUN
app01-4621	80	8	also	also	ADV
app01-4621	80	9	stems	stem	VERB
app01-4621	80	10	from	from	ADP
app01-4621	80	11	the	the	DET
app01-4621	80	12	repetition	repetition	NOUN
app01-4621	80	13	of	of	ADP
app01-4621	80	14	edge	edge	NOUN
app01-4621	80	15	code	code	NOUN
app01-4621	80	16	pairs	pair	NOUN
app01-4621	80	17	within	within	ADP
app01-4621	80	18	the	the	DET
app01-4621	80	19	tile	tile	NOUN
app01-4621	80	20	set	set	NOUN
app01-4621	80	21	(	(	PUNCT
app01-4621	80	22	swapping	swap	VERB
app01-4621	80	23	the	the	DET
app01-4621	80	24	order	order	NOUN
app01-4621	80	25	of	of	ADP
app01-4621	80	26	codes	code	NOUN
app01-4621	80	27	changes	change	VERB
app01-4621	80	28	only	only	ADV
app01-4621	80	29	the	the	DET
app01-4621	80	30	sign	sign	NOUN
app01-4621	80	31	of	of	ADP
app01-4621	80	32	the	the	DET
app01-4621	80	33	edge	edge	NOUN
app01-4621	80	34	contribution	contribution	NOUN
app01-4621	80	35	to	to	ADP
app01-4621	80	36	eq	eq	PROPN
app01-4621	80	37	.	.	PUNCT
app01-4621	81	1	(	(	PUNCT
app01-4621	81	2	5	5	NUM
app01-4621	81	3	)	)	PUNCT
app01-4621	81	4	)	)	PUNCT
app01-4621	81	5	.	.	PUNCT
app01-4621	82	1	in	in	ADP
app01-4621	82	2	certain	certain	ADJ
app01-4621	82	3	cases	case	NOUN
app01-4621	82	4	,	,	PUNCT
app01-4621	82	5	this	this	PRON
app01-4621	82	6	can	can	AUX
app01-4621	82	7	even	even	ADV
app01-4621	82	8	result	result	VERB
app01-4621	82	9	in	in	ADP
app01-4621	82	10	zero	zero	NUM
app01-4621	82	11	matrix	matrix	NOUN
app01-4621	82	12	cii	cii	PROPN
app01-4621	82	13	for	for	ADP
app01-4621	82	14	the	the	DET
app01-4621	82	15	least	least	ADJ
app01-4621	82	16	restrictive	restrictive	ADJ
app01-4621	82	17	constraint	constraint	NOUN
app01-4621	82	18	(	(	PUNCT
app01-4621	82	19	s	s	NOUN
app01-4621	82	20	)	)	PUNCT
app01-4621	82	21	,	,	PUNCT
app01-4621	82	22	in	in	ADP
app01-4621	82	23	which	which	PRON
app01-4621	82	24	tile	tile	NOUN
app01-4621	82	25	contributions	contribution	NOUN
app01-4621	82	26	are	be	AUX
app01-4621	82	27	summed	sum	VERB
app01-4621	82	28	together	together	ADV
app01-4621	82	29	.	.	PUNCT
app01-4621	83	1	one	one	NUM
app01-4621	83	2	way	way	NOUN
app01-4621	83	3	to	to	PART
app01-4621	83	4	treat	treat	VERB
app01-4621	83	5	the	the	DET
app01-4621	83	6	singularity	singularity	NOUN
app01-4621	83	7	of	of	ADP
app01-4621	83	8	cii	cii	PROPN
app01-4621	83	9	is	be	AUX
app01-4621	83	10	to	to	PART
app01-4621	83	11	perform	perform	VERB
app01-4621	83	12	singular	singular	ADJ
app01-4621	83	13	value	value	NOUN
app01-4621	83	14	decomposition	decomposition	NOUN
app01-4621	83	15	on	on	ADP
app01-4621	83	16	the	the	DET
app01-4621	83	17	constraint	constraint	NOUN
app01-4621	83	18	and	and	CCONJ
app01-4621	83	19	take	take	VERB
app01-4621	83	20	into	into	ADP
app01-4621	83	21	account	account	NOUN
app01-4621	83	22	only	only	ADV
app01-4621	83	23	the	the	DET
app01-4621	83	24	non	non	ADJ
app01-4621	83	25	-	-	ADJ
app01-4621	83	26	zero	zero	NUM
app01-4621	83	27	singular	singular	ADJ
app01-4621	83	28	values	value	NOUN
app01-4621	83	29	;	;	PUNCT
app01-4621	83	30	however	however	ADV
app01-4621	83	31	,	,	PUNCT
app01-4621	83	32	such	such	DET
app01-4621	83	33	a	a	DET
app01-4621	83	34	procedure	procedure	NOUN
app01-4621	83	35	is	be	AUX
app01-4621	83	36	sensitive	sensitive	ADJ
app01-4621	83	37	to	to	ADP
app01-4621	83	38	numerical	numerical	ADJ
app01-4621	83	39	precision	precision	NOUN
app01-4621	83	40	.	.	PUNCT
app01-4621	84	1	thanks	thank	NOUN
app01-4621	84	2	to	to	ADP
app01-4621	84	3	the	the	DET
app01-4621	84	4	simple	simple	ADJ
app01-4621	84	5	structure	structure	NOUN
app01-4621	84	6	of	of	ADP
app01-4621	84	7	the	the	DET
app01-4621	84	8	constraint	constraint	NOUN
app01-4621	84	9	,	,	PUNCT
app01-4621	84	10	the	the	DET
app01-4621	84	11	regular	regular	ADJ
app01-4621	84	12	part	part	NOUN
app01-4621	84	13	of	of	ADP
app01-4621	84	14	the	the	DET
app01-4621	84	15	constraint	constraint	NOUN
app01-4621	84	16	can	can	AUX
app01-4621	84	17	be	be	AUX
app01-4621	84	18	directly	directly	ADV
app01-4621	84	19	established	establish	VERB
app01-4621	84	20	as	as	ADP
app01-4621	84	21	a	a	DET
app01-4621	84	22	projection	projection	NOUN
app01-4621	84	23	of	of	ADP
app01-4621	84	24	the	the	DET
app01-4621	84	25	original	original	ADJ
app01-4621	84	26	matrix	matrix	NOUN
app01-4621	84	27	cii	cii	PROPN
app01-4621	84	28	.	.	PUNCT
app01-4621	85	1	first	first	ADV
app01-4621	85	2	,	,	PUNCT
app01-4621	85	3	all	all	DET
app01-4621	85	4	nc	nc	PROPN
app01-4621	85	5	combinations	combination	NOUN
app01-4621	85	6	of	of	ADP
app01-4621	85	7	edge	edge	NOUN
app01-4621	85	8	codes	code	NOUN
app01-4621	85	9	pertinent	pertinent	ADJ
app01-4621	85	10	to	to	ADP
app01-4621	85	11	either	either	CCONJ
app01-4621	85	12	horizontal	horizontal	ADJ
app01-4621	85	13	or	or	CCONJ
app01-4621	85	14	vertical	vertical	ADJ
app01-4621	85	15	edges	edge	NOUN
app01-4621	85	16	are	be	AUX
app01-4621	85	17	identified	identify	VERB
app01-4621	85	18	and	and	CCONJ
app01-4621	85	19	enumerated	enumerate	VERB
app01-4621	85	20	.	.	PUNCT
app01-4621	86	1	next	next	ADV
app01-4621	86	2	,	,	PUNCT
app01-4621	86	3	an	an	DET
app01-4621	86	4	empty	empty	ADJ
app01-4621	86	5	matrix	matrix	NOUN
app01-4621	86	6	p	p	X
app01-4621	86	7	∈	∈	PROPN
app01-4621	86	8	r2nt	r2nt	NOUN
app01-4621	86	9	×nc	×nc	NOUN
app01-4621	86	10	,	,	PUNCT
app01-4621	86	11	for	for	ADP
app01-4621	86	12	(	(	PUNCT
app01-4621	86	13	p	p	NOUN
app01-4621	86	14	)	)	PUNCT
app01-4621	86	15	type	type	NOUN
app01-4621	86	16	of	of	ADP
app01-4621	86	17	the	the	DET
app01-4621	86	18	constraint	constraint	NOUN
app01-4621	86	19	,	,	PUNCT
app01-4621	86	20	or	or	CCONJ
app01-4621	86	21	p	p	NOUN
app01-4621	86	22	∈	∈	PROPN
app01-4621	86	23	r2×nc	r2×nc	PROPN
app01-4621	86	24	,	,	PUNCT
app01-4621	86	25	for	for	ADP
app01-4621	86	26	(	(	PUNCT
app01-4621	86	27	s	s	NOUN
app01-4621	86	28	)	)	PUNCT
app01-4621	86	29	type	type	NOUN
app01-4621	86	30	,	,	PUNCT
app01-4621	86	31	is	be	AUX
app01-4621	86	32	created	create	VERB
app01-4621	86	33	and	and	CCONJ
app01-4621	86	34	populated	populate	VERB
app01-4621	86	35	with	with	ADP
app01-4621	86	36	1	1	NUM
app01-4621	86	37	(	(	PUNCT
app01-4621	86	38	or	or	CCONJ
app01-4621	86	39	−1	−1	NOUN
app01-4621	86	40	)	)	PUNCT
app01-4621	86	41	if	if	SCONJ
app01-4621	86	42	the	the	DET
app01-4621	86	43	tile	tile	NOUN
app01-4621	86	44	contains	contain	VERB
app01-4621	86	45	an	an	DET
app01-4621	86	46	enumerated	enumerate	VERB
app01-4621	86	47	pair	pair	NOUN
app01-4621	86	48	of	of	ADP
app01-4621	86	49	codes	code	NOUN
app01-4621	86	50	(	(	PUNCT
app01-4621	86	51	or	or	CCONJ
app01-4621	86	52	a	a	DET
app01-4621	86	53	pair	pair	NOUN
app01-4621	86	54	in	in	ADP
app01-4621	86	55	the	the	DET
app01-4621	86	56	inverse	inverse	NOUN
app01-4621	86	57	order	order	NOUN
app01-4621	86	58	)	)	PUNCT
app01-4621	86	59	.	.	PUNCT
app01-4621	87	1	odd	odd	ADJ
app01-4621	87	2	and	and	CCONJ
app01-4621	87	3	even	even	ADV
app01-4621	87	4	rows	row	NOUN
app01-4621	87	5	of	of	ADP
app01-4621	87	6	the	the	DET
app01-4621	87	7	matrix	matrix	NOUN
app01-4621	87	8	correspond	correspond	NOUN
app01-4621	87	9	to	to	ADP
app01-4621	87	10	vertical	vertical	ADJ
app01-4621	87	11	and	and	CCONJ
app01-4621	87	12	horizontal	horizontal	ADJ
app01-4621	87	13	edges	edge	NOUN
app01-4621	87	14	,	,	PUNCT
app01-4621	87	15	respectively	respectively	ADV
app01-4621	87	16	.	.	PUNCT
app01-4621	88	1	if	if	SCONJ
app01-4621	88	2	p	p	PRON
app01-4621	88	3	remains	remain	VERB
app01-4621	88	4	empty	empty	ADJ
app01-4621	88	5	for	for	ADP
app01-4621	88	6	(	(	PUNCT
app01-4621	88	7	s	s	NOUN
app01-4621	88	8	)	)	PUNCT
app01-4621	88	9	,	,	PUNCT
app01-4621	88	10	cii	cii	PROPN
app01-4621	88	11	constraint	constraint	NOUN
app01-4621	88	12	is	be	AUX
app01-4621	88	13	discarded	discard	VERB
app01-4621	88	14	entirely	entirely	ADV
app01-4621	88	15	.	.	PUNCT
app01-4621	89	1	otherwise	otherwise	ADV
app01-4621	89	2	,	,	PUNCT
app01-4621	89	3	the	the	DET
app01-4621	89	4	non	non	ADJ
app01-4621	89	5	-	-	ADJ
app01-4621	89	6	singular	singular	ADJ
app01-4621	89	7	constraint	constraint	NOUN
app01-4621	89	8	matrix	matrix	NOUN
app01-4621	89	9	cii	cii	PROPN
app01-4621	89	10	,	,	PUNCT
app01-4621	89	11	replacing	replace	VERB
app01-4621	89	12	cii	cii	PROPN
app01-4621	89	13	in	in	ADP
app01-4621	89	14	eq	eq	ADP
app01-4621	89	15	.	.	PUNCT
app01-4621	90	1	(	(	PUNCT
app01-4621	90	2	10	10	NUM
app01-4621	90	3	)	)	PUNCT
app01-4621	90	4	,	,	PUNCT
app01-4621	90	5	is	be	AUX
app01-4621	90	6	obtained	obtain	VERB
app01-4621	90	7	from	from	ADP
app01-4621	90	8	a	a	DET
app01-4621	90	9	projection	projection	NOUN
app01-4621	90	10	cii	cii	PROPN
app01-4621	90	11	=	=	PROPN
app01-4621	90	12	ptcii	ptcii	PROPN
app01-4621	90	13	.	.	PUNCT
app01-4621	91	1	the	the	DET
app01-4621	91	2	outlined	outline	VERB
app01-4621	91	3	strategy	strategy	NOUN
app01-4621	91	4	allows	allow	VERB
app01-4621	91	5	to	to	PART
app01-4621	91	6	define	define	VERB
app01-4621	91	7	one	one	NUM
app01-4621	91	8	enrichment	enrichment	NOUN
app01-4621	91	9	field	field	NOUN
app01-4621	91	10	θ̃	θ̃	NOUN
app01-4621	91	11	for	for	ADP
app01-4621	91	12	a	a	DET
app01-4621	91	13	prescribed	prescribed	ADJ
app01-4621	91	14	h	h	NOUN
app01-4621	91	15	and	and	CCONJ
app01-4621	91	16	the	the	DET
app01-4621	91	17	selected	select	VERB
app01-4621	91	18	type	type	NOUN
app01-4621	91	19	of	of	ADP
app01-4621	91	20	the	the	DET
app01-4621	91	21	second	second	ADJ
app01-4621	91	22	constraint	constraint	NOUN
app01-4621	91	23	.	.	PUNCT
app01-4621	92	1	for	for	ADP
app01-4621	92	2	the	the	DET
app01-4621	92	3	linear	linear	ADJ
app01-4621	92	4	problem	problem	NOUN
app01-4621	92	5	considered	consider	VERB
app01-4621	92	6	in	in	ADP
app01-4621	92	7	this	this	DET
app01-4621	92	8	work	work	NOUN
app01-4621	92	9	,	,	PUNCT
app01-4621	92	10	two	two	NUM
app01-4621	92	11	mutually	mutually	ADV
app01-4621	92	12	orthonormal	orthonormal	ADJ
app01-4621	92	13	loading	loading	NOUN
app01-4621	92	14	cases	case	NOUN
app01-4621	92	15	h	h	NOUN
app01-4621	92	16	=	=	PUNCT
app01-4621	92	17	{	{	PUNCT
app01-4621	92	18	1	1	NUM
app01-4621	92	19	,	,	PUNCT
app01-4621	92	20	0	0	NUM
app01-4621	92	21	}	}	PUNCT
app01-4621	92	22	t	t	NOUN
app01-4621	92	23	and	and	CCONJ
app01-4621	92	24	h	h	NOUN
app01-4621	92	25	=	=	NOUN
app01-4621	92	26	{	{	PUNCT
app01-4621	92	27	0	0	NUM
app01-4621	92	28	,	,	PUNCT
app01-4621	92	29	1	1	NUM
app01-4621	92	30	}	}	PUNCT
app01-4621	92	31	t	t	NOUN
app01-4621	92	32	cover	cover	VERB
app01-4621	92	33	all	all	DET
app01-4621	92	34	possible	possible	ADJ
app01-4621	92	35	load	load	NOUN
app01-4621	92	36	cases	case	NOUN
app01-4621	92	37	.	.	PUNCT
app01-4621	93	1	combined	combine	VERB
app01-4621	93	2	with	with	ADP
app01-4621	93	3	three	three	NUM
app01-4621	93	4	types	type	NOUN
app01-4621	93	5	of	of	ADP
app01-4621	93	6	cii	cii	PROPN
app01-4621	93	7	,	,	PUNCT
app01-4621	93	8	we	we	PRON
app01-4621	93	9	can	can	AUX
app01-4621	93	10	generate	generate	VERB
app01-4621	93	11	up	up	ADP
app01-4621	93	12	to	to	PART
app01-4621	93	13	six	six	NUM
app01-4621	93	14	enrichment	enrichment	NOUN
app01-4621	93	15	fields	field	NOUN
app01-4621	93	16	.	.	PUNCT
app01-4621	94	1	note	note	VERB
app01-4621	94	2	that	that	SCONJ
app01-4621	94	3	unlike	unlike	ADP
app01-4621	94	4	the	the	DET
app01-4621	94	5	nested	nested	ADJ
app01-4621	94	6	numerical	numerical	ADJ
app01-4621	94	7	homogenization	homogenization	NOUN
app01-4621	94	8	,	,	PUNCT
app01-4621	94	9	where	where	SCONJ
app01-4621	94	10	the	the	DET
app01-4621	94	11	choice	choice	NOUN
app01-4621	94	12	of	of	ADP
app01-4621	94	13	boundary	boundary	ADJ
app01-4621	94	14	conditions	condition	NOUN
app01-4621	94	15	is	be	AUX
app01-4621	94	16	based	base	VERB
app01-4621	94	17	on	on	ADP
app01-4621	94	18	their	their	PRON
app01-4621	94	19	suitability	suitability	NOUN
app01-4621	94	20	in	in	ADP
app01-4621	94	21	capturing	capture	VERB
app01-4621	94	22	effects	effect	NOUN
app01-4621	94	23	of	of	ADP
app01-4621	94	24	a	a	DET
app01-4621	94	25	surrounding	surround	VERB
app01-4621	94	26	medium	medium	NOUN
app01-4621	94	27	,	,	PUNCT
app01-4621	94	28	we	we	PRON
app01-4621	94	29	combine	combine	VERB
app01-4621	94	30	different	different	ADJ
app01-4621	94	31	types	type	NOUN
app01-4621	94	32	of	of	ADP
app01-4621	94	33	cii	cii	PROPN
app01-4621	94	34	to	to	PART
app01-4621	94	35	control	control	VERB
app01-4621	94	36	cardinality	cardinality	NOUN
app01-4621	94	37	of	of	ADP
app01-4621	94	38	the	the	DET
app01-4621	94	39	set	set	NOUN
app01-4621	94	40	of	of	ADP
app01-4621	94	41	compressed	compressed	ADJ
app01-4621	94	42	fluctuations	fluctuation	NOUN
app01-4621	94	43	.	.	PUNCT
app01-4621	95	1	figure	figure	NOUN
app01-4621	95	2	2	2	NUM
app01-4621	95	3	.	.	PUNCT
app01-4621	96	1	a	a	DET
app01-4621	96	2	compressed	compress	VERB
app01-4621	96	3	fluctuation	fluctuation	NOUN
app01-4621	96	4	field	field	NOUN
app01-4621	96	5	obtained	obtain	VERB
app01-4621	96	6	by	by	ADP
app01-4621	96	7	prescribing	prescribe	VERB
app01-4621	96	8	(	(	PUNCT
app01-4621	96	9	s	s	NOUN
app01-4621	96	10	)	)	PUNCT
app01-4621	96	11	variant	variant	NOUN
app01-4621	96	12	of	of	ADP
app01-4621	96	13	the	the	DET
app01-4621	96	14	second	second	ADJ
app01-4621	96	15	constraint	constraint	NOUN
app01-4621	96	16	and	and	CCONJ
app01-4621	96	17	setting	set	VERB
app01-4621	96	18	h	h	NOUN
app01-4621	96	19	=	=	PUNCT
app01-4621	96	20	{	{	PUNCT
app01-4621	96	21	1	1	NUM
app01-4621	96	22	,	,	PUNCT
app01-4621	96	23	0}t	0}t	NOUN
app01-4621	96	24	.	.	NOUN
app01-4621	96	25	4	4	NUM
app01-4621	96	26	.	.	X
app01-4621	96	27	numerical	numerical	ADJ
app01-4621	96	28	strategy	strategy	PROPN
app01-4621	96	29	the	the	DET
app01-4621	96	30	fields	field	NOUN
app01-4621	96	31	introduced	introduce	VERB
app01-4621	96	32	above	above	ADV
app01-4621	96	33	are	be	AUX
app01-4621	96	34	employed	employ	VERB
app01-4621	96	35	as	as	ADP
app01-4621	96	36	enrichments	enrichment	NOUN
app01-4621	96	37	in	in	ADP
app01-4621	96	38	a	a	DET
app01-4621	96	39	upper	upper	ADJ
app01-4621	96	40	-	-	PUNCT
app01-4621	96	41	scale	scale	NOUN
app01-4621	96	42	model	model	NOUN
app01-4621	96	43	whose	whose	DET
app01-4621	96	44	microstructural	microstructural	ADJ
app01-4621	96	45	geometry	geometry	NOUN
app01-4621	96	46	is	be	AUX
app01-4621	96	47	assembled	assemble	VERB
app01-4621	96	48	by	by	ADP
app01-4621	96	49	means	mean	NOUN
app01-4621	96	50	of	of	ADP
app01-4621	96	51	tiling	tile	VERB
app01-4621	96	52	from	from	ADP
app01-4621	96	53	the	the	DET
app01-4621	96	54	set	set	NOUN
app01-4621	96	55	depicted	depict	VERB
app01-4621	96	56	in	in	ADP
app01-4621	96	57	figure	figure	NOUN
app01-4621	96	58	1	1	NUM
app01-4621	96	59	.	.	PUNCT
app01-4621	97	1	assume	assume	VERB
app01-4621	97	2	a	a	DET
app01-4621	97	3	upper	upper	ADJ
app01-4621	97	4	-	-	PUNCT
app01-4621	97	5	scale	scale	NOUN
app01-4621	97	6	problem	problem	NOUN
app01-4621	97	7	governed	govern	VERB
app01-4621	97	8	by	by	ADP
app01-4621	97	9	the	the	DET
app01-4621	97	10	same	same	ADJ
app01-4621	97	11	differential	differential	NOUN
app01-4621	97	12	equation	equation	NOUN
app01-4621	97	13	as	as	ADP
app01-4621	97	14	in	in	ADP
app01-4621	97	15	eq	eq	NOUN
app01-4621	97	16	.	.	PUNCT
app01-4621	98	1	(	(	PUNCT
app01-4621	98	2	1	1	NUM
app01-4621	98	3	)	)	PUNCT
app01-4621	98	4	,	,	PUNCT
app01-4621	98	5	valid	valid	ADJ
app01-4621	98	6	in	in	ADP
app01-4621	98	7	a	a	DET
app01-4621	98	8	upperscale	upperscale	ADJ
app01-4621	98	9	domain	domain	NOUN
app01-4621	98	10	ω	ω	PROPN
app01-4621	98	11	and	and	CCONJ
app01-4621	98	12	accompanied	accompany	VERB
app01-4621	98	13	by	by	ADP
app01-4621	98	14	boundary	boundary	ADJ
app01-4621	98	15	conditions	condition	NOUN
app01-4621	98	16	θ(x	θ(x	PROPN
app01-4621	98	17	)	)	PUNCT
app01-4621	99	1	=	=	SYM
app01-4621	99	2	θ̂(x	θ̂(x	NOUN
app01-4621	99	3	)	)	PUNCT
app01-4621	99	4	x	x	X
app01-4621	99	5	∈	∈	PROPN
app01-4621	99	6	γθ	γθ	PROPN
app01-4621	99	7	6=	6=	NUM
app01-4621	99	8	∅	∅	NOUN
app01-4621	99	9	,	,	PUNCT
app01-4621	99	10	(	(	PUNCT
app01-4621	99	11	11	11	NUM
app01-4621	99	12	)	)	PUNCT
app01-4621	99	13	(	(	PUNCT
app01-4621	99	14	−k(x)∇θ(x	−k(x)∇θ(x	PROPN
app01-4621	99	15	)	)	PUNCT
app01-4621	99	16	)	)	PUNCT
app01-4621	99	17	·	·	PUNCT
app01-4621	100	1	n(x	n(x	X
app01-4621	100	2	)	)	PUNCT
app01-4621	100	3	=	=	SYM
app01-4621	100	4	q̂(x	q̂(x	NOUN
app01-4621	100	5	)	)	PUNCT
app01-4621	100	6	x	x	SYM
app01-4621	100	7	∈	∈	PROPN
app01-4621	100	8	γq	γq	ADP
app01-4621	100	9	,	,	PUNCT
app01-4621	100	10	(	(	PUNCT
app01-4621	100	11	12	12	NUM
app01-4621	100	12	)	)	SYM
app01-4621	100	13	31	31	NUM
app01-4621	100	14	m.	m.	NOUN
app01-4621	100	15	doškář	doškář	PROPN
app01-4621	100	16	,	,	PUNCT
app01-4621	100	17	j.	j.	PROPN
app01-4621	100	18	novák	novák	PROPN
app01-4621	100	19	,	,	PUNCT
app01-4621	100	20	j.	j.	PROPN
app01-4621	100	21	zeman	zeman	PROPN
app01-4621	100	22	acta	acta	PROPN
app01-4621	100	23	polytechnica	polytechnica	PROPN
app01-4621	100	24	ctu	ctu	NOUN
app01-4621	100	25	proceedings	proceeding	NOUN
app01-4621	100	26	where	where	SCONJ
app01-4621	100	27	θ̂	θ̂	NUM
app01-4621	100	28	and	and	CCONJ
app01-4621	100	29	q̂	q̂	NUM
app01-4621	100	30	are	be	AUX
app01-4621	100	31	the	the	DET
app01-4621	100	32	given	give	VERB
app01-4621	100	33	temperature	temperature	NOUN
app01-4621	100	34	and	and	CCONJ
app01-4621	100	35	normal	normal	ADJ
app01-4621	100	36	heat	heat	NOUN
app01-4621	100	37	flux	flux	NOUN
app01-4621	100	38	profiles	profile	NOUN
app01-4621	100	39	,	,	PUNCT
app01-4621	100	40	respectively	respectively	ADV
app01-4621	100	41	,	,	PUNCT
app01-4621	100	42	prescribed	prescribe	VERB
app01-4621	100	43	at	at	ADP
app01-4621	100	44	parts	part	NOUN
app01-4621	100	45	γθ	γθ	NOUN
app01-4621	100	46	and	and	CCONJ
app01-4621	100	47	γq	γq	ADP
app01-4621	100	48	of	of	ADP
app01-4621	100	49	the	the	DET
app01-4621	100	50	domain	domain	NOUN
app01-4621	100	51	boundary	boundary	NOUN
app01-4621	100	52	∂ω	∂ω	PROPN
app01-4621	100	53	.	.	PUNCT
app01-4621	101	1	an	an	DET
app01-4621	101	2	approximate	approximate	ADJ
app01-4621	101	3	numerical	numerical	ADJ
app01-4621	101	4	solution	solution	NOUN
app01-4621	101	5	arises	arise	VERB
app01-4621	101	6	from	from	ADP
app01-4621	101	7	the	the	DET
app01-4621	101	8	weak	weak	ADJ
app01-4621	101	9	form	form	NOUN
app01-4621	101	10	of	of	ADP
app01-4621	101	11	the	the	DET
app01-4621	101	12	problem	problem	NOUN
app01-4621	101	13	find	find	VERB
app01-4621	101	14	θ	θ	PROPN
app01-4621	101	15	∈	∈	PROPN
app01-4621	101	16	v	v	ADP
app01-4621	101	17	such	such	ADJ
app01-4621	101	18	that	that	PRON
app01-4621	101	19	a(θ	a(θ	PROPN
app01-4621	101	20	,	,	PUNCT
app01-4621	101	21	ϑ	ϑ	NOUN
app01-4621	101	22	)	)	PUNCT
app01-4621	101	23	=	=	SYM
app01-4621	101	24	b(ϑ	b(ϑ	PROPN
app01-4621	101	25	)	)	PUNCT
app01-4621	101	26	,	,	PUNCT
app01-4621	101	27	∀ϑ	∀ϑ	PROPN
app01-4621	101	28	∈	∈	PROPN
app01-4621	101	29	v0	v0	NOUN
app01-4621	101	30	.	.	PUNCT
app01-4621	102	1	(	(	PUNCT
app01-4621	102	2	13	13	NUM
app01-4621	102	3	)	)	PUNCT
app01-4621	102	4	and	and	CCONJ
app01-4621	102	5	substitutes	substitute	NOUN
app01-4621	102	6	for	for	ADP
app01-4621	102	7	the	the	DET
app01-4621	102	8	analytical	analytical	ADJ
app01-4621	102	9	solution	solution	NOUN
app01-4621	102	10	that	that	PRON
app01-4621	102	11	is	be	AUX
app01-4621	102	12	usually	usually	ADV
app01-4621	102	13	intractable	intractable	ADJ
app01-4621	102	14	.	.	PUNCT
app01-4621	103	1	in	in	ADP
app01-4621	103	2	eq	eq	ADP
app01-4621	103	3	.	.	PUNCT
app01-4621	104	1	(	(	PUNCT
app01-4621	104	2	13	13	NUM
app01-4621	104	3	)	)	PUNCT
app01-4621	104	4	,	,	PUNCT
app01-4621	104	5	a(θ	a(θ	PROPN
app01-4621	104	6	,	,	PUNCT
app01-4621	104	7	ϑ	ϑ	NOUN
app01-4621	104	8	)	)	PUNCT
app01-4621	104	9	and	and	CCONJ
app01-4621	104	10	b(ϑ	b(ϑ	PROPN
app01-4621	104	11	)	)	PUNCT
app01-4621	104	12	denote	denote	VERB
app01-4621	104	13	the	the	DET
app01-4621	104	14	bilinear	bilinear	NOUN
app01-4621	104	15	and	and	CCONJ
app01-4621	104	16	linear	linear	ADJ
app01-4621	104	17	form	form	NOUN
app01-4621	104	18	pertinent	pertinent	ADJ
app01-4621	104	19	to	to	ADP
app01-4621	104	20	eq	eq	PROPN
app01-4621	104	21	.	.	PUNCT
app01-4621	105	1	(	(	PUNCT
app01-4621	105	2	1	1	NUM
app01-4621	105	3	)	)	PUNCT
app01-4621	105	4	;	;	PUNCT
app01-4621	105	5	v	v	NOUN
app01-4621	105	6	and	and	CCONJ
app01-4621	105	7	v0	v0	NOUN
app01-4621	105	8	stand	stand	NOUN
app01-4621	105	9	for	for	ADP
app01-4621	105	10	the	the	DET
app01-4621	105	11	space	space	NOUN
app01-4621	105	12	of	of	ADP
app01-4621	105	13	admissible	admissible	ADJ
app01-4621	105	14	temperature	temperature	NOUN
app01-4621	105	15	fields	field	NOUN
app01-4621	105	16	.	.	PUNCT
app01-4621	106	1	quality	quality	NOUN
app01-4621	106	2	of	of	ADP
app01-4621	106	3	the	the	DET
app01-4621	106	4	approximate	approximate	ADJ
app01-4621	106	5	solution	solution	NOUN
app01-4621	106	6	is	be	AUX
app01-4621	106	7	governed	govern	VERB
app01-4621	106	8	by	by	ADP
app01-4621	106	9	suitability	suitability	NOUN
app01-4621	106	10	of	of	ADP
app01-4621	106	11	a	a	DET
app01-4621	106	12	finite	finite	ADJ
app01-4621	106	13	-	-	ADJ
app01-4621	106	14	dimensional	dimensional	ADJ
app01-4621	106	15	subspace	subspace	NOUN
app01-4621	106	16	vc	vc	PROPN
app01-4621	106	17	⊂	⊂	PROPN
app01-4621	106	18	v	v	PROPN
app01-4621	106	19	in	in	ADP
app01-4621	106	20	which	which	PRON
app01-4621	106	21	the	the	DET
app01-4621	106	22	solution	solution	NOUN
app01-4621	106	23	is	be	AUX
app01-4621	106	24	sought	seek	VERB
app01-4621	106	25	for	for	ADP
app01-4621	106	26	.	.	PUNCT
app01-4621	107	1	in	in	ADP
app01-4621	107	2	particular	particular	ADJ
app01-4621	107	3	,	,	PUNCT
app01-4621	107	4	domain	domain	NOUN
app01-4621	107	5	discretization	discretization	NOUN
app01-4621	107	6	must	must	AUX
app01-4621	107	7	accurately	accurately	ADV
app01-4621	107	8	resolve	resolve	VERB
app01-4621	107	9	all	all	DET
app01-4621	107	10	geometrical	geometrical	ADJ
app01-4621	107	11	details	detail	NOUN
app01-4621	107	12	in	in	ADP
app01-4621	107	13	the	the	DET
app01-4621	107	14	standard	standard	ADJ
app01-4621	107	15	finite	finite	ADJ
app01-4621	107	16	element	element	NOUN
app01-4621	107	17	(	(	PUNCT
app01-4621	107	18	fe	fe	NOUN
app01-4621	107	19	)	)	PUNCT
app01-4621	107	20	setting	setting	NOUN
app01-4621	107	21	.	.	PUNCT
app01-4621	108	1	this	this	DET
app01-4621	108	2	requirement	requirement	NOUN
app01-4621	108	3	leads	lead	VERB
app01-4621	108	4	to	to	ADP
app01-4621	108	5	very	very	ADV
app01-4621	108	6	fine	fine	ADJ
app01-4621	108	7	meshes	mesh	NOUN
app01-4621	108	8	in	in	ADP
app01-4621	108	9	applications	application	NOUN
app01-4621	108	10	where	where	SCONJ
app01-4621	108	11	microstructural	microstructural	ADJ
app01-4621	108	12	geometry	geometry	NOUN
app01-4621	108	13	of	of	ADP
app01-4621	108	14	the	the	DET
app01-4621	108	15	domain	domain	NOUN
app01-4621	108	16	is	be	AUX
app01-4621	108	17	involved	involve	VERB
app01-4621	108	18	.	.	PUNCT
app01-4621	109	1	besides	besides	SCONJ
app01-4621	109	2	local	local	ADJ
app01-4621	109	3	mesh	mesh	NOUN
app01-4621	109	4	refinements	refinement	NOUN
app01-4621	109	5	,	,	PUNCT
app01-4621	109	6	the	the	DET
app01-4621	109	7	approximation	approximation	NOUN
app01-4621	109	8	space	space	NOUN
app01-4621	109	9	can	can	AUX
app01-4621	109	10	be	be	AUX
app01-4621	109	11	enhanced	enhance	VERB
app01-4621	109	12	by	by	ADP
app01-4621	109	13	incorporating	incorporate	VERB
app01-4621	109	14	prior	prior	ADJ
app01-4621	109	15	knowledge	knowledge	NOUN
app01-4621	109	16	of	of	ADP
app01-4621	109	17	local	local	ADJ
app01-4621	109	18	character	character	NOUN
app01-4621	109	19	of	of	ADP
app01-4621	109	20	the	the	DET
app01-4621	109	21	solution	solution	NOUN
app01-4621	109	22	.	.	PUNCT
app01-4621	110	1	concretely	concretely	ADV
app01-4621	110	2	,	,	PUNCT
app01-4621	110	3	in	in	ADP
app01-4621	110	4	the	the	DET
app01-4621	110	5	extended	extend	VERB
app01-4621	110	6	finite	finite	ADJ
app01-4621	110	7	element	element	NOUN
app01-4621	110	8	framework	framework	NOUN
app01-4621	110	9	[	[	X
app01-4621	110	10	5	5	NUM
app01-4621	110	11	,	,	PUNCT
app01-4621	110	12	6	6	NUM
app01-4621	110	13	]	]	PUNCT
app01-4621	110	14	,	,	PUNCT
app01-4621	110	15	the	the	DET
app01-4621	110	16	approximate	approximate	ADJ
app01-4621	110	17	solution	solution	NOUN
app01-4621	110	18	θc	θc	NOUN
app01-4621	110	19	∈	∈	PROPN
app01-4621	110	20	vc	vc	NOUN
app01-4621	110	21	takes	take	VERB
app01-4621	110	22	the	the	DET
app01-4621	110	23	form	form	NOUN
app01-4621	110	24	θc(x	θc(x	NOUN
app01-4621	110	25	)	)	PUNCT
app01-4621	111	1	=	=	SYM
app01-4621	111	2	nc∑	nc∑	PROPN
app01-4621	111	3	i=1	i=1	NUM
app01-4621	111	4	ni(x	ni(x	NUM
app01-4621	111	5	)	)	PUNCT
app01-4621	111	6	θi	θi	ADP
app01-4621	112	1	+	+	CCONJ
app01-4621	112	2	nc∑	nc∑	PROPN
app01-4621	112	3	i=1	i=1	X
app01-4621	112	4	ne∑	ne∑	PROPN
app01-4621	112	5	j=1	j=1	ADJ
app01-4621	112	6	ni(x)ψj(x	ni(x)ψj(x	X
app01-4621	112	7	)	)	PUNCT
app01-4621	112	8	θji	θji	NOUN
app01-4621	112	9	,	,	PUNCT
app01-4621	112	10	(	(	PUNCT
app01-4621	112	11	14	14	NUM
app01-4621	112	12	)	)	PUNCT
app01-4621	112	13	where	where	SCONJ
app01-4621	112	14	the	the	DET
app01-4621	112	15	first	first	ADJ
app01-4621	112	16	sum	sum	NOUN
app01-4621	112	17	contains	contain	VERB
app01-4621	112	18	the	the	DET
app01-4621	112	19	standard	standard	ADJ
app01-4621	112	20	finite	finite	ADJ
app01-4621	112	21	element	element	NOUN
app01-4621	112	22	shape	shape	NOUN
app01-4621	112	23	functions	function	NOUN
app01-4621	112	24	ni(x	ni(x	NUM
app01-4621	112	25	)	)	PUNCT
app01-4621	112	26	and	and	CCONJ
app01-4621	112	27	the	the	DET
app01-4621	112	28	second	second	ADJ
app01-4621	112	29	term	term	NOUN
app01-4621	112	30	adds	add	VERB
app01-4621	112	31	ne	ne	ADP
app01-4621	112	32	enrichment	enrichment	NOUN
app01-4621	112	33	functions	function	NOUN
app01-4621	112	34	ψj	ψj	ADV
app01-4621	112	35	for	for	ADP
app01-4621	112	36	each	each	DET
app01-4621	112	37	discretization	discretization	NOUN
app01-4621	112	38	node	node	NOUN
app01-4621	112	39	;	;	PUNCT
app01-4621	112	40	θi	θi	NUM
app01-4621	112	41	denotes	denote	NOUN
app01-4621	112	42	the	the	DET
app01-4621	112	43	regular	regular	ADJ
app01-4621	112	44	degree	degree	NOUN
app01-4621	112	45	of	of	ADP
app01-4621	112	46	freedom	freedom	NOUN
app01-4621	112	47	(	(	PUNCT
app01-4621	112	48	dof	dof	NOUN
app01-4621	112	49	)	)	PUNCT
app01-4621	112	50	associated	associate	VERB
app01-4621	112	51	with	with	ADP
app01-4621	112	52	finite	finite	ADJ
app01-4621	112	53	-	-	ADJ
app01-4621	112	54	element	element	ADJ
app01-4621	112	55	mesh	mesh	NOUN
app01-4621	112	56	node	node	NOUN
app01-4621	112	57	xi	xi	PROPN
app01-4621	112	58	,	,	PUNCT
app01-4621	112	59	θji	θji	INTJ
app01-4621	112	60	are	be	AUX
app01-4621	112	61	the	the	DET
app01-4621	112	62	additional	additional	ADJ
app01-4621	112	63	dofs	dof	NOUN
app01-4621	112	64	.	.	PUNCT
app01-4621	113	1	in	in	ADP
app01-4621	113	2	traditional	traditional	ADJ
app01-4621	113	3	xfem	xfem	PROPN
app01-4621	113	4	,	,	PUNCT
app01-4621	113	5	only	only	ADV
app01-4621	113	6	patches	patch	NOUN
app01-4621	113	7	of	of	ADP
app01-4621	113	8	the	the	DET
app01-4621	113	9	domain	domain	NOUN
app01-4621	113	10	are	be	AUX
app01-4621	113	11	usually	usually	ADV
app01-4621	113	12	enriched	enrich	VERB
app01-4621	113	13	with	with	ADP
app01-4621	113	14	ψj	ψj	ADV
app01-4621	113	15	,	,	PUNCT
app01-4621	113	16	suited	suit	VERB
app01-4621	113	17	for	for	ADP
app01-4621	113	18	one	one	NUM
app01-4621	113	19	geometrical	geometrical	ADJ
app01-4621	113	20	feature	feature	NOUN
app01-4621	113	21	.	.	PUNCT
app01-4621	114	1	typically	typically	ADV
app01-4621	114	2	,	,	PUNCT
app01-4621	114	3	the	the	DET
app01-4621	114	4	enrichment	enrichment	NOUN
app01-4621	114	5	provides	provide	VERB
app01-4621	114	6	asymptotic	asymptotic	ADJ
app01-4621	114	7	solution	solution	NOUN
app01-4621	114	8	near	near	ADP
app01-4621	114	9	a	a	DET
app01-4621	114	10	crack	crack	NOUN
app01-4621	114	11	tip	tip	NOUN
app01-4621	114	12	or	or	CCONJ
app01-4621	114	13	introduces	introduce	VERB
app01-4621	114	14	strong	strong	ADJ
app01-4621	114	15	/	/	SYM
app01-4621	114	16	weak	weak	ADJ
app01-4621	114	17	discontinuities	discontinuity	NOUN
app01-4621	114	18	[	[	X
app01-4621	114	19	6	6	NUM
app01-4621	114	20	]	]	PUNCT
app01-4621	114	21	.	.	PUNCT
app01-4621	115	1	here	here	ADV
app01-4621	115	2	,	,	PUNCT
app01-4621	115	3	we	we	PRON
app01-4621	115	4	add	add	VERB
app01-4621	115	5	global	global	ADJ
app01-4621	115	6	enrichments	enrichment	NOUN
app01-4621	115	7	that	that	PRON
app01-4621	115	8	capture	capture	VERB
app01-4621	115	9	collective	collective	ADJ
app01-4621	115	10	response	response	NOUN
app01-4621	115	11	of	of	ADP
app01-4621	115	12	a	a	DET
app01-4621	115	13	material	material	NOUN
app01-4621	115	14	microstructure	microstructure	NOUN
app01-4621	115	15	.	.	PUNCT
app01-4621	116	1	the	the	DET
app01-4621	116	2	original	original	ADJ
app01-4621	116	3	shape	shape	NOUN
app01-4621	116	4	functions	function	NOUN
app01-4621	116	5	ni(x	ni(x	NUM
app01-4621	116	6	)	)	PUNCT
app01-4621	116	7	model	model	NOUN
app01-4621	116	8	the	the	DET
app01-4621	116	9	macroscopic	macroscopic	ADJ
app01-4621	116	10	response	response	NOUN
app01-4621	116	11	of	of	ADP
app01-4621	116	12	the	the	DET
app01-4621	116	13	domain	domain	NOUN
app01-4621	116	14	,	,	PUNCT
app01-4621	116	15	while	while	SCONJ
app01-4621	116	16	products	product	NOUN
app01-4621	116	17	ni(x)ψj(x	ni(x)ψj(x	PART
app01-4621	116	18	)	)	PUNCT
app01-4621	116	19	cover	cover	VERB
app01-4621	116	20	the	the	DET
app01-4621	116	21	fluctuations	fluctuation	NOUN
app01-4621	116	22	caused	cause	VERB
app01-4621	116	23	by	by	ADP
app01-4621	116	24	material	material	NOUN
app01-4621	116	25	heterogeneity	heterogeneity	NOUN
app01-4621	116	26	.	.	PUNCT
app01-4621	117	1	a	a	DET
app01-4621	117	2	similar	similar	ADJ
app01-4621	117	3	idea	idea	NOUN
app01-4621	117	4	was	be	AUX
app01-4621	117	5	introduced	introduce	VERB
app01-4621	117	6	by	by	ADP
app01-4621	117	7	strouboulis	strouboulis	PROPN
app01-4621	117	8	et	et	PROPN
app01-4621	117	9	al	al	PROPN
app01-4621	117	10	.	.	PUNCT
app01-4621	118	1	[	[	X
app01-4621	118	2	10	10	NUM
app01-4621	118	3	]	]	PUNCT
app01-4621	118	4	,	,	PUNCT
app01-4621	118	5	who	who	PRON
app01-4621	118	6	used	use	VERB
app01-4621	118	7	numerical	numerical	ADJ
app01-4621	118	8	“	"	PUNCT
app01-4621	118	9	handbook	handbook	NOUN
app01-4621	118	10	”	"	PUNCT
app01-4621	118	11	functions	function	NOUN
app01-4621	118	12	for	for	ADP
app01-4621	118	13	assemblies	assembly	NOUN
app01-4621	118	14	of	of	ADP
app01-4621	118	15	closely	closely	ADV
app01-4621	118	16	packed	pack	VERB
app01-4621	118	17	inclusions	inclusion	NOUN
app01-4621	118	18	,	,	PUNCT
app01-4621	118	19	or	or	CCONJ
app01-4621	118	20	plews	plew	NOUN
app01-4621	118	21	and	and	CCONJ
app01-4621	118	22	duarte	duarte	NOUN
app01-4621	119	1	[	[	X
app01-4621	119	2	11	11	NUM
app01-4621	119	3	]	]	PUNCT
app01-4621	119	4	.	.	PUNCT
app01-4621	120	1	however	however	ADV
app01-4621	120	2	,	,	PUNCT
app01-4621	120	3	both	both	DET
app01-4621	120	4	approaches	approach	VERB
app01-4621	120	5	solve	solve	VERB
app01-4621	120	6	local	local	ADJ
app01-4621	120	7	boundary	boundary	ADJ
app01-4621	120	8	value	value	NOUN
app01-4621	120	9	problems	problem	NOUN
app01-4621	120	10	defined	define	VERB
app01-4621	120	11	on	on	ADP
app01-4621	120	12	subdomains	subdomain	NOUN
app01-4621	120	13	first	first	ADV
app01-4621	120	14	and	and	CCONJ
app01-4621	120	15	subsequently	subsequently	ADV
app01-4621	120	16	run	run	VERB
app01-4621	120	17	the	the	DET
app01-4621	120	18	analysis	analysis	NOUN
app01-4621	120	19	of	of	ADP
app01-4621	120	20	the	the	DET
app01-4621	120	21	whole	whole	ADJ
app01-4621	120	22	domain	domain	NOUN
app01-4621	120	23	.	.	PUNCT
app01-4621	121	1	in	in	ADP
app01-4621	121	2	contrast	contrast	NOUN
app01-4621	121	3	,	,	PUNCT
app01-4621	121	4	we	we	PRON
app01-4621	121	5	precompute	precompute	VERB
app01-4621	121	6	the	the	DET
app01-4621	121	7	fluctuations	fluctuation	NOUN
app01-4621	121	8	purely	purely	ADV
app01-4621	121	9	“	"	PUNCT
app01-4621	121	10	off	off	ADP
app01-4621	121	11	-	-	PUNCT
app01-4621	121	12	line	line	NOUN
app01-4621	121	13	”	"	PUNCT
app01-4621	121	14	at	at	ADP
app01-4621	121	15	the	the	DET
app01-4621	121	16	level	level	NOUN
app01-4621	121	17	of	of	ADP
app01-4621	121	18	microstructure	microstructure	ADJ
app01-4621	121	19	compression	compression	NOUN
app01-4621	121	20	.	.	PUNCT
app01-4621	122	1	i.e.	i.e.	X
app01-4621	122	2	,	,	PUNCT
app01-4621	122	3	without	without	ADP
app01-4621	122	4	any	any	DET
app01-4621	122	5	information	information	NOUN
app01-4621	122	6	of	of	ADP
app01-4621	122	7	the	the	DET
app01-4621	122	8	domain	domain	NOUN
app01-4621	122	9	geometry	geometry	NOUN
app01-4621	122	10	or	or	CCONJ
app01-4621	122	11	loading	loading	NOUN
app01-4621	122	12	,	,	PUNCT
app01-4621	122	13	and	and	CCONJ
app01-4621	122	14	construct	construct	VERB
app01-4621	122	15	the	the	DET
app01-4621	122	16	enrichments	enrichment	NOUN
app01-4621	122	17	as	as	ADP
app01-4621	122	18	an	an	DET
app01-4621	122	19	assembly	assembly	NOUN
app01-4621	122	20	of	of	ADP
app01-4621	122	21	the	the	DET
app01-4621	122	22	tiledefined	tiledefine	VERB
app01-4621	122	23	fluctuation	fluctuation	NOUN
app01-4621	122	24	fields	field	NOUN
app01-4621	122	25	.	.	PUNCT
app01-4621	123	1	in	in	ADP
app01-4621	123	2	our	our	PRON
app01-4621	123	3	approach	approach	NOUN
app01-4621	123	4	,	,	PUNCT
app01-4621	123	5	the	the	DET
app01-4621	123	6	upper	upper	ADJ
app01-4621	123	7	scale	scale	NOUN
app01-4621	123	8	discretization	discretization	NOUN
app01-4621	123	9	is	be	AUX
app01-4621	123	10	constructed	construct	VERB
app01-4621	123	11	irrespectively	irrespectively	ADV
app01-4621	123	12	of	of	ADP
app01-4621	123	13	the	the	DET
app01-4621	123	14	underlying	underlying	ADJ
app01-4621	123	15	microstructural	microstructural	ADJ
app01-4621	123	16	geometry	geometry	NOUN
app01-4621	123	17	of	of	ADP
app01-4621	123	18	ω	ω	PROPN
app01-4621	123	19	.	.	PUNCT
app01-4621	124	1	hence	hence	ADV
app01-4621	124	2	,	,	PUNCT
app01-4621	124	3	the	the	DET
app01-4621	124	4	approximation	approximation	NOUN
app01-4621	124	5	basis	basis	NOUN
app01-4621	124	6	functions	function	NOUN
app01-4621	124	7	in	in	ADP
app01-4621	124	8	the	the	DET
app01-4621	124	9	form	form	NOUN
app01-4621	124	10	of	of	ADP
app01-4621	124	11	eq	eq	PROPN
app01-4621	124	12	.	.	PUNCT
app01-4621	125	1	(	(	PUNCT
app01-4621	125	2	14	14	NUM
app01-4621	125	3	)	)	PUNCT
app01-4621	125	4	together	together	ADV
app01-4621	125	5	with	with	ADP
app01-4621	125	6	fluctuations	fluctuation	NOUN
app01-4621	125	7	in	in	ADP
app01-4621	125	8	material	material	NOUN
app01-4621	125	9	parameters	parameter	NOUN
app01-4621	125	10	due	due	ADP
app01-4621	125	11	to	to	ADP
app01-4621	125	12	the	the	DET
app01-4621	125	13	presence	presence	NOUN
app01-4621	125	14	of	of	ADP
app01-4621	125	15	microstructural	microstructural	ADJ
app01-4621	125	16	geometry	geometry	NOUN
app01-4621	125	17	preclude	preclude	VERB
app01-4621	125	18	efficient	efficient	ADJ
app01-4621	125	19	use	use	NOUN
app01-4621	125	20	of	of	ADP
app01-4621	125	21	standard	standard	ADJ
app01-4621	125	22	numerical	numerical	ADJ
app01-4621	125	23	procedures	procedure	NOUN
app01-4621	125	24	for	for	ADP
app01-4621	125	25	evaluation	evaluation	NOUN
app01-4621	125	26	of	of	ADP
app01-4621	125	27	the	the	DET
app01-4621	125	28	bi	bi	ADJ
app01-4621	125	29	-	-	ADJ
app01-4621	125	30	linear	linear	ADJ
app01-4621	125	31	form	form	NOUN
app01-4621	125	32	in	in	ADP
app01-4621	125	33	eq	eq	ADP
app01-4621	125	34	.	.	PUNCT
app01-4621	126	1	(	(	PUNCT
app01-4621	126	2	13	13	NUM
app01-4621	126	3	)	)	PUNCT
app01-4621	126	4	.	.	PUNCT
app01-4621	127	1	in	in	ADP
app01-4621	127	2	order	order	NOUN
app01-4621	127	3	to	to	PART
app01-4621	127	4	circumvent	circumvent	VERB
app01-4621	127	5	this	this	DET
app01-4621	127	6	drawback	drawback	NOUN
app01-4621	127	7	,	,	PUNCT
app01-4621	127	8	we	we	PRON
app01-4621	127	9	construct	construct	VERB
app01-4621	127	10	another	another	PRON
app01-4621	127	11	,	,	PUNCT
app01-4621	127	12	finer	fine	ADJ
app01-4621	127	13	domain	domain	NOUN
app01-4621	127	14	discretization	discretization	NOUN
app01-4621	127	15	space	space	NOUN
app01-4621	127	16	vf	vf	PROPN
app01-4621	127	17	,	,	PUNCT
app01-4621	127	18	assembled	assemble	VERB
app01-4621	127	19	from	from	ADP
app01-4621	127	20	the	the	DET
app01-4621	127	21	tile	tile	NOUN
app01-4621	127	22	discretization	discretization	NOUN
app01-4621	127	23	used	use	VERB
app01-4621	127	24	in	in	ADP
app01-4621	127	25	the	the	DET
app01-4621	127	26	off	off	ADJ
app01-4621	127	27	-	-	PUNCT
app01-4621	127	28	line	line	NOUN
app01-4621	127	29	phase	phase	NOUN
app01-4621	127	30	for	for	ADP
app01-4621	127	31	extracting	extract	VERB
app01-4621	127	32	fluctuation	fluctuation	NOUN
app01-4621	127	33	fields	field	NOUN
app01-4621	127	34	.	.	PUNCT
app01-4621	128	1	the	the	DET
app01-4621	128	2	shape	shape	NOUN
app01-4621	128	3	functions	function	NOUN
app01-4621	128	4	ni(x	ni(x	NUM
app01-4621	128	5	)	)	PUNCT
app01-4621	128	6	,	,	PUNCT
app01-4621	128	7	defined	define	VERB
app01-4621	128	8	at	at	ADP
app01-4621	128	9	the	the	DET
app01-4621	128	10	coarser	coarse	ADJ
app01-4621	128	11	discretization	discretization	NOUN
app01-4621	128	12	,	,	PUNCT
app01-4621	128	13	are	be	AUX
app01-4621	128	14	projected	project	VERB
app01-4621	128	15	onto	onto	ADP
app01-4621	128	16	the	the	DET
app01-4621	128	17	fine	fine	ADJ
app01-4621	128	18	mesh	mesh	NOUN
app01-4621	128	19	;	;	PUNCT
app01-4621	128	20	enrichments	enrichment	NOUN
app01-4621	128	21	ψj(x	ψj(x	PUNCT
app01-4621	128	22	)	)	PUNCT
app01-4621	128	23	are	be	AUX
app01-4621	128	24	already	already	ADV
app01-4621	128	25	defined	define	VERB
app01-4621	128	26	within	within	ADP
app01-4621	128	27	the	the	DET
app01-4621	128	28	fine	fine	ADJ
app01-4621	128	29	discretization	discretization	NOUN
app01-4621	128	30	by	by	ADP
app01-4621	128	31	construction	construction	NOUN
app01-4621	128	32	.	.	PUNCT
app01-4621	129	1	consequently	consequently	ADV
app01-4621	129	2	,	,	PUNCT
app01-4621	129	3	eq	eq	NOUN
app01-4621	129	4	.	.	PUNCT
app01-4621	130	1	(	(	PUNCT
app01-4621	130	2	14	14	NUM
app01-4621	130	3	)	)	PUNCT
app01-4621	130	4	can	can	AUX
app01-4621	130	5	be	be	AUX
app01-4621	130	6	understood	understand	VERB
app01-4621	130	7	as	as	ADP
app01-4621	130	8	a	a	DET
app01-4621	130	9	definition	definition	NOUN
app01-4621	130	10	of	of	ADP
app01-4621	130	11	reduced	reduce	VERB
app01-4621	130	12	modes	mode	NOUN
app01-4621	130	13	for	for	ADP
app01-4621	130	14	the	the	DET
app01-4621	130	15	fine	fine	ADJ
app01-4621	130	16	discretization	discretization	NOUN
app01-4621	130	17	.	.	PUNCT
app01-4621	131	1	let	let	VERB
app01-4621	131	2	matrix	matrix	NOUN
app01-4621	131	3	φ	φ	PROPN
app01-4621	131	4	comprises	comprise	VERB
app01-4621	131	5	individual	individual	ADJ
app01-4621	131	6	reduced	reduce	VERB
app01-4621	131	7	modes	mode	NOUN
app01-4621	131	8	as	as	ADP
app01-4621	131	9	its	its	PRON
app01-4621	131	10	columns	column	NOUN
app01-4621	131	11	,	,	PUNCT
app01-4621	131	12	computed	compute	VERB
app01-4621	131	13	as	as	ADP
app01-4621	131	14	an	an	DET
app01-4621	131	15	element	element	ADJ
app01-4621	131	16	-	-	PUNCT
app01-4621	131	17	wise	wise	ADJ
app01-4621	131	18	product	product	NOUN
app01-4621	131	19	of	of	ADP
app01-4621	131	20	the	the	DET
app01-4621	131	21	projectedni(x	projectedni(x	NOUN
app01-4621	131	22	)	)	PUNCT
app01-4621	131	23	and	and	CCONJ
app01-4621	131	24	ψj(x	ψj(x	NUM
app01-4621	131	25	)	)	PUNCT
app01-4621	131	26	following	follow	VERB
app01-4621	131	27	eq	eq	ADP
app01-4621	131	28	.	.	PUNCT
app01-4621	132	1	(	(	PUNCT
app01-4621	132	2	14	14	NUM
app01-4621	132	3	)	)	PUNCT
app01-4621	132	4	.	.	PUNCT
app01-4621	133	1	the	the	DET
app01-4621	133	2	range	range	NOUN
app01-4621	133	3	of	of	ADP
app01-4621	133	4	φ	φ	PROPN
app01-4621	133	5	thus	thus	ADV
app01-4621	133	6	defines	define	VERB
app01-4621	133	7	a	a	DET
app01-4621	133	8	subspace	subspace	NOUN
app01-4621	133	9	of	of	ADP
app01-4621	133	10	vf	vf	PROPN
app01-4621	133	11	corresponding	correspond	VERB
app01-4621	133	12	to	to	ADP
app01-4621	133	13	vc	vc	PROPN
app01-4621	133	14	.	.	PUNCT
app01-4621	134	1	instead	instead	ADV
app01-4621	134	2	of	of	ADP
app01-4621	134	3	solving	solve	VERB
app01-4621	134	4	the	the	DET
app01-4621	134	5	large	large	ADJ
app01-4621	134	6	,	,	PUNCT
app01-4621	134	7	fine	fine	ADJ
app01-4621	134	8	-	-	PUNCT
app01-4621	134	9	discretization	discretization	NOUN
app01-4621	134	10	system	system	NOUN
app01-4621	134	11	kfθf	kfθf	NOUN
app01-4621	134	12	=	=	SYM
app01-4621	134	13	ff	ff	NOUN
app01-4621	134	14	,	,	PUNCT
app01-4621	134	15	we	we	PRON
app01-4621	134	16	restrict	restrict	VERB
app01-4621	134	17	the	the	DET
app01-4621	134	18	fine	fine	ADJ
app01-4621	134	19	-	-	PUNCT
app01-4621	134	20	discretization	discretization	NOUN
app01-4621	134	21	unknowns	unknown	NOUN
app01-4621	134	22	θf	θf	VERB
app01-4621	134	23	via	via	ADP
app01-4621	134	24	θf	θf	NOUN
app01-4621	134	25	=	=	PROPN
app01-4621	134	26	φ	φ	PROPN
app01-4621	134	27	a	a	PRON
app01-4621	134	28	,	,	PUNCT
app01-4621	134	29	(	(	PUNCT
app01-4621	134	30	15	15	NUM
app01-4621	134	31	)	)	PUNCT
app01-4621	134	32	where	where	SCONJ
app01-4621	134	33	a	a	DET
app01-4621	134	34	denotes	denote	NOUN
app01-4621	134	35	the	the	DET
app01-4621	134	36	vector	vector	NOUN
app01-4621	134	37	of	of	ADP
app01-4621	134	38	unknown	unknown	ADJ
app01-4621	134	39	coefficients	coefficient	NOUN
app01-4621	134	40	pertinent	pertinent	ADJ
app01-4621	134	41	to	to	ADP
app01-4621	134	42	the	the	DET
app01-4621	134	43	reduced	reduce	VERB
app01-4621	134	44	modes	mode	NOUN
app01-4621	134	45	.	.	PUNCT
app01-4621	135	1	the	the	DET
app01-4621	135	2	final	final	ADJ
app01-4621	135	3	algebraic	algebraic	ADJ
app01-4621	135	4	system	system	NOUN
app01-4621	135	5	then	then	ADV
app01-4621	135	6	takes	take	VERB
app01-4621	135	7	the	the	DET
app01-4621	135	8	form	form	NOUN
app01-4621	135	9	φtkfφa	φtkfφa	NOUN
app01-4621	135	10	=	=	SYM
app01-4621	135	11	φtff	φtff	NOUN
app01-4621	135	12	.	.	PUNCT
app01-4621	136	1	(	(	PUNCT
app01-4621	136	2	16	16	NUM
app01-4621	136	3	)	)	PUNCT
app01-4621	136	4	5	5	NUM
app01-4621	136	5	.	.	PUNCT
app01-4621	136	6	results	result	NOUN
app01-4621	136	7	we	we	PRON
app01-4621	136	8	considered	consider	VERB
app01-4621	136	9	the	the	DET
app01-4621	136	10	material	material	NOUN
app01-4621	136	11	microstructure	microstructure	NOUN
app01-4621	136	12	of	of	ADP
app01-4621	136	13	monodisperse	monodisperse	ADJ
app01-4621	136	14	elliptical	elliptical	ADJ
app01-4621	136	15	inclusions	inclusion	NOUN
app01-4621	136	16	,	,	PUNCT
app01-4621	136	17	shown	show	VERB
app01-4621	136	18	in	in	ADP
app01-4621	136	19	figure	figure	NOUN
app01-4621	136	20	1	1	NUM
app01-4621	136	21	.	.	PUNCT
app01-4621	137	1	both	both	DET
app01-4621	137	2	phases	phase	NOUN
app01-4621	137	3	were	be	AUX
app01-4621	137	4	assumed	assume	VERB
app01-4621	137	5	isotropic	isotropic	NOUN
app01-4621	137	6	,	,	PUNCT
app01-4621	137	7	with	with	ADP
app01-4621	137	8	the	the	DET
app01-4621	137	9	inclusion	inclusion	NOUN
app01-4621	137	10	material	material	NOUN
app01-4621	137	11	being	be	AUX
app01-4621	137	12	more	more	ADV
app01-4621	137	13	conductive	conductive	ADJ
app01-4621	137	14	(	(	PUNCT
app01-4621	137	15	k(x	k(x	PROPN
app01-4621	137	16	)	)	PUNCT
app01-4621	137	17	=	=	PUNCT
app01-4621	138	1	100	100	NUM
app01-4621	138	2	i	i	NOUN
app01-4621	138	3	)	)	PUNCT
app01-4621	138	4	than	than	ADP
app01-4621	138	5	the	the	DET
app01-4621	138	6	matrix	matrix	NOUN
app01-4621	138	7	phase	phase	NOUN
app01-4621	138	8	(	(	PUNCT
app01-4621	138	9	k(x	k(x	PROPN
app01-4621	138	10	)	)	PUNCT
app01-4621	138	11	=	=	SYM
app01-4621	138	12	1	1	NUM
app01-4621	138	13	i	i	NOUN
app01-4621	138	14	)	)	PUNCT
app01-4621	138	15	.	.	PUNCT
app01-4621	139	1	six	six	NUM
app01-4621	139	2	fluctuation	fluctuation	NOUN
app01-4621	139	3	fields	field	NOUN
app01-4621	139	4	in	in	ADP
app01-4621	139	5	total	total	ADJ
app01-4621	139	6	,	,	PUNCT
app01-4621	139	7	discretized	discretize	VERB
app01-4621	139	8	with	with	ADP
app01-4621	139	9	linear	linear	ADJ
app01-4621	139	10	triangular	triangular	NOUN
app01-4621	139	11	elements	element	NOUN
app01-4621	139	12	,	,	PUNCT
app01-4621	139	13	were	be	AUX
app01-4621	139	14	extracted	extract	VERB
app01-4621	139	15	,	,	PUNCT
app01-4621	139	16	see	see	VERB
app01-4621	139	17	figure	figure	NOUN
app01-4621	139	18	2	2	NUM
app01-4621	139	19	.	.	PUNCT
app01-4621	140	1	the	the	DET
app01-4621	140	2	microstructure	microstructure	NOUN
app01-4621	140	3	was	be	AUX
app01-4621	140	4	superimposed	superimpose	VERB
app01-4621	140	5	to	to	ADP
app01-4621	140	6	an	an	DET
app01-4621	140	7	upperscale	upperscale	ADJ
app01-4621	140	8	problem	problem	NOUN
app01-4621	140	9	represented	represent	VERB
app01-4621	140	10	by	by	ADP
app01-4621	140	11	an	an	DET
app01-4621	140	12	l	l	ADV
app01-4621	140	13	-	-	ADJ
app01-4621	140	14	shaped	shape	VERB
app01-4621	140	15	domain	domain	NOUN
app01-4621	140	16	with	with	ADP
app01-4621	140	17	uniform	uniform	ADJ
app01-4621	140	18	temperature	temperature	NOUN
app01-4621	140	19	profiles	profile	NOUN
app01-4621	140	20	prescribed	prescribe	VERB
app01-4621	140	21	at	at	ADP
app01-4621	140	22	the	the	DET
app01-4621	140	23	bottom	bottom	NOUN
app01-4621	140	24	and	and	CCONJ
app01-4621	140	25	right	right	ADJ
app01-4621	140	26	-	-	PUNCT
app01-4621	140	27	hand	hand	NOUN
app01-4621	140	28	side	side	NOUN
app01-4621	140	29	edges	edge	NOUN
app01-4621	140	30	.	.	PUNCT
app01-4621	141	1	the	the	DET
app01-4621	141	2	initial	initial	ADJ
app01-4621	141	3	coarse	coarse	ADJ
app01-4621	141	4	discretization	discretization	NOUN
app01-4621	141	5	of	of	ADP
app01-4621	141	6	the	the	DET
app01-4621	141	7	domain	domain	NOUN
app01-4621	141	8	is	be	AUX
app01-4621	141	9	depicted	depict	VERB
app01-4621	141	10	in	in	ADP
app01-4621	141	11	figure	figure	NOUN
app01-4621	141	12	3	3	NUM
app01-4621	141	13	.	.	PUNCT
app01-4621	142	1	the	the	DET
app01-4621	142	2	linear	linear	PROPN
app01-4621	142	3	lagrange	lagrange	PROPN
app01-4621	142	4	basis	basis	NOUN
app01-4621	142	5	functions	function	NOUN
app01-4621	142	6	were	be	AUX
app01-4621	142	7	assumed	assume	VERB
app01-4621	142	8	at	at	ADP
app01-4621	142	9	the	the	DET
app01-4621	142	10	coarse	coarse	ADJ
app01-4621	142	11	level	level	NOUN
app01-4621	142	12	,	,	PUNCT
app01-4621	142	13	whilst	whilst	SCONJ
app01-4621	142	14	the	the	DET
app01-4621	142	15	fine	fine	ADJ
app01-4621	142	16	space	space	NOUN
app01-4621	142	17	comprised	comprise	VERB
app01-4621	142	18	the	the	DET
app01-4621	142	19	quadratic	quadratic	ADJ
app01-4621	142	20	lagrange	lagrange	NOUN
app01-4621	142	21	approximation	approximation	NOUN
app01-4621	142	22	arising	arise	VERB
app01-4621	142	23	from	from	ADP
app01-4621	142	24	the	the	DET
app01-4621	142	25	product	product	NOUN
app01-4621	142	26	of	of	ADP
app01-4621	142	27	linear	linear	PROPN
app01-4621	142	28	coarse	coarse	NOUN
app01-4621	142	29	shape	shape	NOUN
app01-4621	142	30	functions	function	NOUN
app01-4621	142	31	and	and	CCONJ
app01-4621	142	32	the	the	DET
app01-4621	142	33	enrichments	enrichment	NOUN
app01-4621	142	34	.	.	PUNCT
app01-4621	143	1	the	the	DET
app01-4621	143	2	solution	solution	NOUN
app01-4621	143	3	θxfem	θxfem	NOUN
app01-4621	143	4	of	of	ADP
app01-4621	143	5	eq	eq	PROPN
app01-4621	143	6	.	.	PUNCT
app01-4621	144	1	(	(	PUNCT
app01-4621	144	2	16	16	NUM
app01-4621	144	3	)	)	PUNCT
app01-4621	144	4	was	be	AUX
app01-4621	144	5	compared	compare	VERB
app01-4621	144	6	against	against	ADP
app01-4621	144	7	direct	direct	PROPN
app01-4621	144	8	numerical	numerical	PROPN
app01-4621	144	9	simulation	simulation	PROPN
app01-4621	144	10	(	(	PUNCT
app01-4621	144	11	dns	dns	PROPN
app01-4621	144	12	)	)	PUNCT
app01-4621	144	13	θdns	θdns	PROPN
app01-4621	144	14	,	,	PUNCT
app01-4621	144	15	which	which	PRON
app01-4621	144	16	was	be	AUX
app01-4621	144	17	taken	take	VERB
app01-4621	144	18	as	as	ADP
app01-4621	144	19	the	the	DET
app01-4621	144	20	reference	reference	NOUN
app01-4621	144	21	solution	solution	NOUN
app01-4621	144	22	.	.	PUNCT
app01-4621	145	1	a	a	DET
app01-4621	145	2	sequence	sequence	NOUN
app01-4621	145	3	of	of	ADP
app01-4621	145	4	five	five	NUM
app01-4621	145	5	uniformly	uniformly	ADV
app01-4621	145	6	refined	refined	ADJ
app01-4621	145	7	coarse	coarse	NOUN
app01-4621	145	8	discretizations	discretization	NOUN
app01-4621	145	9	,	,	PUNCT
app01-4621	145	10	the	the	DET
app01-4621	145	11	first	first	ADJ
app01-4621	145	12	one	one	NOUN
app01-4621	145	13	shown	show	VERB
app01-4621	145	14	in	in	ADP
app01-4621	145	15	figure	figure	NOUN
app01-4621	145	16	3	3	NUM
app01-4621	145	17	,	,	PUNCT
app01-4621	145	18	was	be	AUX
app01-4621	145	19	investigated	investigate	VERB
app01-4621	145	20	.	.	PUNCT
app01-4621	146	1	the	the	DET
app01-4621	146	2	proximity	proximity	NOUN
app01-4621	146	3	of	of	ADP
app01-4621	146	4	the	the	DET
app01-4621	146	5	reference	reference	NOUN
app01-4621	146	6	(	(	PUNCT
app01-4621	146	7	dns	dns	PROPN
app01-4621	146	8	)	)	PUNCT
app01-4621	146	9	and	and	CCONJ
app01-4621	146	10	xfem	xfem	PROPN
app01-4621	146	11	solutions	solution	VERB
app01-4621	146	12	32	32	NUM
app01-4621	146	13	vol	vol	NOUN
app01-4621	146	14	.	.	PUNCT
app01-4621	147	1	13/2017	13/2017	NUM
app01-4621	147	2	synthesized	synthesize	VERB
app01-4621	147	3	microstructure	microstructure	NOUN
app01-4621	147	4	-	-	PUNCT
app01-4621	147	5	informed	inform	VERB
app01-4621	147	6	enrichments	enrichment	NOUN
app01-4621	147	7	for	for	ADP
app01-4621	147	8	xfem	xfem	PROPN
app01-4621	147	9	analyses	analysis	NOUN
app01-4621	147	10	θ̂	θ̂	NUM
app01-4621	147	11	=	=	SYM
app01-4621	147	12	20	20	NUM
app01-4621	147	13	10	10	NUM
app01-4621	147	14	tx	tx	PROPN
app01-4621	147	15	10	10	NUM
app01-4621	147	16	ty	ty	NOUN
app01-4621	147	17	θ̂	θ̂	PUNCT
app01-4621	147	18	=	=	SYM
app01-4621	147	19	0	0	NUM
app01-4621	147	20	10	10	NUM
app01-4621	147	21	tx	tx	PROPN
app01-4621	147	22	10	10	NUM
app01-4621	147	23	ty	ty	NUM
app01-4621	147	24	figure	figure	NOUN
app01-4621	147	25	3	3	NUM
app01-4621	147	26	.	.	PUNCT
app01-4621	148	1	a	a	DET
app01-4621	148	2	scheme	scheme	NOUN
app01-4621	148	3	of	of	ADP
app01-4621	148	4	the	the	DET
app01-4621	148	5	problem	problem	NOUN
app01-4621	148	6	definition	definition	NOUN
app01-4621	148	7	.	.	PUNCT
app01-4621	149	1	the	the	DET
app01-4621	149	2	edge	edge	NOUN
app01-4621	149	3	lengths	length	NOUN
app01-4621	149	4	tx	tx	VERB
app01-4621	149	5	and	and	CCONJ
app01-4621	149	6	ty	ty	NUM
app01-4621	149	7	of	of	ADP
app01-4621	149	8	the	the	DET
app01-4621	149	9	tiles	tile	NOUN
app01-4621	149	10	were	be	AUX
app01-4621	149	11	set	set	VERB
app01-4621	149	12	as	as	ADP
app01-4621	149	13	tx	tx	PROPN
app01-4621	149	14	=	=	PUNCT
app01-4621	149	15	ty	ty	NOUN
app01-4621	149	16	=	=	NOUN
app01-4621	149	17	6	6	NUM
app01-4621	149	18	.	.	PUNCT
app01-4621	150	1	all	all	DET
app01-4621	150	2	quantities	quantity	NOUN
app01-4621	150	3	are	be	AUX
app01-4621	150	4	in	in	ADP
app01-4621	150	5	consistent	consistent	ADJ
app01-4621	150	6	units	unit	NOUN
app01-4621	150	7	.	.	PUNCT
app01-4621	151	1	was	be	AUX
app01-4621	151	2	quantified	quantify	VERB
app01-4621	151	3	via	via	ADP
app01-4621	151	4	relative	relative	ADJ
app01-4621	151	5	errors	error	NOUN
app01-4621	151	6	εl2	εl2	VERB
app01-4621	152	1	=	=	SYM
app01-4621	152	2	∥∥θdns	∥∥θdns	NOUN
app01-4621	152	3	−	−	NOUN
app01-4621	152	4	θxfem	θxfem	NOUN
app01-4621	152	5	∥∥	∥∥	PRON
app01-4621	152	6	l2	l2	VERB
app01-4621	152	7	‖θdns‖l2	‖θdns‖l2	PROPN
app01-4621	152	8	and	and	CCONJ
app01-4621	152	9	(	(	PUNCT
app01-4621	152	10	17	17	NUM
app01-4621	152	11	)	)	PUNCT
app01-4621	152	12	εh1	εh1	NOUN
app01-4621	152	13	=	=	SYM
app01-4621	153	1	∥∥θdns	∥∥θdns	NOUN
app01-4621	153	2	−	−	NOUN
app01-4621	153	3	θxfem	θxfem	VERB
app01-4621	153	4	∥∥	∥∥	X
app01-4621	153	5	h1	h1	VERB
app01-4621	153	6	‖θdns‖h1	‖θdns‖h1	SYM
app01-4621	153	7	,	,	PUNCT
app01-4621	153	8	(	(	PUNCT
app01-4621	153	9	18	18	NUM
app01-4621	153	10	)	)	PUNCT
app01-4621	153	11	where	where	SCONJ
app01-4621	153	12	‖u‖2l2	‖u‖2l2	PROPN
app01-4621	153	13	=	=	SYM
app01-4621	153	14	∫	∫	PROPN
app01-4621	153	15	ω	ω	NUM
app01-4621	153	16	u2(x	u2(x	NUM
app01-4621	153	17	)	)	PUNCT
app01-4621	153	18	dx	dx	PROPN
app01-4621	153	19	and	and	CCONJ
app01-4621	153	20	(	(	PUNCT
app01-4621	153	21	19	19	NUM
app01-4621	153	22	)	)	PUNCT
app01-4621	153	23	‖u‖2h1	‖u‖2h1	NOUN
app01-4621	153	24	=	=	SYM
app01-4621	153	25	∫	∫	PROPN
app01-4621	153	26	ω	ω	NUM
app01-4621	153	27	u2(x	u2(x	NOUN
app01-4621	153	28	)	)	PUNCT
app01-4621	153	29	+	+	ADJ
app01-4621	153	30	∇u(x	∇u(x	NOUN
app01-4621	153	31	)	)	PUNCT
app01-4621	153	32	·	·	PUNCT
app01-4621	153	33	∇u(x	∇u(x	NOUN
app01-4621	153	34	)	)	PUNCT
app01-4621	153	35	dx	dx	PROPN
app01-4621	153	36	.	.	PUNCT
app01-4621	154	1	(	(	PUNCT
app01-4621	154	2	20	20	NUM
app01-4621	154	3	)	)	PUNCT
app01-4621	154	4	mean	mean	NOUN
app01-4621	154	5	and	and	CCONJ
app01-4621	154	6	standard	standard	ADJ
app01-4621	154	7	deviations	deviation	NOUN
app01-4621	154	8	of	of	ADP
app01-4621	154	9	the	the	DET
app01-4621	154	10	errors	error	NOUN
app01-4621	154	11	computed	compute	VERB
app01-4621	154	12	for	for	ADP
app01-4621	154	13	five	five	NUM
app01-4621	154	14	coarse	coarse	ADJ
app01-4621	154	15	discretizations	discretization	NOUN
app01-4621	154	16	and	and	CCONJ
app01-4621	154	17	six	six	NUM
app01-4621	154	18	different	different	ADJ
app01-4621	154	19	tiling	tiling	NOUN
app01-4621	154	20	realizations	realization	NOUN
app01-4621	154	21	are	be	AUX
app01-4621	154	22	given	give	VERB
app01-4621	154	23	in	in	ADP
app01-4621	154	24	figure	figure	NOUN
app01-4621	154	25	4	4	NUM
app01-4621	154	26	.	.	PUNCT
app01-4621	155	1	10!4	10!4	NOUN
app01-4621	155	2	10!3	10!3	NUM
app01-4621	155	3	10!2	10!2	PROPN
app01-4621	155	4	xfem	xfem	PROPN
app01-4621	155	5	/	/	SYM
app01-4621	155	6	dns	dns	NOUN
app01-4621	155	7	dofs	dof	NOUN
app01-4621	155	8	10!2	10!2	PROPN
app01-4621	155	9	10!1	10!1	NUM
app01-4621	155	10	0	0	SYM
app01-4621	155	11	0	0	NUM
app01-4621	155	12	l2	l2	NOUN
app01-4621	155	13	h1	h1	NOUN
app01-4621	155	14	figure	figure	NOUN
app01-4621	155	15	4	4	NUM
app01-4621	155	16	.	.	PUNCT
app01-4621	155	17	convergence	convergence	NOUN
app01-4621	155	18	of	of	ADP
app01-4621	155	19	l2	l2	NOUN
app01-4621	155	20	and	and	CCONJ
app01-4621	155	21	h1	h1	VERB
app01-4621	155	22	errors	error	NOUN
app01-4621	155	23	with	with	ADP
app01-4621	155	24	increasing	increase	VERB
app01-4621	155	25	number	number	NOUN
app01-4621	155	26	of	of	ADP
app01-4621	155	27	dofs	dof	NOUN
app01-4621	155	28	in	in	ADP
app01-4621	155	29	the	the	DET
app01-4621	155	30	coarse	coarse	ADJ
app01-4621	155	31	discretization	discretization	NOUN
app01-4621	155	32	.	.	PUNCT
app01-4621	156	1	6	6	X
app01-4621	156	2	.	.	X
app01-4621	156	3	conclusions	conclusion	NOUN
app01-4621	156	4	we	we	PRON
app01-4621	156	5	have	have	AUX
app01-4621	156	6	presented	present	VERB
app01-4621	156	7	a	a	DET
app01-4621	156	8	method	method	NOUN
app01-4621	156	9	for	for	ADP
app01-4621	156	10	extracting	extract	VERB
app01-4621	156	11	continuous	continuous	ADJ
app01-4621	156	12	fluctuation	fluctuation	NOUN
app01-4621	156	13	fields	field	NOUN
app01-4621	156	14	from	from	ADP
app01-4621	156	15	a	a	DET
app01-4621	156	16	microstructure	microstructure	NOUN
app01-4621	156	17	compressed	compress	VERB
app01-4621	156	18	by	by	ADP
app01-4621	156	19	means	mean	NOUN
app01-4621	156	20	of	of	ADP
app01-4621	156	21	wang	wang	PROPN
app01-4621	156	22	tiles	tiles	PROPN
app01-4621	156	23	.	.	PUNCT
app01-4621	157	1	we	we	PRON
app01-4621	157	2	have	have	AUX
app01-4621	157	3	also	also	ADV
app01-4621	157	4	demonstrated	demonstrate	VERB
app01-4621	157	5	utilization	utilization	NOUN
app01-4621	157	6	of	of	ADP
app01-4621	157	7	these	these	DET
app01-4621	157	8	fields	field	NOUN
app01-4621	157	9	as	as	ADP
app01-4621	157	10	enrichments	enrichment	NOUN
app01-4621	157	11	in	in	ADP
app01-4621	157	12	xfem	xfem	PROPN
app01-4621	157	13	.	.	PUNCT
app01-4621	158	1	in	in	ADP
app01-4621	158	2	order	order	NOUN
app01-4621	158	3	to	to	PART
app01-4621	158	4	avoid	avoid	VERB
app01-4621	158	5	non	non	ADJ
app01-4621	158	6	-	-	ADJ
app01-4621	158	7	standard	standard	ADJ
app01-4621	158	8	quadratures	quadrature	NOUN
app01-4621	158	9	,	,	PUNCT
app01-4621	158	10	xfem	xfem	PROPN
app01-4621	158	11	basis	basis	NOUN
app01-4621	158	12	functions	function	NOUN
app01-4621	158	13	were	be	AUX
app01-4621	158	14	projected	project	VERB
app01-4621	158	15	onto	onto	ADP
app01-4621	158	16	a	a	DET
app01-4621	158	17	discretization	discretization	NOUN
app01-4621	158	18	arising	arise	VERB
app01-4621	158	19	from	from	ADP
app01-4621	158	20	assembly	assembly	NOUN
app01-4621	158	21	of	of	ADP
app01-4621	158	22	the	the	DET
app01-4621	158	23	tile	tile	NOUN
app01-4621	158	24	discretization	discretization	NOUN
app01-4621	158	25	used	use	VERB
app01-4621	158	26	for	for	ADP
app01-4621	158	27	computing	compute	VERB
app01-4621	158	28	the	the	DET
app01-4621	158	29	fluctuation	fluctuation	NOUN
app01-4621	158	30	fields	field	NOUN
app01-4621	158	31	.	.	PUNCT
app01-4621	159	1	the	the	DET
app01-4621	159	2	proposed	propose	VERB
app01-4621	159	3	methodology	methodology	NOUN
app01-4621	159	4	was	be	AUX
app01-4621	159	5	applied	apply	VERB
app01-4621	159	6	to	to	ADP
app01-4621	159	7	a	a	DET
app01-4621	159	8	steadystate	steadystate	ADJ
app01-4621	159	9	heat	heat	NOUN
app01-4621	159	10	conduction	conduction	NOUN
app01-4621	159	11	problem	problem	NOUN
app01-4621	159	12	defined	define	VERB
app01-4621	159	13	in	in	ADP
app01-4621	159	14	an	an	DET
app01-4621	159	15	l	l	NOUN
app01-4621	159	16	-	-	ADJ
app01-4621	159	17	shaped	shape	VERB
app01-4621	159	18	domain	domain	NOUN
app01-4621	159	19	with	with	ADP
app01-4621	159	20	microstructural	microstructural	ADJ
app01-4621	159	21	geometry	geometry	NOUN
app01-4621	159	22	provided	provide	VERB
app01-4621	159	23	by	by	ADP
app01-4621	159	24	the	the	DET
app01-4621	159	25	tiling	tile	VERB
app01-4621	159	26	concept	concept	NOUN
app01-4621	159	27	.	.	PUNCT
app01-4621	160	1	only	only	ADV
app01-4621	160	2	1.6	1.6	NUM
app01-4621	160	3	%	%	NOUN
app01-4621	160	4	of	of	ADP
app01-4621	160	5	the	the	DET
app01-4621	160	6	original	original	ADJ
app01-4621	160	7	degrees	degree	NOUN
app01-4621	160	8	of	of	ADP
app01-4621	160	9	freedom	freedom	NOUN
app01-4621	160	10	were	be	AUX
app01-4621	160	11	sufficient	sufficient	ADJ
app01-4621	160	12	to	to	PART
app01-4621	160	13	obtain	obtain	VERB
app01-4621	160	14	2	2	NUM
app01-4621	160	15	%	%	NOUN
app01-4621	160	16	relative	relative	ADJ
app01-4621	160	17	error	error	NOUN
app01-4621	160	18	compared	compare	VERB
app01-4621	160	19	to	to	ADP
app01-4621	160	20	dns	dns	PROPN
app01-4621	160	21	.	.	PUNCT
app01-4621	161	1	on	on	ADP
app01-4621	161	2	the	the	DET
app01-4621	161	3	other	other	ADJ
app01-4621	161	4	hand	hand	NOUN
app01-4621	161	5	,	,	PUNCT
app01-4621	161	6	the	the	DET
app01-4621	161	7	reduction	reduction	NOUN
app01-4621	161	8	in	in	ADP
app01-4621	161	9	dofs	dof	NOUN
app01-4621	161	10	accelerates	accelerate	VERB
app01-4621	161	11	only	only	ADV
app01-4621	161	12	the	the	DET
app01-4621	161	13	solution	solution	NOUN
app01-4621	161	14	of	of	ADP
app01-4621	161	15	eq	eq	PROPN
app01-4621	161	16	.	.	PUNCT
app01-4621	162	1	(	(	PUNCT
app01-4621	162	2	16	16	NUM
app01-4621	162	3	)	)	PUNCT
app01-4621	162	4	.	.	PUNCT
app01-4621	163	1	for	for	ADP
app01-4621	163	2	more	more	ADV
app01-4621	163	3	significant	significant	ADJ
app01-4621	163	4	time	time	NOUN
app01-4621	163	5	savings	saving	NOUN
app01-4621	163	6	,	,	PUNCT
app01-4621	163	7	a	a	DET
app01-4621	163	8	low	low	ADJ
app01-4621	163	9	-	-	PUNCT
app01-4621	163	10	rank	rank	NOUN
app01-4621	163	11	additional	additional	ADJ
app01-4621	163	12	approximation	approximation	NOUN
app01-4621	163	13	of	of	ADP
app01-4621	163	14	kf	kf	PROPN
app01-4621	163	15	,	,	PUNCT
app01-4621	163	16	e.g.	e.g.	ADV
app01-4621	163	17	using	use	VERB
app01-4621	163	18	the	the	DET
app01-4621	163	19	idea	idea	NOUN
app01-4621	163	20	of	of	ADP
app01-4621	163	21	hyper	hyper	NOUN
app01-4621	163	22	-	-	NOUN
app01-4621	163	23	reduction	reduction	NOUN
app01-4621	163	24	[	[	X
app01-4621	163	25	12	12	NUM
app01-4621	163	26	]	]	PUNCT
app01-4621	163	27	,	,	PUNCT
app01-4621	163	28	has	have	VERB
app01-4621	163	29	to	to	PART
app01-4621	163	30	be	be	AUX
app01-4621	163	31	introduced	introduce	VERB
app01-4621	163	32	and	and	CCONJ
app01-4621	163	33	is	be	AUX
app01-4621	163	34	the	the	DET
app01-4621	163	35	focus	focus	NOUN
app01-4621	163	36	of	of	ADP
app01-4621	163	37	our	our	PRON
app01-4621	163	38	current	current	ADJ
app01-4621	163	39	work	work	NOUN
app01-4621	163	40	.	.	PUNCT
app01-4621	164	1	we	we	PRON
app01-4621	164	2	have	have	AUX
app01-4621	164	3	also	also	ADV
app01-4621	164	4	restricted	restrict	VERB
app01-4621	164	5	ourself	ourself	PRON
app01-4621	164	6	to	to	ADP
app01-4621	164	7	the	the	DET
app01-4621	164	8	first	first	ADJ
app01-4621	164	9	-	-	PUNCT
app01-4621	164	10	order	order	NOUN
app01-4621	164	11	decomposition	decomposition	NOUN
app01-4621	164	12	,	,	PUNCT
app01-4621	164	13	eq	eq	NOUN
app01-4621	164	14	.	.	PUNCT
app01-4621	165	1	(	(	PUNCT
app01-4621	165	2	2	2	NUM
app01-4621	165	3	)	)	PUNCT
app01-4621	165	4	;	;	PUNCT
app01-4621	165	5	higher	high	ADJ
app01-4621	165	6	order	order	NOUN
app01-4621	165	7	expansion	expansion	NOUN
app01-4621	165	8	of	of	ADP
app01-4621	165	9	the	the	DET
app01-4621	165	10	macroscopic	macroscopic	ADJ
app01-4621	165	11	loading	loading	NOUN
app01-4621	165	12	can	can	AUX
app01-4621	165	13	be	be	AUX
app01-4621	165	14	considered	consider	VERB
app01-4621	165	15	to	to	PART
app01-4621	165	16	further	far	ADV
app01-4621	165	17	enrich	enrich	VERB
app01-4621	165	18	the	the	DET
app01-4621	165	19	approximation	approximation	NOUN
app01-4621	165	20	space	space	NOUN
app01-4621	165	21	.	.	PUNCT
app01-4621	166	1	acknowledgements	acknowledgement	NOUN
app01-4621	166	2	m.	m.	NOUN
app01-4621	166	3	doškář	doškář	PROPN
app01-4621	166	4	and	and	CCONJ
app01-4621	166	5	j.	j.	PROPN
app01-4621	166	6	novák	novák	PROPN
app01-4621	166	7	acknowledge	acknowledge	VERB
app01-4621	166	8	the	the	DET
app01-4621	166	9	endowment	endowment	NOUN
app01-4621	166	10	of	of	ADP
app01-4621	166	11	the	the	DET
app01-4621	166	12	ministry	ministry	PROPN
app01-4621	166	13	of	of	ADP
app01-4621	166	14	industry	industry	NOUN
app01-4621	166	15	and	and	CCONJ
app01-4621	166	16	trade	trade	NOUN
app01-4621	166	17	of	of	ADP
app01-4621	166	18	the	the	DET
app01-4621	166	19	czech	czech	PROPN
app01-4621	166	20	republic	republic	NOUN
app01-4621	166	21	under	under	ADP
app01-4621	166	22	the	the	DET
app01-4621	166	23	project	project	NOUN
app01-4621	166	24	no	no	INTJ
app01-4621	166	25	.	.	PUNCT
app01-4621	167	1	fv10202	fv10202	PROPN
app01-4621	167	2	.	.	PUNCT
app01-4621	168	1	in	in	ADP
app01-4621	168	2	addition	addition	NOUN
app01-4621	168	3	,	,	PUNCT
app01-4621	168	4	m.	m.	NOUN
app01-4621	168	5	doškář	doškář	PROPN
app01-4621	168	6	was	be	AUX
app01-4621	168	7	supported	support	VERB
app01-4621	168	8	by	by	ADP
app01-4621	168	9	the	the	DET
app01-4621	168	10	grant	grant	PROPN
app01-4621	168	11	agency	agency	NOUN
app01-4621	168	12	of	of	ADP
app01-4621	168	13	the	the	DET
app01-4621	168	14	czech	czech	PROPN
app01-4621	168	15	technical	technical	PROPN
app01-4621	168	16	university	university	PROPN
app01-4621	168	17	in	in	ADP
app01-4621	168	18	prague	prague	PROPN
app01-4621	168	19	,	,	PUNCT
app01-4621	168	20	project	project	VERB
app01-4621	168	21	no	no	NOUN
app01-4621	168	22	.	.	PUNCT
app01-4621	169	1	sgs17/042	sgs17/042	NOUN
app01-4621	169	2	/	/	SYM
app01-4621	169	3	ohk1/1t/11	ohk1/1t/11	PROPN
app01-4621	169	4	“	"	PUNCT
app01-4621	169	5	numerical	numerical	ADJ
app01-4621	169	6	methods	method	NOUN
app01-4621	169	7	for	for	ADP
app01-4621	169	8	modeling	model	VERB
app01-4621	169	9	uncertainties	uncertainty	NOUN
app01-4621	169	10	in	in	ADP
app01-4621	169	11	civil	civil	ADJ
app01-4621	169	12	engineering	engineering	NOUN
app01-4621	169	13	”	"	PUNCT
app01-4621	169	14	.	.	PUNCT
app01-4621	170	1	references	reference	NOUN
app01-4621	170	2	[	[	X
app01-4621	170	3	1	1	NUM
app01-4621	170	4	]	]	PUNCT
app01-4621	170	5	f.	f.	PROPN
app01-4621	170	6	feyel	feyel	PROPN
app01-4621	170	7	,	,	PUNCT
app01-4621	170	8	j.-l	j.-l	PROPN
app01-4621	170	9	.	.	PUNCT
app01-4621	171	1	chaboche	chaboche	NOUN
app01-4621	171	2	.	.	PUNCT
app01-4621	172	1	fe2	fe2	PROPN
app01-4621	172	2	multiscale	multiscale	ADJ
app01-4621	172	3	approach	approach	NOUN
app01-4621	172	4	for	for	ADP
app01-4621	172	5	modelling	model	VERB
app01-4621	172	6	the	the	DET
app01-4621	172	7	elastoviscoplastic	elastoviscoplastic	ADJ
app01-4621	172	8	behaviour	behaviour	NOUN
app01-4621	172	9	of	of	ADP
app01-4621	172	10	long	long	ADJ
app01-4621	172	11	fibre	fibre	NOUN
app01-4621	172	12	sic	sic	ADJ
app01-4621	172	13	/	/	SYM
app01-4621	172	14	ti	ti	NOUN
app01-4621	172	15	composite	composite	ADJ
app01-4621	172	16	materials	material	NOUN
app01-4621	172	17	.	.	PUNCT
app01-4621	173	1	computer	computer	NOUN
app01-4621	173	2	methods	method	NOUN
app01-4621	173	3	in	in	ADP
app01-4621	173	4	applied	applied	ADJ
app01-4621	173	5	mechanics	mechanic	NOUN
app01-4621	173	6	and	and	CCONJ
app01-4621	173	7	engineering	engineering	NOUN
app01-4621	173	8	183(3	183(3	PROPN
app01-4621	173	9	-	-	SYM
app01-4621	173	10	4):309–330	4):309–330	NOUN
app01-4621	173	11	,	,	PUNCT
app01-4621	173	12	2000	2000	NUM
app01-4621	173	13	.	.	PUNCT
app01-4621	174	1	doi:10.1016	doi:10.1016	PROPN
app01-4621	174	2	/	/	SYM
app01-4621	174	3	s0045	s0045	PROPN
app01-4621	174	4	-	-	PUNCT
app01-4621	174	5	7825(99)00224	7825(99)00224	NOUN
app01-4621	174	6	-	-	PUNCT
app01-4621	174	7	8	8	NUM
app01-4621	174	8	.	.	PUNCT
app01-4621	175	1	[	[	X
app01-4621	175	2	2	2	NUM
app01-4621	175	3	]	]	PUNCT
app01-4621	175	4	m.	m.	NOUN
app01-4621	175	5	g.	g.	PROPN
app01-4621	175	6	d.	d.	PROPN
app01-4621	175	7	geers	geers	PROPN
app01-4621	175	8	,	,	PUNCT
app01-4621	175	9	v.	v.	PROPN
app01-4621	175	10	g.	g.	PROPN
app01-4621	175	11	kouznetsova	kouznetsova	PROPN
app01-4621	175	12	,	,	PUNCT
app01-4621	175	13	k.	k.	PROPN
app01-4621	175	14	matouš	matouš	PROPN
app01-4621	175	15	,	,	PUNCT
app01-4621	175	16	j.	j.	PROPN
app01-4621	175	17	yvonnet	yvonnet	PROPN
app01-4621	175	18	.	.	PUNCT
app01-4621	176	1	homogenization	homogenization	NOUN
app01-4621	176	2	methods	method	NOUN
app01-4621	176	3	and	and	CCONJ
app01-4621	176	4	multiscale	multiscale	NOUN
app01-4621	176	5	modeling	modeling	NOUN
app01-4621	176	6	:	:	PUNCT
app01-4621	176	7	nonlinear	nonlinear	ADJ
app01-4621	176	8	problems	problem	NOUN
app01-4621	176	9	.	.	PUNCT
app01-4621	177	1	in	in	ADP
app01-4621	177	2	e.	e.	PROPN
app01-4621	177	3	stein	stein	PROPN
app01-4621	177	4	,	,	PUNCT
app01-4621	177	5	r.	r.	PROPN
app01-4621	177	6	de	de	X
app01-4621	177	7	borst	borst	PROPN
app01-4621	177	8	,	,	PUNCT
app01-4621	177	9	t.	t.	PROPN
app01-4621	177	10	j.	j.	PROPN
app01-4621	177	11	r.	r.	PROPN
app01-4621	177	12	hughes	hughes	PROPN
app01-4621	177	13	(	(	PUNCT
app01-4621	177	14	eds	eds	PROPN
app01-4621	177	15	.	.	PUNCT
app01-4621	177	16	)	)	PUNCT
app01-4621	177	17	,	,	PUNCT
app01-4621	177	18	encyclopedia	encyclopedia	NOUN
app01-4621	177	19	of	of	ADP
app01-4621	177	20	computational	computational	ADJ
app01-4621	177	21	mechanics	mechanic	NOUN
app01-4621	177	22	second	second	NOUN
app01-4621	177	23	edition	edition	NOUN
app01-4621	177	24	,	,	PUNCT
app01-4621	177	25	pp	pp	PROPN
app01-4621	177	26	.	.	PUNCT
app01-4621	177	27	1–34	1–34	NOUN
app01-4621	177	28	.	.	PUNCT
app01-4621	178	1	john	john	PROPN
app01-4621	178	2	wiley	wiley	PROPN
app01-4621	178	3	&	&	CCONJ
app01-4621	178	4	sons	sons	PROPN
app01-4621	178	5	,	,	PUNCT
app01-4621	178	6	ltd	ltd	PROPN
app01-4621	178	7	,	,	PUNCT
app01-4621	178	8	chichester	chichester	PROPN
app01-4621	178	9	,	,	PUNCT
app01-4621	178	10	uk	uk	PROPN
app01-4621	178	11	,	,	PUNCT
app01-4621	178	12	2017	2017	NUM
app01-4621	178	13	.	.	PUNCT
app01-4621	179	1	doi	doi	NOUN
app01-4621	179	2	:	:	PUNCT
app01-4621	179	3	10.1002/9781119176817.ecm107	10.1002/9781119176817.ecm107	NUM
app01-4621	179	4	.	.	PUNCT
app01-4621	180	1	[	[	X
app01-4621	180	2	3	3	X
app01-4621	180	3	]	]	X
app01-4621	180	4	j.	j.	PROPN
app01-4621	180	5	novák	novák	PROPN
app01-4621	180	6	,	,	PUNCT
app01-4621	180	7	a.	a.	PROPN
app01-4621	180	8	kučerová	kučerová	PROPN
app01-4621	180	9	,	,	PUNCT
app01-4621	180	10	j.	j.	PROPN
app01-4621	180	11	zeman	zeman	PROPN
app01-4621	180	12	.	.	PUNCT
app01-4621	180	13	compressing	compress	VERB
app01-4621	180	14	random	random	ADJ
app01-4621	180	15	microstructures	microstructure	NOUN
app01-4621	180	16	via	via	ADP
app01-4621	180	17	stochastic	stochastic	ADJ
app01-4621	180	18	wang	wang	PROPN
app01-4621	180	19	tilings	tiling	NOUN
app01-4621	180	20	.	.	PUNCT
app01-4621	181	1	physical	physical	ADJ
app01-4621	181	2	review	review	NOUN
app01-4621	181	3	e	e	NOUN
app01-4621	181	4	86(4):040104(r	86(4):040104(r	NUM
app01-4621	181	5	)	)	PUNCT
app01-4621	181	6	,	,	PUNCT
app01-4621	181	7	2012	2012	NUM
app01-4621	181	8	.	.	PUNCT
app01-4621	182	1	doi:10.1103	doi:10.1103	NOUN
app01-4621	182	2	/	/	SYM
app01-4621	182	3	physreve.86.040104	physreve.86.040104	NOUN
app01-4621	182	4	.	.	PUNCT
app01-4621	183	1	[	[	X
app01-4621	183	2	4	4	X
app01-4621	183	3	]	]	PUNCT
app01-4621	183	4	m.	m.	NOUN
app01-4621	183	5	doškář	doškář	PROPN
app01-4621	183	6	,	,	PUNCT
app01-4621	183	7	j.	j.	PROPN
app01-4621	183	8	novák	novák	PROPN
app01-4621	183	9	,	,	PUNCT
app01-4621	183	10	j.	j.	PROPN
app01-4621	183	11	zeman	zeman	PROPN
app01-4621	183	12	.	.	PUNCT
app01-4621	183	13	aperiodic	aperiodic	ADJ
app01-4621	183	14	compression	compression	NOUN
app01-4621	183	15	and	and	CCONJ
app01-4621	183	16	reconstruction	reconstruction	NOUN
app01-4621	183	17	of	of	ADP
app01-4621	183	18	real	real	ADJ
app01-4621	183	19	-	-	PUNCT
app01-4621	183	20	world	world	NOUN
app01-4621	183	21	material	material	NOUN
app01-4621	183	22	systems	system	NOUN
app01-4621	183	23	based	base	VERB
app01-4621	183	24	on	on	ADP
app01-4621	183	25	wang	wang	PROPN
app01-4621	183	26	tiles	tiles	PROPN
app01-4621	183	27	.	.	PUNCT
app01-4621	184	1	physical	physical	ADJ
app01-4621	184	2	review	review	PROPN
app01-4621	184	3	e	e	PROPN
app01-4621	184	4	90(6):062118	90(6):062118	NUM
app01-4621	184	5	,	,	PUNCT
app01-4621	184	6	2014	2014	NUM
app01-4621	184	7	.	.	PUNCT
app01-4621	185	1	doi:10.1103	doi:10.1103	NOUN
app01-4621	185	2	/	/	SYM
app01-4621	185	3	physreve.90.062118	physreve.90.062118	NOUN
app01-4621	185	4	.	.	PUNCT
app01-4621	186	1	[	[	X
app01-4621	186	2	5	5	NUM
app01-4621	186	3	]	]	PUNCT
app01-4621	186	4	t.-p	t.-p	PROPN
app01-4621	186	5	.	.	PUNCT
app01-4621	186	6	fries	fry	NOUN
app01-4621	186	7	,	,	PUNCT
app01-4621	186	8	t.	t.	PROPN
app01-4621	186	9	belytschko	belytschko	PROPN
app01-4621	186	10	.	.	PUNCT
app01-4621	187	1	the	the	DET
app01-4621	187	2	extended	extend	VERB
app01-4621	187	3	/	/	SYM
app01-4621	187	4	generalized	generalize	VERB
app01-4621	187	5	finite	finite	ADJ
app01-4621	187	6	element	element	NOUN
app01-4621	187	7	method	method	NOUN
app01-4621	187	8	:	:	PUNCT
app01-4621	187	9	an	an	DET
app01-4621	187	10	overview	overview	NOUN
app01-4621	187	11	of	of	ADP
app01-4621	187	12	the	the	DET
app01-4621	187	13	method	method	NOUN
app01-4621	187	14	and	and	CCONJ
app01-4621	187	15	its	its	PRON
app01-4621	187	16	applications	application	NOUN
app01-4621	187	17	.	.	PUNCT
app01-4621	188	1	international	international	ADJ
app01-4621	188	2	journal	journal	PROPN
app01-4621	188	3	for	for	ADP
app01-4621	188	4	numerical	numerical	ADJ
app01-4621	188	5	methods	method	NOUN
app01-4621	188	6	in	in	ADP
app01-4621	188	7	engineering	engineering	NOUN
app01-4621	188	8	84(3):253–304	84(3):253–304	NUM
app01-4621	188	9	,	,	PUNCT
app01-4621	188	10	2010	2010	NUM
app01-4621	188	11	.	.	PUNCT
app01-4621	189	1	doi:10.1002	doi:10.1002	NOUN
app01-4621	189	2	/	/	SYM
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app01-4621	189	4	.	.	PUNCT
app01-4621	190	1	[	[	X
app01-4621	190	2	6	6	NUM
app01-4621	190	3	]	]	PUNCT
app01-4621	190	4	t.	t.	PROPN
app01-4621	190	5	strouboulis	strouboulis	PROPN
app01-4621	190	6	,	,	PUNCT
app01-4621	190	7	k.	k.	PROPN
app01-4621	190	8	copps	copps	PROPN
app01-4621	190	9	,	,	PUNCT
app01-4621	190	10	i.	i.	PROPN
app01-4621	190	11	babuška	babuška	PROPN
app01-4621	190	12	.	.	PUNCT
app01-4621	191	1	the	the	DET
app01-4621	191	2	generalized	generalize	VERB
app01-4621	191	3	finite	finite	ADJ
app01-4621	191	4	element	element	NOUN
app01-4621	191	5	method	method	NOUN
app01-4621	191	6	.	.	PUNCT
app01-4621	192	1	computer	computer	NOUN
app01-4621	192	2	methods	method	NOUN
app01-4621	192	3	in	in	ADP
app01-4621	192	4	applied	applied	ADJ
app01-4621	192	5	mechanics	mechanic	NOUN
app01-4621	192	6	and	and	CCONJ
app01-4621	192	7	engineering	engineering	NOUN
app01-4621	192	8	190(32	190(32	NUM
app01-4621	192	9	-	-	PUNCT
app01-4621	192	10	33):4081–4193	33):4081–4193	NUM
app01-4621	192	11	,	,	PUNCT
app01-4621	192	12	2001	2001	NUM
app01-4621	192	13	.	.	PUNCT
app01-4621	193	1	doi:10.1016	doi:10.1016	PROPN
app01-4621	193	2	/	/	SYM
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app01-4621	193	4	-	-	PUNCT
app01-4621	193	5	7825(01)00188	7825(01)00188	NUM
app01-4621	193	6	-	-	SYM
app01-4621	193	7	8	8	NUM
app01-4621	193	8	.	.	NOUN
app01-4621	193	9	33	33	NUM
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app01-4621	193	11	http://dx.doi.org/10.1103/physreve.86.040104	http://dx.doi.org/10.1103/physreve.86.040104	PROPN
app01-4621	193	12	http://dx.doi.org/10.1103/physreve.90.062118	http://dx.doi.org/10.1103/physreve.90.062118	PROPN
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app01-4621	193	15	m.	m.	NOUN
app01-4621	193	16	doškář	doškář	PROPN
app01-4621	193	17	,	,	PUNCT
app01-4621	193	18	j.	j.	PROPN
app01-4621	193	19	novák	novák	PROPN
app01-4621	193	20	,	,	PUNCT
app01-4621	193	21	j.	j.	PROPN
app01-4621	193	22	zeman	zeman	PROPN
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app01-4621	193	32	,	,	PUNCT
app01-4621	193	33	q.-c	q.-c	PROPN
app01-4621	193	34	.	.	PUNCT
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app01-4621	194	2	.	.	PUNCT
app01-4621	195	1	the	the	DET
app01-4621	195	2	reduced	reduce	VERB
app01-4621	195	3	model	model	NOUN
app01-4621	195	4	multiscale	multiscale	PROPN
app01-4621	195	5	method	method	NOUN
app01-4621	195	6	(	(	PUNCT
app01-4621	195	7	r3	r3	PROPN
app01-4621	195	8	m	m	PROPN
app01-4621	195	9	)	)	PUNCT
app01-4621	195	10	for	for	ADP
app01-4621	195	11	the	the	DET
app01-4621	195	12	non	non	ADJ
app01-4621	195	13	-	-	ADJ
app01-4621	195	14	linear	linear	ADJ
app01-4621	195	15	homogenization	homogenization	NOUN
app01-4621	195	16	of	of	ADP
app01-4621	195	17	hyperelastic	hyperelastic	ADJ
app01-4621	195	18	media	medium	NOUN
app01-4621	195	19	at	at	ADP
app01-4621	195	20	finite	finite	ADJ
app01-4621	195	21	strains	strain	NOUN
app01-4621	195	22	.	.	PUNCT
app01-4621	196	1	journal	journal	NOUN
app01-4621	196	2	of	of	ADP
app01-4621	196	3	computational	computational	ADJ
app01-4621	196	4	physics	physics	NOUN
app01-4621	196	5	223(1):341–368	223(1):341–368	NUM
app01-4621	196	6	,	,	PUNCT
app01-4621	196	7	2007	2007	NUM
app01-4621	196	8	.	.	PUNCT
app01-4621	197	1	doi:10.1016	doi:10.1016	PROPN
app01-4621	197	2	/	/	SYM
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app01-4621	197	4	.	.	PUNCT
app01-4621	198	1	[	[	X
app01-4621	198	2	8	8	NUM
app01-4621	198	3	]	]	X
app01-4621	198	4	m.	m.	NOUN
app01-4621	198	5	doškář	doškář	PROPN
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app01-4621	198	9	.	.	PUNCT
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app01-4621	199	4	framework	framework	NOUN
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app01-4621	199	7	of	of	ADP
app01-4621	199	8	high	high	ADJ
app01-4621	199	9	porosity	porosity	NOUN
app01-4621	199	10	foams	foam	NOUN
app01-4621	199	11	.	.	PUNCT
app01-4621	200	1	computers	computer	NOUN
app01-4621	200	2	&	&	CCONJ
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app01-4621	200	4	166:33–41	166:33–41	NUM
app01-4621	200	5	,	,	PUNCT
app01-4621	200	6	2016	2016	NUM
app01-4621	200	7	.	.	PUNCT
app01-4621	201	1	doi:10.1016	doi:10.1016	PROPN
app01-4621	201	2	/	/	SYM
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app01-4621	201	4	.	.	PUNCT
app01-4621	202	1	[	[	X
app01-4621	202	2	9	9	NUM
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app01-4621	202	4	j.	j.	PROPN
app01-4621	202	5	novák	novák	PROPN
app01-4621	202	6	,	,	PUNCT
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app01-4621	202	8	kučerová	kučerová	PROPN
app01-4621	202	9	,	,	PUNCT
app01-4621	202	10	j.	j.	PROPN
app01-4621	202	11	zeman	zeman	PROPN
app01-4621	202	12	.	.	PUNCT
app01-4621	203	1	microstructural	microstructural	ADJ
app01-4621	203	2	enrichment	enrichment	NOUN
app01-4621	203	3	functions	function	NOUN
app01-4621	203	4	based	base	VERB
app01-4621	203	5	on	on	ADP
app01-4621	203	6	stochastic	stochastic	ADJ
app01-4621	203	7	wang	wang	PROPN
app01-4621	203	8	tilings	tiling	NOUN
app01-4621	203	9	.	.	PUNCT
app01-4621	204	1	modelling	modelling	NOUN
app01-4621	204	2	and	and	CCONJ
app01-4621	204	3	simulation	simulation	NOUN
app01-4621	204	4	in	in	ADP
app01-4621	204	5	materials	material	NOUN
app01-4621	204	6	science	science	NOUN
app01-4621	204	7	and	and	CCONJ
app01-4621	204	8	engineering	engineering	NOUN
app01-4621	204	9	21(2):025014	21(2):025014	NUM
app01-4621	204	10	,	,	PUNCT
app01-4621	204	11	2013	2013	NUM
app01-4621	204	12	.	.	PUNCT
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app01-4621	205	2	-	-	PUNCT
app01-4621	205	3	0393/21/2/025014	0393/21/2/025014	NOUN
app01-4621	205	4	.	.	PUNCT
app01-4621	206	1	[	[	X
app01-4621	206	2	10	10	NUM
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app01-4621	206	4	t.	t.	PROPN
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app01-4621	206	7	l.	l.	PROPN
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app01-4621	206	9	,	,	PUNCT
app01-4621	206	10	i.	i.	PROPN
app01-4621	206	11	babuška	babuška	PROPN
app01-4621	206	12	.	.	PUNCT
app01-4621	207	1	generalized	generalize	VERB
app01-4621	207	2	finite	finite	PROPN
app01-4621	207	3	element	element	NOUN
app01-4621	207	4	method	method	NOUN
app01-4621	207	5	using	use	VERB
app01-4621	207	6	mesh	mesh	NOUN
app01-4621	207	7	-	-	PUNCT
app01-4621	207	8	based	base	VERB
app01-4621	207	9	handbooks	handbook	NOUN
app01-4621	207	10	:	:	PUNCT
app01-4621	207	11	application	application	NOUN
app01-4621	207	12	to	to	ADP
app01-4621	207	13	problems	problem	NOUN
app01-4621	207	14	in	in	ADP
app01-4621	207	15	domains	domain	NOUN
app01-4621	207	16	with	with	ADP
app01-4621	207	17	many	many	ADJ
app01-4621	207	18	voids	void	NOUN
app01-4621	207	19	.	.	PUNCT
app01-4621	208	1	computer	computer	NOUN
app01-4621	208	2	methods	method	NOUN
app01-4621	208	3	in	in	ADP
app01-4621	208	4	applied	applied	ADJ
app01-4621	208	5	mechanics	mechanic	NOUN
app01-4621	208	6	and	and	CCONJ
app01-4621	208	7	engineering	engineering	NOUN
app01-4621	208	8	192(28	192(28	NUM
app01-4621	208	9	-	-	PUNCT
app01-4621	208	10	30):3109–3161	30):3109–3161	NOUN
app01-4621	208	11	,	,	PUNCT
app01-4621	208	12	2003	2003	NUM
app01-4621	208	13	.	.	PUNCT
app01-4621	209	1	doi:10.1016	doi:10.1016	PROPN
app01-4621	209	2	/	/	SYM
app01-4621	209	3	s0045	s0045	ADJ
app01-4621	209	4	-	-	PUNCT
app01-4621	209	5	7825(03)00347	7825(03)00347	NUM
app01-4621	209	6	-	-	PUNCT
app01-4621	209	7	5	5	NUM
app01-4621	209	8	.	.	PUNCT
app01-4621	210	1	[	[	X
app01-4621	210	2	11	11	NUM
app01-4621	210	3	]	]	PUNCT
app01-4621	210	4	j.	j.	PROPN
app01-4621	210	5	plews	plews	PROPN
app01-4621	210	6	,	,	PUNCT
app01-4621	210	7	c.	c.	PROPN
app01-4621	210	8	duarte	duarte	PROPN
app01-4621	210	9	.	.	PUNCT
app01-4621	211	1	bridging	bridge	VERB
app01-4621	211	2	multiple	multiple	ADJ
app01-4621	211	3	structural	structural	ADJ
app01-4621	211	4	scales	scale	NOUN
app01-4621	211	5	with	with	ADP
app01-4621	211	6	a	a	DET
app01-4621	211	7	generalized	generalize	VERB
app01-4621	211	8	finite	finite	ADJ
app01-4621	211	9	element	element	NOUN
app01-4621	211	10	method	method	NOUN
app01-4621	211	11	.	.	PUNCT
app01-4621	212	1	international	international	ADJ
app01-4621	212	2	journal	journal	PROPN
app01-4621	212	3	for	for	ADP
app01-4621	212	4	numerical	numerical	ADJ
app01-4621	212	5	methods	method	NOUN
app01-4621	212	6	in	in	ADP
app01-4621	212	7	engineering	engineer	VERB
app01-4621	212	8	102(3	102(3	NUM
app01-4621	212	9	-	-	SYM
app01-4621	212	10	4):180–201	4):180–201	NUM
app01-4621	212	11	,	,	PUNCT
app01-4621	212	12	2015	2015	NUM
app01-4621	212	13	.	.	PUNCT
app01-4621	213	1	doi:10.1002	doi:10.1002	NOUN
app01-4621	213	2	/	/	SYM
app01-4621	213	3	nme.4703	nme.4703	NUM
app01-4621	213	4	.	.	PUNCT
app01-4621	214	1	[	[	X
app01-4621	214	2	12	12	NUM
app01-4621	214	3	]	]	PUNCT
app01-4621	214	4	d.	d.	NOUN
app01-4621	214	5	ryckelynck	ryckelynck	PROPN
app01-4621	214	6	.	.	PUNCT
app01-4621	215	1	hyper	hyper	NOUN
app01-4621	215	2	-	-	NOUN
app01-4621	215	3	reduction	reduction	NOUN
app01-4621	215	4	of	of	ADP
app01-4621	215	5	mechanical	mechanical	ADJ
app01-4621	215	6	models	model	NOUN
app01-4621	215	7	involving	involve	VERB
app01-4621	215	8	internal	internal	ADJ
app01-4621	215	9	variables	variable	NOUN
app01-4621	215	10	.	.	PUNCT
app01-4621	216	1	international	international	ADJ
app01-4621	216	2	journal	journal	PROPN
app01-4621	216	3	for	for	ADP
app01-4621	216	4	numerical	numerical	ADJ
app01-4621	216	5	methods	method	NOUN
app01-4621	216	6	in	in	ADP
app01-4621	216	7	engineering	engineer	VERB
app01-4621	216	8	77(1):75–89	77(1):75–89	NUM
app01-4621	216	9	,	,	PUNCT
app01-4621	216	10	2009	2009	NUM
app01-4621	216	11	.	.	PUNCT
app01-4621	217	1	doi:10.1002	doi:10.1002	NOUN
app01-4621	217	2	/	/	SYM
app01-4621	217	3	nme.2406	nme.2406	PROPN
app01-4621	217	4	.	.	PUNCT
app01-4621	218	1	34	34	NUM
app01-4621	218	2	http://dx.doi.org/10.1016/j.jcp.2006.09.019	http://dx.doi.org/10.1016/j.jcp.2006.09.019	NOUN
app01-4621	218	3	http://dx.doi.org/10.1016/j.compstruc.2016.01.003	http://dx.doi.org/10.1016/j.compstruc.2016.01.003	PROPN
app01-4621	218	4	http://dx.doi.org/10.1088/0965-0393/21/2/025014	http://dx.doi.org/10.1088/0965-0393/21/2/025014	PROPN
app01-4621	218	5	http://dx.doi.org/10.1016/s0045-7825(03)00347-5	http://dx.doi.org/10.1016/s0045-7825(03)00347-5	PROPN
app01-4621	218	6	http://dx.doi.org/10.1002/nme.4703	http://dx.doi.org/10.1002/nme.4703	PROPN
app01-4621	218	7	http://dx.doi.org/10.1002/nme.2406	http://dx.doi.org/10.1002/nme.2406	PROPN
app01-4621	218	8	acta	acta	PROPN
app01-4621	218	9	polytechnica	polytechnica	PROPN
app01-4621	218	10	ctu	ctu	PROPN
app01-4621	218	11	proceedings	proceeding	NOUN
app01-4621	218	12	13:29–34	13:29–34	NUM
app01-4621	218	13	,	,	PUNCT
app01-4621	218	14	2017	2017	NUM
app01-4621	218	15	1	1	NUM
app01-4621	218	16	introduction	introduction	NOUN
app01-4621	218	17	2	2	NUM
app01-4621	218	18	wang	wang	NOUN
app01-4621	218	19	tiling	tile	VERB
app01-4621	218	20	concept	concept	NOUN
app01-4621	218	21	3	3	NUM
app01-4621	218	22	synthesized	synthesize	VERB
app01-4621	218	23	enrichments	enrichment	NOUN
app01-4621	218	24	fields	field	VERB
app01-4621	218	25	4	4	NUM
app01-4621	218	26	numerical	numerical	ADJ
app01-4621	218	27	strategy	strategy	NOUN
app01-4621	218	28	5	5	NUM
app01-4621	218	29	results	result	NOUN
app01-4621	218	30	6	6	NUM
app01-4621	218	31	conclusions	conclusion	NOUN
app01-4621	218	32	acknowledgements	acknowledgement	NOUN
app01-4621	218	33	references	reference	NOUN