id	sid	tid	token	lemma	pos
ma-241	1	1	2025	2025	NUM
ma-241	1	2	ada	ada	PROPN
ma-241	1	3	academica	academica	PROPN
ma-241	1	4	https://adac.eeeur	https://adac.eeeur	PROPN
ma-241	1	5	.	.	PUNCT
ma-241	2	1	j.	j.	PROPN
ma-241	2	2	math	math	PROPN
ma-241	2	3	.	.	PUNCT
ma-241	3	1	anal	anal	ADJ
ma-241	3	2	.	.	PUNCT
ma-241	4	1	5	5	NUM
ma-241	4	2	(	(	PUNCT
ma-241	4	3	2025	2025	NUM
ma-241	4	4	)	)	PUNCT
ma-241	4	5	6doi	6doi	NOUN
ma-241	4	6	:	:	PUNCT
ma-241	4	7	10.28924	10.28924	NUM
ma-241	4	8	/	/	SYM
ma-241	4	9	ada	ada	PROPN
ma-241	4	10	/	/	SYM
ma-241	4	11	ma.5.6	ma.5.6	PROPN
ma-241	4	12	schwarz	schwarz	NOUN
ma-241	4	13	algorithms	algorithm	VERB
ma-241	4	14	for	for	ADP
ma-241	4	15	stokes	stokes	PROPN
ma-241	4	16	-	-	PUNCT
ma-241	4	17	stokes	stokes	PROPN
ma-241	4	18	coupling	couple	VERB
ma-241	4	19	alexandros	alexandros	PROPN
ma-241	4	20	kyriakis	kyriakis	PROPN
ma-241	4	21	boston	boston	PROPN
ma-241	4	22	college	college	PROPN
ma-241	4	23	uk	uk	PROPN
ma-241	4	24	,	,	PUNCT
ma-241	4	25	department	department	NOUN
ma-241	4	26	of	of	ADP
ma-241	4	27	mathematics	mathematics	PROPN
ma-241	4	28	,	,	PUNCT
ma-241	4	29	skirbeck	skirbeck	NOUN
ma-241	4	30	road	road	NOUN
ma-241	4	31	,	,	PUNCT
ma-241	4	32	pe21	pe21	PROPN
ma-241	4	33	6jf	6jf	NOUN
ma-241	4	34	,	,	PUNCT
ma-241	4	35	uk	uk	PROPN
ma-241	4	36	alex-k@boston.ac.uk	alex-k@boston.ac.uk	VERB
ma-241	4	37	abstract	abstract	NOUN
ma-241	4	38	.	.	PUNCT
ma-241	5	1	in	in	ADP
ma-241	5	2	this	this	DET
ma-241	5	3	article	article	NOUN
ma-241	5	4	,	,	PUNCT
ma-241	5	5	we	we	PRON
ma-241	5	6	exhibit	exhibit	VERB
ma-241	5	7	the	the	DET
ma-241	5	8	behavior	behavior	NOUN
ma-241	5	9	of	of	ADP
ma-241	5	10	the	the	DET
ma-241	5	11	schwarz	schwarz	PROPN
ma-241	5	12	algorithms	algorithm	NOUN
ma-241	5	13	for	for	ADP
ma-241	5	14	the	the	DET
ma-241	5	15	steady	steady	ADJ
ma-241	5	16	stokesequation	stokesequation	NOUN
ma-241	5	17	in	in	ADP
ma-241	5	18	the	the	DET
ma-241	5	19	case	case	NOUN
ma-241	5	20	of	of	ADP
ma-241	5	21	two	two	NUM
ma-241	5	22	unbounded	unbounded	ADJ
ma-241	5	23	subdomains	subdomain	NOUN
ma-241	5	24	at	at	ADP
ma-241	5	25	the	the	DET
ma-241	5	26	continuous	continuous	ADJ
ma-241	5	27	level	level	NOUN
ma-241	5	28	.	.	PUNCT
ma-241	6	1	the	the	DET
ma-241	6	2	schwarz	schwarz	PROPN
ma-241	6	3	methods	method	NOUN
ma-241	6	4	havereceived	havereceive	VERB
ma-241	6	5	a	a	DET
ma-241	6	6	lot	lot	NOUN
ma-241	6	7	of	of	ADP
ma-241	6	8	attention	attention	NOUN
ma-241	6	9	during	during	ADP
ma-241	6	10	the	the	DET
ma-241	6	11	last	last	ADJ
ma-241	6	12	decades	decade	NOUN
ma-241	6	13	with	with	ADP
ma-241	6	14	the	the	DET
ma-241	6	15	vast	vast	ADJ
ma-241	6	16	development	development	NOUN
ma-241	6	17	of	of	ADP
ma-241	6	18	parallel	parallel	ADJ
ma-241	6	19	computingdevices	computingdevice	NOUN
ma-241	6	20	.	.	PUNCT
ma-241	7	1	hermann	hermann	PROPN
ma-241	7	2	amandus	amandus	PROPN
ma-241	7	3	schwarz	schwarz	PROPN
ma-241	7	4	,	,	PUNCT
ma-241	7	5	a	a	DET
ma-241	7	6	german	german	ADJ
ma-241	7	7	analyst	analyst	NOUN
ma-241	7	8	,	,	PUNCT
ma-241	7	9	is	be	AUX
ma-241	7	10	considered	consider	VERB
ma-241	7	11	to	to	PART
ma-241	7	12	be	be	AUX
ma-241	7	13	the	the	DET
ma-241	7	14	pioneer	pioneer	NOUN
ma-241	7	15	of	of	ADP
ma-241	7	16	the	the	DET
ma-241	7	17	domaindecomposition	domaindecomposition	NOUN
ma-241	7	18	methods	method	NOUN
ma-241	7	19	.	.	PUNCT
ma-241	8	1	we	we	PRON
ma-241	8	2	will	will	AUX
ma-241	8	3	closely	closely	ADV
ma-241	8	4	observe	observe	VERB
ma-241	8	5	how	how	SCONJ
ma-241	8	6	the	the	DET
ma-241	8	7	overlapping	overlapping	NOUN
ma-241	8	8	and	and	CCONJ
ma-241	8	9	non	non	ADJ
ma-241	8	10	overlapping	overlap	VERB
ma-241	8	11	schwarzmethods	schwarzmethod	NOUN
ma-241	8	12	work	work	VERB
ma-241	8	13	for	for	ADP
ma-241	8	14	the	the	DET
ma-241	8	15	steady	steady	ADJ
ma-241	8	16	stokes	stoke	NOUN
ma-241	8	17	problem	problem	NOUN
ma-241	8	18	.	.	PUNCT
ma-241	9	1	this	this	DET
ma-241	9	2	problem	problem	NOUN
ma-241	9	3	has	have	VERB
ma-241	9	4	immediate	immediate	ADJ
ma-241	9	5	practical	practical	ADJ
ma-241	9	6	application	application	NOUN
ma-241	9	7	,	,	PUNCT
ma-241	9	8	modeling	model	VERB
ma-241	9	9	the	the	DET
ma-241	9	10	flow	flow	NOUN
ma-241	9	11	of	of	ADP
ma-241	9	12	an	an	DET
ma-241	9	13	incompressible	incompressible	ADJ
ma-241	9	14	fluid	fluid	NOUN
ma-241	9	15	.	.	PUNCT
ma-241	10	1	for	for	ADP
ma-241	10	2	the	the	DET
ma-241	10	3	analysis	analysis	NOUN
ma-241	10	4	,	,	PUNCT
ma-241	10	5	we	we	PRON
ma-241	10	6	rely	rely	VERB
ma-241	10	7	on	on	ADP
ma-241	10	8	fourier	fourier	ADJ
ma-241	10	9	analysis	analysis	NOUN
ma-241	10	10	techniquesand	techniquesand	NOUN
ma-241	10	11	we	we	PRON
ma-241	10	12	provide	provide	VERB
ma-241	10	13	comparison	comparison	NOUN
ma-241	10	14	of	of	ADP
ma-241	10	15	the	the	DET
ma-241	10	16	exhibited	exhibit	VERB
ma-241	10	17	methods	method	NOUN
ma-241	10	18	.	.	PUNCT
ma-241	11	1	1	1	X
ma-241	11	2	.	.	X
ma-241	11	3	introduction	introduction	NOUN
ma-241	11	4	many	many	ADJ
ma-241	11	5	people	people	NOUN
ma-241	11	6	have	have	AUX
ma-241	11	7	been	be	AUX
ma-241	11	8	fascinated	fascinate	VERB
ma-241	11	9	by	by	ADP
ma-241	11	10	the	the	DET
ma-241	11	11	motion	motion	NOUN
ma-241	11	12	of	of	ADP
ma-241	11	13	fluids	fluid	NOUN
ma-241	11	14	,	,	PUNCT
ma-241	11	15	and	and	CCONJ
ma-241	11	16	wonder	wonder	VERB
ma-241	11	17	how	how	SCONJ
ma-241	11	18	we	we	PRON
ma-241	11	19	are	be	AUX
ma-241	11	20	able	able	ADJ
ma-241	11	21	tosimulate	tosimulate	VERB
ma-241	11	22	the	the	DET
ma-241	11	23	motion	motion	NOUN
ma-241	11	24	of	of	ADP
ma-241	11	25	fluids	fluid	NOUN
ma-241	11	26	with	with	ADP
ma-241	11	27	such	such	DET
ma-241	11	28	an	an	DET
ma-241	11	29	accuracy	accuracy	NOUN
ma-241	11	30	.	.	PUNCT
ma-241	12	1	of	of	ADP
ma-241	12	2	course	course	NOUN
ma-241	12	3	,	,	PUNCT
ma-241	12	4	the	the	DET
ma-241	12	5	answer	answer	NOUN
ma-241	12	6	is	be	AUX
ma-241	12	7	simple	simple	ADJ
ma-241	12	8	but	but	CCONJ
ma-241	12	9	at	at	ADP
ma-241	12	10	thesame	thesame	ADJ
ma-241	12	11	time	time	NOUN
ma-241	12	12	complicated	complicated	ADJ
ma-241	12	13	.	.	PUNCT
ma-241	13	1	firstly	firstly	ADV
ma-241	13	2	,	,	PUNCT
ma-241	13	3	in	in	ADP
ma-241	13	4	order	order	NOUN
ma-241	13	5	to	to	PART
ma-241	13	6	model	model	VERB
ma-241	13	7	various	various	ADJ
ma-241	13	8	phenomena	phenomenon	NOUN
ma-241	13	9	,	,	PUNCT
ma-241	13	10	we	we	PRON
ma-241	13	11	use	use	VERB
ma-241	13	12	partial	partial	ADJ
ma-241	13	13	differentialequations	differentialequation	NOUN
ma-241	13	14	(	(	PUNCT
ma-241	13	15	pdes	pde	NOUN
ma-241	13	16	)	)	PUNCT
ma-241	13	17	.	.	PUNCT
ma-241	14	1	pdes	pde	NOUN
ma-241	14	2	are	be	AUX
ma-241	14	3	equations	equation	NOUN
ma-241	14	4	that	that	PRON
ma-241	14	5	involve	involve	VERB
ma-241	14	6	partial	partial	ADJ
ma-241	14	7	derivatives	derivative	NOUN
ma-241	14	8	and	and	CCONJ
ma-241	14	9	most	most	ADJ
ma-241	14	10	of	of	ADP
ma-241	14	11	the	the	DET
ma-241	14	12	times	time	NOUN
ma-241	14	13	weare	weare	NOUN
ma-241	14	14	not	not	PART
ma-241	14	15	able	able	ADJ
ma-241	14	16	to	to	PART
ma-241	14	17	obtain	obtain	VERB
ma-241	14	18	solutions	solution	NOUN
ma-241	14	19	in	in	ADP
ma-241	14	20	closed	closed	ADJ
ma-241	14	21	form	form	NOUN
ma-241	14	22	.	.	PUNCT
ma-241	15	1	as	as	ADP
ma-241	15	2	a	a	DET
ma-241	15	3	result	result	NOUN
ma-241	15	4	,	,	PUNCT
ma-241	15	5	we	we	PRON
ma-241	15	6	use	use	VERB
ma-241	15	7	numerical	numerical	ADJ
ma-241	15	8	algorithms	algorithm	NOUN
ma-241	15	9	in	in	ADP
ma-241	15	10	orderto	orderto	NOUN
ma-241	15	11	obtain	obtain	VERB
ma-241	15	12	the	the	DET
ma-241	15	13	approximate	approximate	ADJ
ma-241	15	14	solution	solution	NOUN
ma-241	15	15	of	of	ADP
ma-241	15	16	a	a	DET
ma-241	15	17	pde	pde	NOUN
ma-241	15	18	.	.	PUNCT
ma-241	16	1	this	this	DET
ma-241	16	2	field	field	NOUN
ma-241	16	3	is	be	AUX
ma-241	16	4	called	call	VERB
ma-241	16	5	numerical	numerical	ADJ
ma-241	16	6	analysis	analysis	NOUN
ma-241	16	7	of	of	ADP
ma-241	16	8	pdesand	pdesand	NOUN
ma-241	16	9	it	it	PRON
ma-241	16	10	is	be	AUX
ma-241	16	11	gaining	gain	VERB
ma-241	16	12	increasing	increase	VERB
ma-241	16	13	interest	interest	NOUN
ma-241	16	14	from	from	ADP
ma-241	16	15	mathematical	mathematical	ADJ
ma-241	16	16	and	and	CCONJ
ma-241	16	17	engineering	engineering	NOUN
ma-241	16	18	communities	community	NOUN
ma-241	16	19	worldwide.especially	worldwide.especially	ADV
ma-241	16	20	,	,	PUNCT
ma-241	16	21	the	the	DET
ma-241	16	22	last	last	ADJ
ma-241	16	23	two	two	NUM
ma-241	16	24	decades	decade	NOUN
ma-241	16	25	domain	domain	NOUN
ma-241	16	26	decomposition	decomposition	NOUN
ma-241	16	27	methods	method	NOUN
ma-241	16	28	[	[	X
ma-241	16	29	7	7	NUM
ma-241	16	30	]	]	PUNCT
ma-241	16	31	,	,	PUNCT
ma-241	16	32	[	[	X
ma-241	16	33	8	8	NUM
ma-241	16	34	]	]	PUNCT
ma-241	16	35	,	,	PUNCT
ma-241	16	36	[	[	X
ma-241	16	37	9	9	NUM
ma-241	16	38	]	]	PUNCT
ma-241	16	39	,	,	PUNCT
ma-241	16	40	[	[	X
ma-241	16	41	10	10	NUM
ma-241	16	42	]	]	PUNCT
ma-241	16	43	are	be	AUX
ma-241	16	44	gaining	gain	VERB
ma-241	16	45	grounddue	grounddue	ADJ
ma-241	16	46	to	to	ADP
ma-241	16	47	the	the	DET
ma-241	16	48	increased	increase	VERB
ma-241	16	49	use	use	NOUN
ma-241	16	50	of	of	ADP
ma-241	16	51	parallel	parallel	ADJ
ma-241	16	52	computing	computing	NOUN
ma-241	16	53	.	.	PUNCT
ma-241	17	1	the	the	DET
ma-241	17	2	pioneer	pioneer	NOUN
ma-241	17	3	of	of	ADP
ma-241	17	4	these	these	DET
ma-241	17	5	methods	method	NOUN
ma-241	17	6	was	be	AUX
ma-241	17	7	the	the	DET
ma-241	17	8	germananalyst	germananalyst	PROPN
ma-241	17	9	hermann	hermann	PROPN
ma-241	17	10	schwarz	schwarz	PROPN
ma-241	18	1	[	[	X
ma-241	18	2	4	4	NUM
ma-241	18	3	]	]	PUNCT
ma-241	18	4	,	,	PUNCT
ma-241	18	5	[	[	X
ma-241	18	6	5	5	NUM
ma-241	18	7	]	]	PUNCT
ma-241	18	8	,	,	PUNCT
ma-241	18	9	[	[	X
ma-241	18	10	6	6	NUM
ma-241	18	11	]	]	PUNCT
ma-241	18	12	who	who	PRON
ma-241	18	13	devised	devise	VERB
ma-241	18	14	an	an	DET
ma-241	18	15	algorithm	algorithm	NOUN
ma-241	18	16	to	to	PART
ma-241	18	17	solve	solve	VERB
ma-241	18	18	the	the	DET
ma-241	18	19	poisson	poisson	NOUN
ma-241	18	20	equation	equation	NOUN
ma-241	18	21	inan	inan	VERB
ma-241	18	22	irregular	irregular	ADJ
ma-241	18	23	domain	domain	NOUN
ma-241	18	24	(	(	PUNCT
ma-241	18	25	union	union	NOUN
ma-241	18	26	of	of	ADP
ma-241	18	27	rectangle	rectangle	NOUN
ma-241	18	28	and	and	CCONJ
ma-241	18	29	a	a	DET
ma-241	18	30	circle	circle	NOUN
ma-241	18	31	)	)	PUNCT
ma-241	18	32	,	,	PUNCT
ma-241	18	33	in	in	ADP
ma-241	18	34	order	order	NOUN
ma-241	18	35	to	to	PART
ma-241	18	36	fix	fix	VERB
ma-241	18	37	a	a	DET
ma-241	18	38	glitch	glitch	NOUN
ma-241	18	39	in	in	ADP
ma-241	18	40	riemann	riemann	PROPN
ma-241	18	41	’s	’s	PART
ma-241	18	42	mappingtheorem	mappingtheorem	PROPN
ma-241	18	43	.	.	PUNCT
ma-241	19	1	the	the	DET
ma-241	19	2	algorithm	algorithm	NOUN
ma-241	19	3	is	is	PROPN
ma-241	20	1	∆u	∆u	PROPN
ma-241	20	2	(	(	PUNCT
ma-241	20	3	k	k	NOUN
ma-241	20	4	)	)	PUNCT
ma-241	20	5	1	1	NUM
ma-241	20	6	=	=	SYM
ma-241	20	7	−f	−f	PROPN
ma-241	20	8	,	,	PUNCT
ma-241	20	9	in	in	ADP
ma-241	20	10	ω1	ω1	PROPN
ma-241	20	11	u	u	PROPN
ma-241	20	12	(	(	PUNCT
ma-241	20	13	k	k	NOUN
ma-241	20	14	)	)	PUNCT
ma-241	20	15	1	1	NUM
ma-241	20	16	=	=	SYM
ma-241	20	17	u	u	NOUN
ma-241	20	18	(	(	PUNCT
ma-241	20	19	k−1	k−1	PROPN
ma-241	20	20	)	)	PUNCT
ma-241	20	21	2	2	NUM
ma-241	20	22	,	,	PUNCT
ma-241	20	23	at	at	ADP
ma-241	20	24	γ1	γ1	PROPN
ma-241	20	25	u	u	PROPN
ma-241	20	26	(	(	PUNCT
ma-241	20	27	k	k	NOUN
ma-241	20	28	)	)	PUNCT
ma-241	20	29	1	1	NUM
ma-241	20	30	=	=	SYM
ma-241	20	31	g1	g1	NOUN
ma-241	20	32	,	,	PUNCT
ma-241	20	33	on	on	ADP
ma-241	20	34	∂ω1	∂ω1	PROPN
ma-241	20	35	\	\	PROPN
ma-241	20	36	γ1	γ1	PROPN
ma-241	20	37	,	,	PUNCT
ma-241	20	38	then	then	ADV
ma-241	20	39			PROPN
ma-241	20	40	∆u	∆u	PROPN
ma-241	20	41	(	(	PUNCT
ma-241	20	42	k	k	NOUN
ma-241	20	43	)	)	PUNCT
ma-241	20	44	2	2	NUM
ma-241	20	45	=	=	SYM
ma-241	20	46	−f	−f	PROPN
ma-241	20	47	,	,	PUNCT
ma-241	20	48	in	in	ADP
ma-241	20	49	ω2	ω2	PROPN
ma-241	20	50	u	u	PROPN
ma-241	20	51	(	(	PUNCT
ma-241	20	52	k	k	NOUN
ma-241	20	53	)	)	PUNCT
ma-241	20	54	2	2	NUM
ma-241	20	55	=	=	SYM
ma-241	20	56	u	u	X
ma-241	20	57	(	(	PUNCT
ma-241	20	58	k	k	NOUN
ma-241	20	59	)	)	PUNCT
ma-241	20	60	1	1	NUM
ma-241	20	61	,	,	PUNCT
ma-241	20	62	at	at	ADP
ma-241	20	63	γ2	γ2	PROPN
ma-241	20	64	u	u	PROPN
ma-241	20	65	(	(	PUNCT
ma-241	20	66	k	k	NOUN
ma-241	20	67	)	)	PUNCT
ma-241	20	68	2	2	NUM
ma-241	20	69	=	=	SYM
ma-241	20	70	g2	g2	PROPN
ma-241	20	71	,	,	PUNCT
ma-241	20	72	on	on	ADP
ma-241	20	73	∂ω2	∂ω2	PROPN
ma-241	20	74	\	\	NOUN
ma-241	20	75	γ2	γ2	PROPN
ma-241	20	76	.	.	PUNCT
ma-241	21	1	(	(	PUNCT
ma-241	21	2	1	1	X
ma-241	21	3	)	)	PUNCT
ma-241	21	4	received	receive	VERB
ma-241	21	5	:	:	PUNCT
ma-241	21	6	18	18	NUM
ma-241	21	7	may	may	PROPN
ma-241	21	8	2024	2024	NUM
ma-241	21	9	.	.	PUNCT
ma-241	22	1	key	key	ADJ
ma-241	22	2	words	word	NOUN
ma-241	22	3	and	and	CCONJ
ma-241	22	4	phrases	phrase	NOUN
ma-241	22	5	.	.	PUNCT
ma-241	23	1	schwarz	schwarz	PROPN
ma-241	23	2	algorithms	algorithm	NOUN
ma-241	23	3	;	;	PUNCT
ma-241	23	4	steady	steady	ADJ
ma-241	23	5	stokes	stoke	NOUN
ma-241	23	6	equation	equation	NOUN
ma-241	23	7	;	;	PUNCT
ma-241	23	8	convergence	convergence	NOUN
ma-241	23	9	analysis.1	analysis.1	PROPN
ma-241	23	10	https://adac.ee	https://adac.ee	PROPN
ma-241	23	11	https://doi.org/10.28924/ada/ma.5.6	https://doi.org/10.28924/ada/ma.5.6	PROPN
ma-241	23	12	eur	eur	PROPN
ma-241	23	13	.	.	PUNCT
ma-241	24	1	j.	j.	PROPN
ma-241	24	2	math	math	PROPN
ma-241	24	3	.	.	PUNCT
ma-241	25	1	anal	anal	PROPN
ma-241	25	2	.	.	PUNCT
ma-241	26	1	10.28924	10.28924	NUM
ma-241	26	2	/	/	SYM
ma-241	26	3	ada	ada	PROPN
ma-241	26	4	/	/	SYM
ma-241	26	5	ma.5.6	ma.5.6	ADJ
ma-241	26	6	2	2	NUM
ma-241	26	7	ω1	ω1	ADJ
ma-241	26	8	ω2γ1γ2	ω2γ1γ2	ADJ
ma-241	26	9	figure	figure	NOUN
ma-241	26	10	1	1	NUM
ma-241	26	11	.	.	PUNCT
ma-241	26	12	domain	domain	NOUN
ma-241	26	13	decomposition	decomposition	NOUN
ma-241	26	14	of	of	ADP
ma-241	26	15	the	the	DET
ma-241	26	16	global	global	ADJ
ma-241	26	17	domain	domain	NOUN
ma-241	26	18	into	into	ADP
ma-241	26	19	a	a	DET
ma-241	26	20	union	union	NOUN
ma-241	26	21	of	of	ADP
ma-241	26	22	a	a	DET
ma-241	26	23	circle	circle	NOUN
ma-241	26	24	and	and	CCONJ
ma-241	26	25	a	a	DET
ma-241	26	26	rectangle.having	rectangle.having	NOUN
ma-241	26	27	a	a	DET
ma-241	26	28	close	close	ADJ
ma-241	26	29	look	look	NOUN
ma-241	26	30	at	at	ADP
ma-241	26	31	the	the	DET
ma-241	26	32	above	above	ADJ
ma-241	26	33	figure	figure	NOUN
ma-241	26	34	we	we	PRON
ma-241	26	35	notice	notice	VERB
ma-241	26	36	the	the	DET
ma-241	26	37	following	following	NOUN
ma-241	26	38	:	:	PUNCT
ma-241	26	39	firstly	firstly	ADV
ma-241	26	40	,	,	PUNCT
ma-241	26	41	the	the	DET
ma-241	26	42	poisson	poisson	PROPN
ma-241	26	43	problemis	problemis	NOUN
ma-241	26	44	solved	solve	VERB
ma-241	26	45	in	in	ADP
ma-241	26	46	the	the	DET
ma-241	26	47	circle	circle	NOUN
ma-241	26	48	and	and	CCONJ
ma-241	26	49	then	then	ADV
ma-241	26	50	in	in	ADP
ma-241	26	51	the	the	DET
ma-241	26	52	rectangle	rectangle	NOUN
ma-241	26	53	,	,	PUNCT
ma-241	26	54	going	go	VERB
ma-241	26	55	back	back	ADV
ma-241	26	56	and	and	CCONJ
ma-241	26	57	forth	forth	ADV
ma-241	26	58	,	,	PUNCT
ma-241	26	59	passing	pass	VERB
ma-241	26	60	the	the	DET
ma-241	26	61	values	value	NOUN
ma-241	26	62	at	at	ADP
ma-241	26	63	theinterfaces	theinterface	NOUN
ma-241	26	64	γ1	γ1	NOUN
ma-241	26	65	and	and	CCONJ
ma-241	26	66	γ2	γ2	NOUN
ma-241	26	67	.	.	PUNCT
ma-241	27	1	this	this	DET
ma-241	27	2	iteration	iteration	NOUN
ma-241	27	3	process	process	NOUN
ma-241	27	4	is	be	AUX
ma-241	27	5	repeated	repeat	VERB
ma-241	27	6	until	until	SCONJ
ma-241	27	7	the	the	DET
ma-241	27	8	convergence	convergence	NOUN
ma-241	27	9	is	be	AUX
ma-241	27	10	reached	reach	VERB
ma-241	27	11	.	.	PUNCT
ma-241	28	1	theindex	theindex	NOUN
ma-241	28	2	(	(	PUNCT
ma-241	28	3	k	k	NOUN
ma-241	28	4	)	)	PUNCT
ma-241	28	5	denotes	denote	VERB
ma-241	28	6	the	the	DET
ma-241	28	7	iterations	iteration	NOUN
ma-241	28	8	,	,	PUNCT
ma-241	28	9	and	and	CCONJ
ma-241	28	10	f	f	PROPN
ma-241	28	11	is	be	AUX
ma-241	28	12	the	the	DET
ma-241	28	13	source	source	NOUN
ma-241	28	14	function	function	NOUN
ma-241	28	15	.	.	PUNCT
ma-241	29	1	this	this	PRON
ma-241	29	2	is	be	AUX
ma-241	29	3	the	the	DET
ma-241	29	4	so	so	ADV
ma-241	29	5	called	call	VERB
ma-241	29	6	alternatingschwarz	alternatingschwarz	PROPN
ma-241	29	7	algorithm	algorithm	PROPN
ma-241	29	8	proposed	propose	VERB
ma-241	29	9	by	by	ADP
ma-241	29	10	schwarz	schwarz	PROPN
ma-241	29	11	back	back	ADV
ma-241	29	12	in	in	ADP
ma-241	29	13	1870	1870	NUM
ma-241	29	14	.	.	PUNCT
ma-241	30	1	after	after	ADP
ma-241	30	2	a	a	DET
ma-241	30	3	significant	significant	ADJ
ma-241	30	4	amount	amount	NOUN
ma-241	30	5	of	of	ADP
ma-241	30	6	time	time	NOUN
ma-241	30	7	,	,	PUNCT
ma-241	30	8	the	the	DET
ma-241	30	9	fieldsmedalist	fieldsmedalist	PROPN
ma-241	30	10	pierre	pierre	PROPN
ma-241	30	11	luis	luis	PROPN
ma-241	30	12	lions	lion	NOUN
ma-241	30	13	[	[	X
ma-241	30	14	3	3	NUM
ma-241	30	15	]	]	PUNCT
ma-241	30	16	,	,	PUNCT
ma-241	30	17	[	[	X
ma-241	30	18	13	13	NUM
ma-241	30	19	]	]	PUNCT
ma-241	30	20	proposed	propose	VERB
ma-241	30	21	a	a	DET
ma-241	30	22	modification	modification	NOUN
ma-241	30	23	in	in	ADP
ma-241	30	24	the	the	DET
ma-241	30	25	alternating	alternate	VERB
ma-241	30	26	schwarz	schwarz	PROPN
ma-241	30	27	method	method	NOUN
ma-241	30	28	(	(	PUNCT
ma-241	30	29	1).after	1).after	NUM
ma-241	30	30	imposing	impose	VERB
ma-241	30	31	this	this	DET
ma-241	30	32	modification	modification	NOUN
ma-241	30	33	,	,	PUNCT
ma-241	30	34	the	the	DET
ma-241	30	35	algorithm	algorithm	NOUN
ma-241	30	36	(	(	PUNCT
ma-241	30	37	1	1	X
ma-241	30	38	)	)	PUNCT
ma-241	30	39	takes	take	VERB
ma-241	30	40	the	the	DET
ma-241	30	41	form	form	NOUN
ma-241	30	42	∆u	∆u	PROPN
ma-241	30	43	(	(	PUNCT
ma-241	30	44	k	k	NOUN
ma-241	30	45	)	)	PUNCT
ma-241	31	1	1	1	NUM
ma-241	31	2	=	=	SYM
ma-241	31	3	−f	−f	PROPN
ma-241	31	4	,	,	PUNCT
ma-241	31	5	in	in	ADP
ma-241	31	6	ω1	ω1	PROPN
ma-241	31	7	u	u	PROPN
ma-241	31	8	(	(	PUNCT
ma-241	31	9	k	k	NOUN
ma-241	31	10	)	)	PUNCT
ma-241	31	11	1	1	NUM
ma-241	31	12	=	=	SYM
ma-241	31	13	u	u	NOUN
ma-241	31	14	(	(	PUNCT
ma-241	31	15	k−1	k−1	PROPN
ma-241	31	16	)	)	PUNCT
ma-241	31	17	2	2	NUM
ma-241	31	18	,	,	PUNCT
ma-241	31	19	at	at	ADP
ma-241	31	20	γ1	γ1	PROPN
ma-241	31	21	u	u	PROPN
ma-241	31	22	(	(	PUNCT
ma-241	31	23	k	k	NOUN
ma-241	31	24	)	)	PUNCT
ma-241	31	25	1	1	NUM
ma-241	31	26	=	=	SYM
ma-241	31	27	g1	g1	NOUN
ma-241	31	28	,	,	PUNCT
ma-241	31	29	on	on	ADP
ma-241	31	30	∂ω1	∂ω1	PROPN
ma-241	31	31	\	\	PROPN
ma-241	31	32	γ1	γ1	PROPN
ma-241	31	33	,	,	PUNCT
ma-241	31	34	and	and	CCONJ
ma-241	31	35			PROPN
ma-241	31	36	∆u	∆u	PROPN
ma-241	31	37	(	(	PUNCT
ma-241	31	38	k	k	NOUN
ma-241	31	39	)	)	PUNCT
ma-241	31	40	2	2	NUM
ma-241	31	41	=	=	SYM
ma-241	31	42	−f	−f	PROPN
ma-241	31	43	,	,	PUNCT
ma-241	31	44	in	in	ADP
ma-241	31	45	ω2	ω2	PROPN
ma-241	31	46	u	u	PROPN
ma-241	31	47	(	(	PUNCT
ma-241	31	48	k	k	NOUN
ma-241	31	49	)	)	PUNCT
ma-241	31	50	2	2	NUM
ma-241	31	51	=	=	SYM
ma-241	31	52	u	u	NOUN
ma-241	31	53	(	(	PUNCT
ma-241	31	54	k−1	k−1	PROPN
ma-241	31	55	)	)	PUNCT
ma-241	31	56	1	1	NUM
ma-241	31	57	,	,	PUNCT
ma-241	31	58	at	at	ADP
ma-241	31	59	γ2	γ2	PROPN
ma-241	31	60	u	u	PROPN
ma-241	31	61	(	(	PUNCT
ma-241	31	62	k	k	NOUN
ma-241	31	63	)	)	PUNCT
ma-241	31	64	2	2	NUM
ma-241	31	65	=	=	SYM
ma-241	31	66	g2	g2	PROPN
ma-241	31	67	,	,	PUNCT
ma-241	31	68	on	on	ADP
ma-241	31	69	∂ω2	∂ω2	PROPN
ma-241	31	70	\	\	NOUN
ma-241	31	71	γ2	γ2	PROPN
ma-241	31	72	.	.	PUNCT
ma-241	32	1	(	(	PUNCT
ma-241	32	2	2	2	X
ma-241	32	3	)	)	PUNCT
ma-241	32	4	in	in	ADP
ma-241	32	5	this	this	DET
ma-241	32	6	iterative	iterative	NOUN
ma-241	32	7	algorithm	algorithm	NOUN
ma-241	32	8	,	,	PUNCT
ma-241	32	9	the	the	DET
ma-241	32	10	two	two	NUM
ma-241	32	11	local	local	ADJ
ma-241	32	12	subproblems	subproblem	NOUN
ma-241	32	13	are	be	AUX
ma-241	32	14	solved	solve	VERB
ma-241	32	15	in	in	ADP
ma-241	32	16	parallel	parallel	ADJ
ma-241	32	17	passing	pass	VERB
ma-241	32	18	the	the	DET
ma-241	32	19	dirichletvalues	dirichletvalue	NOUN
ma-241	32	20	at	at	ADP
ma-241	32	21	the	the	DET
ma-241	32	22	two	two	NUM
ma-241	32	23	interfaces	interface	NOUN
ma-241	32	24	.	.	PUNCT
ma-241	33	1	this	this	DET
ma-241	33	2	algorithm	algorithm	NOUN
ma-241	33	3	(	(	PUNCT
ma-241	33	4	2	2	NUM
ma-241	33	5	)	)	PUNCT
ma-241	33	6	is	be	AUX
ma-241	33	7	known	know	VERB
ma-241	33	8	as	as	ADP
ma-241	33	9	the	the	DET
ma-241	33	10	parallel	parallel	ADJ
ma-241	33	11	schwarz	schwarz	PROPN
ma-241	33	12	algorithm	algorithm	PROPN
ma-241	33	13	.	.	PUNCT
ma-241	34	1	thisiterative	thisiterative	ADJ
ma-241	34	2	scheme	scheme	NOUN
ma-241	34	3	provides	provide	VERB
ma-241	34	4	two	two	NUM
ma-241	34	5	great	great	ADJ
ma-241	34	6	benefits	benefit	NOUN
ma-241	34	7	.	.	PUNCT
ma-241	35	1	the	the	DET
ma-241	35	2	first	first	ADJ
ma-241	35	3	is	be	AUX
ma-241	35	4	balancing	balance	VERB
ma-241	35	5	the	the	DET
ma-241	35	6	computational	computational	ADJ
ma-241	35	7	cost	cost	NOUN
ma-241	35	8	bybreaking	bybreake	VERB
ma-241	35	9	the	the	DET
ma-241	35	10	global	global	ADJ
ma-241	35	11	problem	problem	NOUN
ma-241	35	12	into	into	ADP
ma-241	35	13	smaller	small	ADJ
ma-241	35	14	subproblems	subproblem	NOUN
ma-241	35	15	.	.	PUNCT
ma-241	36	1	the	the	DET
ma-241	36	2	second	second	ADJ
ma-241	36	3	benefit	benefit	NOUN
ma-241	36	4	is	be	AUX
ma-241	36	5	that	that	SCONJ
ma-241	36	6	with	with	ADP
ma-241	36	7	the	the	DET
ma-241	36	8	increas	increas	NOUN
ma-241	36	9	-	-	PUNCT
ma-241	36	10	ing	ing	ADJ
ma-241	36	11	amount	amount	NOUN
ma-241	36	12	of	of	ADP
ma-241	36	13	computational	computational	ADJ
ma-241	36	14	resources	resource	NOUN
ma-241	36	15	,	,	PUNCT
ma-241	36	16	the	the	DET
ma-241	36	17	schwarz	schwarz	PROPN
ma-241	36	18	method	method	NOUN
ma-241	36	19	(	(	PUNCT
ma-241	36	20	2	2	NUM
ma-241	36	21	)	)	PUNCT
ma-241	36	22	is	be	AUX
ma-241	36	23	ideal	ideal	ADJ
ma-241	36	24	for	for	ADP
ma-241	36	25	parallel	parallel	ADJ
ma-241	36	26	computations.there	computations.there	PRON
ma-241	36	27	has	have	AUX
ma-241	36	28	been	be	AUX
ma-241	36	29	an	an	DET
ma-241	36	30	avalanche	avalanche	NOUN
ma-241	36	31	of	of	ADP
ma-241	36	32	new	new	ADJ
ma-241	36	33	research	research	NOUN
ma-241	36	34	results	result	NOUN
ma-241	36	35	and	and	CCONJ
ma-241	36	36	there	there	PRON
ma-241	36	37	is	be	VERB
ma-241	36	38	a	a	DET
ma-241	36	39	great	great	ADJ
ma-241	36	40	avenue	avenue	NOUN
ma-241	36	41	of	of	ADP
ma-241	36	42	research	research	NOUN
ma-241	36	43	ondomain	ondomain	NOUN
ma-241	36	44	decomposition	decomposition	NOUN
ma-241	36	45	methods	method	NOUN
ma-241	36	46	.	.	PUNCT
ma-241	37	1	in	in	ADP
ma-241	37	2	this	this	DET
ma-241	37	3	article	article	NOUN
ma-241	37	4	,	,	PUNCT
ma-241	37	5	we	we	PRON
ma-241	37	6	will	will	AUX
ma-241	37	7	observe	observe	VERB
ma-241	37	8	the	the	DET
ma-241	37	9	behaviour	behaviour	NOUN
ma-241	37	10	of	of	ADP
ma-241	37	11	the	the	DET
ma-241	37	12	schwarzmethods	schwarzmethod	NOUN
ma-241	37	13	for	for	ADP
ma-241	37	14	the	the	DET
ma-241	37	15	steady	steady	ADJ
ma-241	37	16	stokes	stoke	NOUN
ma-241	37	17	equation	equation	NOUN
ma-241	37	18	,	,	PUNCT
ma-241	37	19	for	for	ADP
ma-241	37	20	two	two	NUM
ma-241	37	21	unbounded	unbounded	ADJ
ma-241	37	22	subdomains	subdomain	NOUN
ma-241	37	23	using	use	VERB
ma-241	37	24	fourier	fourier	NOUN
ma-241	37	25	analysistechniques	analysistechnique	NOUN
ma-241	37	26	which	which	PRON
ma-241	37	27	is	be	AUX
ma-241	37	28	a	a	DET
ma-241	37	29	standard	standard	ADJ
ma-241	37	30	approach	approach	NOUN
ma-241	37	31	in	in	ADP
ma-241	37	32	the	the	DET
ma-241	37	33	literature	literature	NOUN
ma-241	37	34	[	[	X
ma-241	37	35	1	1	NUM
ma-241	37	36	]	]	PUNCT
ma-241	37	37	,	,	PUNCT
ma-241	37	38	[	[	X
ma-241	37	39	2	2	NUM
ma-241	37	40	]	]	PUNCT
ma-241	37	41	,	,	PUNCT
ma-241	37	42	[	[	X
ma-241	37	43	11	11	NUM
ma-241	37	44	]	]	PUNCT
ma-241	37	45	,	,	PUNCT
ma-241	37	46	[	[	X
ma-241	37	47	12	12	NUM
ma-241	37	48	]	]	PUNCT
ma-241	37	49	,	,	PUNCT
ma-241	37	50	[	[	X
ma-241	37	51	14	14	NUM
ma-241	37	52	]	]	PUNCT
ma-241	37	53	,	,	PUNCT
ma-241	37	54	[	[	X
ma-241	37	55	15	15	NUM
ma-241	37	56	]	]	PUNCT
ma-241	37	57	,	,	PUNCT
ma-241	37	58	[	[	X
ma-241	37	59	16	16	NUM
ma-241	37	60	]	]	PUNCT
ma-241	37	61	,	,	PUNCT
ma-241	37	62	[	[	X
ma-241	37	63	17	17	NUM
ma-241	37	64	]	]	PUNCT
ma-241	37	65	.	.	PUNCT
ma-241	38	1	thesteady	thesteady	PROPN
ma-241	38	2	stokes	stokes	PROPN
ma-241	38	3	equation	equation	NOUN
ma-241	38	4	is	be	AUX
ma-241	38	5	derived	derive	VERB
ma-241	38	6	from	from	ADP
ma-241	38	7	the	the	DET
ma-241	38	8	navier	navier	NOUN
ma-241	38	9	-	-	PUNCT
ma-241	38	10	stokes	stoke	NOUN
ma-241	38	11	equation	equation	NOUN
ma-241	38	12	,	,	PUNCT
ma-241	38	13	which	which	PRON
ma-241	38	14	is	be	AUX
ma-241	38	15	a	a	DET
ma-241	38	16	pde	pde	NOUN
ma-241	38	17	for	for	ADP
ma-241	38	18	modelingthe	modelingthe	ADJ
ma-241	38	19	flow	flow	NOUN
ma-241	38	20	of	of	ADP
ma-241	38	21	incompressible	incompressible	ADJ
ma-241	38	22	fluids	fluid	NOUN
ma-241	38	23	.	.	PUNCT
ma-241	39	1	it	it	PRON
ma-241	39	2	is	be	AUX
ma-241	39	3	a	a	DET
ma-241	39	4	generalization	generalization	NOUN
ma-241	39	5	of	of	ADP
ma-241	39	6	the	the	DET
ma-241	39	7	equations	equation	NOUN
ma-241	39	8	proposed	propose	VERB
ma-241	39	9	by	by	ADP
ma-241	39	10	the	the	DET
ma-241	39	11	swissmathematician	swissmathematician	ADJ
ma-241	39	12	leonhard	leonhard	PROPN
ma-241	39	13	euler	euler	PROPN
ma-241	39	14	in	in	ADP
ma-241	39	15	the	the	DET
ma-241	39	16	18th	18th	ADJ
ma-241	39	17	century	century	NOUN
ma-241	39	18	.	.	PUNCT
ma-241	40	1	in	in	ADP
ma-241	40	2	1821	1821	NUM
ma-241	40	3	,	,	PUNCT
ma-241	40	4	claude	claude	PROPN
ma-241	40	5	-	-	PUNCT
ma-241	40	6	luis	luis	PROPN
ma-241	40	7	navier	navier	NOUN
ma-241	40	8	introduced	introduce	VERB
ma-241	40	9	theelement	theelement	NOUN
ma-241	40	10	of	of	ADP
ma-241	40	11	the	the	DET
ma-241	40	12	viscosity	viscosity	NOUN
ma-241	40	13	.	.	PUNCT
ma-241	41	1	later	later	ADV
ma-241	41	2	in	in	ADP
ma-241	41	3	the	the	DET
ma-241	41	4	mid	mid	ADJ
ma-241	41	5	19th	19th	ADJ
ma-241	41	6	century	century	NOUN
ma-241	41	7	,	,	PUNCT
ma-241	41	8	sir	sir	PROPN
ma-241	41	9	gabriel	gabriel	PROPN
ma-241	41	10	stokes	stokes	PROPN
ma-241	41	11	worked	work	VERB
ma-241	41	12	extensively	extensively	ADV
ma-241	41	13	onthe	onthe	NOUN
ma-241	41	14	equation	equation	NOUN
ma-241	41	15	.	.	PUNCT
ma-241	42	1	the	the	DET
ma-241	42	2	steady	steady	ADJ
ma-241	42	3	stokes	stoke	NOUN
ma-241	42	4	equation	equation	NOUN
ma-241	42	5	in	in	ADP
ma-241	42	6	strong	strong	ADJ
ma-241	42	7	form	form	NOUN
ma-241	42	8	reads	reads	PROPN
ma-241	42	9	−ν∆~u	−ν∆~u	PROPN
ma-241	42	10	+	+	CCONJ
ma-241	42	11	op	op	NOUN
ma-241	42	12	=	=	PUNCT
ma-241	42	13	~f	~f	PUNCT
ma-241	42	14	in	in	ADP
ma-241	42	15	ω	ω	NUM
ma-241	42	16	=	=	SYM
ma-241	42	17	(	(	PUNCT
ma-241	42	18	−∞,+∞)×	−∞,+∞)×	NOUN
ma-241	42	19	(	(	PUNCT
ma-241	42	20	−∞,+∞	−∞,+∞	NUM
ma-241	42	21	)	)	PUNCT
ma-241	42	22	,	,	PUNCT
ma-241	42	23	d	d	NOUN
ma-241	42	24	iv	iv	X
ma-241	42	25	~u	~u	PUNCT
ma-241	42	26	=	=	SYM
ma-241	42	27	0	0	NUM
ma-241	42	28	in	in	ADP
ma-241	42	29	ω	ω	NUM
ma-241	42	30	,	,	PUNCT
ma-241	42	31	~u	~u	NUM
ma-241	42	32	:	:	PUNCT
ma-241	42	33	bounded	bound	VERB
ma-241	42	34	at	at	ADP
ma-241	42	35	±∞	±∞	PROPN
ma-241	42	36	,	,	PUNCT
ma-241	42	37	p	p	X
ma-241	42	38	:	:	PUNCT
ma-241	42	39	bounded	bound	VERB
ma-241	42	40	at	at	ADP
ma-241	42	41	±∞	±∞	PROPN
ma-241	42	42	(	(	PUNCT
ma-241	42	43	3	3	NUM
ma-241	42	44	)	)	PUNCT
ma-241	42	45	https://doi.org/10.28924/ada/ma.5.6	https://doi.org/10.28924/ada/ma.5.6	PROPN
ma-241	42	46	eur	eur	PROPN
ma-241	42	47	.	.	PUNCT
ma-241	43	1	j.	j.	PROPN
ma-241	43	2	math	math	PROPN
ma-241	43	3	.	.	PUNCT
ma-241	44	1	anal	anal	PROPN
ma-241	44	2	.	.	PUNCT
ma-241	45	1	10.28924	10.28924	NUM
ma-241	45	2	/	/	SYM
ma-241	45	3	ada	ada	PROPN
ma-241	45	4	/	/	SYM
ma-241	45	5	ma.5.6	ma.5.6	NOUN
ma-241	45	6	3where	3where	NUM
ma-241	45	7	ν	ν	X
ma-241	45	8	>	>	X
ma-241	45	9	0	0	NUM
ma-241	45	10	is	be	AUX
ma-241	45	11	the	the	DET
ma-241	45	12	kinematic	kinematic	ADJ
ma-241	45	13	viscosity	viscosity	NOUN
ma-241	45	14	of	of	ADP
ma-241	45	15	the	the	DET
ma-241	45	16	fluid	fluid	NOUN
ma-241	45	17	,	,	PUNCT
ma-241	45	18	~u	~u	NUM
ma-241	45	19	is	be	AUX
ma-241	45	20	the	the	DET
ma-241	45	21	velocity	velocity	NOUN
ma-241	45	22	of	of	ADP
ma-241	45	23	the	the	DET
ma-241	45	24	fluid	fluid	NOUN
ma-241	45	25	and	and	CCONJ
ma-241	45	26	p	p	NOUN
ma-241	45	27	is	be	AUX
ma-241	45	28	thepressure	thepressure	NOUN
ma-241	45	29	field	field	NOUN
ma-241	45	30	.	.	PUNCT
ma-241	46	1	the	the	DET
ma-241	46	2	function	function	NOUN
ma-241	46	3	~f	~f	PUNCT
ma-241	46	4	is	be	AUX
ma-241	46	5	called	call	VERB
ma-241	46	6	the	the	DET
ma-241	46	7	sink	sink	ADJ
ma-241	46	8	term	term	NOUN
ma-241	46	9	.	.	PUNCT
ma-241	47	1	the	the	DET
ma-241	47	2	function	function	NOUN
ma-241	47	3	spaces	space	VERB
ma-241	47	4	for	for	ADP
ma-241	47	5	the	the	DET
ma-241	47	6	velocity	velocity	NOUN
ma-241	47	7	field	field	NOUN
ma-241	47	8	,	,	PUNCT
ma-241	47	9	pressure	pressure	NOUN
ma-241	47	10	field	field	NOUN
ma-241	47	11	and	and	CCONJ
ma-241	47	12	sink	sink	NOUN
ma-241	47	13	term	term	NOUN
ma-241	47	14	are	be	AUX
ma-241	47	15	(	(	PUNCT
ma-241	47	16	h1(ω	h1(ω	PROPN
ma-241	47	17	)	)	PUNCT
ma-241	47	18	)	)	PUNCT
ma-241	47	19	2	2	NUM
ma-241	47	20	,	,	PUNCT
ma-241	47	21	l2(ω	l2(ω	NOUN
ma-241	47	22	)	)	PUNCT
ma-241	47	23	,	,	PUNCT
ma-241	47	24	(	(	PUNCT
ma-241	47	25	l2(ω))2	l2(ω))2	NOUN
ma-241	47	26	respectively	respectively	ADV
ma-241	47	27	.	.	PUNCT
ma-241	48	1	the	the	DET
ma-241	48	2	space	space	NOUN
ma-241	48	3	h1(ω	h1(ω	NOUN
ma-241	48	4	)	)	PUNCT
ma-241	48	5	isclassical	isclassical	ADJ
ma-241	48	6	sobolev	sobolev	NOUN
ma-241	48	7	space	space	NOUN
ma-241	48	8	,	,	PUNCT
ma-241	48	9	and	and	CCONJ
ma-241	48	10	l2(ω	l2(ω	NUM
ma-241	48	11	)	)	PUNCT
ma-241	48	12	is	be	AUX
ma-241	48	13	the	the	DET
ma-241	48	14	space	space	NOUN
ma-241	48	15	of	of	ADP
ma-241	48	16	square	square	ADJ
ma-241	48	17	integrable	integrable	ADJ
ma-241	48	18	functions	function	NOUN
ma-241	48	19	.	.	PUNCT
ma-241	49	1	the	the	DET
ma-241	49	2	(	(	PUNCT
ma-241	49	3	3)2	3)2	NUM
ma-241	49	4	denotesthe	denotesthe	NOUN
ma-241	49	5	incompressibility	incompressibility	NOUN
ma-241	49	6	condition	condition	NOUN
ma-241	49	7	,	,	PUNCT
ma-241	49	8	with	with	ADP
ma-241	49	9	the	the	DET
ma-241	49	10	divergence	divergence	NOUN
ma-241	49	11	free	free	ADJ
ma-241	49	12	velocity	velocity	NOUN
ma-241	49	13	field	field	NOUN
ma-241	49	14	.	.	PUNCT
ma-241	50	1	furthermore	furthermore	ADV
ma-241	50	2	as	as	SCONJ
ma-241	50	3	(	(	PUNCT
ma-241	50	4	3)3	3)3	NUM
ma-241	50	5	,	,	PUNCT
ma-241	50	6	(	(	PUNCT
ma-241	50	7	3)4suggest	3)4suggest	NUM
ma-241	50	8	,	,	PUNCT
ma-241	50	9	the	the	DET
ma-241	50	10	velocity	velocity	NOUN
ma-241	50	11	and	and	CCONJ
ma-241	50	12	the	the	DET
ma-241	50	13	pressure	pressure	NOUN
ma-241	50	14	field	field	NOUN
ma-241	50	15	stay	stay	VERB
ma-241	50	16	bounded	bounded	ADJ
ma-241	50	17	at	at	ADP
ma-241	50	18	infinity	infinity	NOUN
ma-241	50	19	.	.	PUNCT
ma-241	51	1	2	2	X
ma-241	51	2	.	.	X
ma-241	51	3	parallel	parallel	ADJ
ma-241	51	4	schwarz	schwarz	PROPN
ma-241	51	5	method	method	PROPN
ma-241	51	6	-	-	PUNCT
ma-241	51	7	dirichlet	dirichlet	NOUN
ma-241	51	8	ic	ic	PRON
ma-241	51	9	we	we	PRON
ma-241	51	10	decompose	decompose	VERB
ma-241	51	11	the	the	DET
ma-241	51	12	domain	domain	NOUN
ma-241	51	13	ω	ω	NOUN
ma-241	51	14	=	=	SYM
ma-241	51	15	r2	r2	PROPN
ma-241	51	16	into	into	ADP
ma-241	51	17	two	two	NUM
ma-241	51	18	subdomains	subdomain	NOUN
ma-241	51	19	ω1	ω1	X
ma-241	51	20	=	=	SYM
ma-241	51	21	(	(	PUNCT
ma-241	51	22	−∞	−∞	NOUN
ma-241	51	23	,	,	PUNCT
ma-241	51	24	h	h	NOUN
ma-241	51	25	)	)	PUNCT
ma-241	51	26	×	×	NOUN
ma-241	51	27	(	(	PUNCT
ma-241	51	28	−∞,+∞	−∞,+∞	NUM
ma-241	51	29	)	)	PUNCT
ma-241	51	30	and	and	CCONJ
ma-241	51	31	ω2	ω2	NOUN
ma-241	51	32	=	=	SYM
ma-241	51	33	(	(	PUNCT
ma-241	51	34	0,+∞)×	0,+∞)×	NUM
ma-241	51	35	(	(	PUNCT
ma-241	51	36	−∞,+∞	−∞,+∞	NUM
ma-241	51	37	)	)	PUNCT
ma-241	51	38	.	.	PUNCT
ma-241	52	1	the	the	DET
ma-241	52	2	parallel	parallel	ADJ
ma-241	52	3	schwarz	schwarz	PROPN
ma-241	52	4	method	method	NOUN
ma-241	52	5	in	in	ADP
ma-241	52	6	strong	strong	ADJ
ma-241	52	7	form	form	NOUN
ma-241	52	8	reads	reads	NOUN
ma-241	52	9	−ν∆−→u1	−ν∆−→u1	NOUN
ma-241	52	10	(	(	PUNCT
ma-241	52	11	k	k	NOUN
ma-241	52	12	)	)	PUNCT
ma-241	52	13	+	+	NUM
ma-241	52	14	op(k	op(k	X
ma-241	52	15	)	)	PUNCT
ma-241	52	16	1	1	NUM
ma-241	52	17	=	=	SYM
ma-241	52	18	~f	~f	PUNCT
ma-241	52	19	in	in	ADP
ma-241	52	20	ω1	ω1	PROPN
ma-241	52	21	,	,	PUNCT
ma-241	52	22	d	d	NOUN
ma-241	52	23	iv−→u1	iv−→u1	NOUN
ma-241	52	24	(	(	PUNCT
ma-241	52	25	k	k	NOUN
ma-241	52	26	)	)	PUNCT
ma-241	52	27	=	=	SYM
ma-241	52	28	0	0	NUM
ma-241	52	29	in	in	ADP
ma-241	52	30	ω1	ω1	PROPN
ma-241	52	31	,	,	PUNCT
ma-241	52	32	−→u1	−→u1	PROPN
ma-241	52	33	(	(	PUNCT
ma-241	52	34	k	k	NOUN
ma-241	52	35	)	)	PUNCT
ma-241	52	36	=	=	SYM
ma-241	52	37	−→u2	−→u2	NOUN
ma-241	52	38	(	(	PUNCT
ma-241	52	39	k−1)at	k−1)at	NOUN
ma-241	52	40	x	x	SYM
ma-241	52	41	=	=	SYM
ma-241	52	42	h	h	PROPN
ma-241	52	43	,	,	PUNCT
ma-241	52	44	−→u1	−→u1	PROPN
ma-241	52	45	(	(	PUNCT
ma-241	52	46	k	k	NOUN
ma-241	52	47	)	)	PUNCT
ma-241	52	48	:	:	PUNCT
ma-241	52	49	bounded	bound	VERB
ma-241	52	50	at	at	ADP
ma-241	52	51	−∞	−∞	PROPN
ma-241	52	52	,	,	PUNCT
ma-241	52	53	p	p	X
ma-241	52	54	(	(	PUNCT
ma-241	52	55	k	k	NOUN
ma-241	52	56	)	)	PUNCT
ma-241	52	57	1	1	NUM
ma-241	52	58	:	:	PUNCT
ma-241	52	59	bounded	bound	VERB
ma-241	52	60	at	at	ADP
ma-241	52	61	−∞	−∞	NOUN
ma-241	52	62	,	,	PUNCT
ma-241	52	63	,	,	PUNCT
ma-241	52	64	and	and	CCONJ
ma-241	53	1			NUM
ma-241	53	2	−ν∆−→u2	−ν∆−→u2	PROPN
ma-241	53	3	(	(	PUNCT
ma-241	53	4	k	k	NOUN
ma-241	53	5	)	)	PUNCT
ma-241	53	6	+	+	NUM
ma-241	53	7	op(k	op(k	X
ma-241	53	8	)	)	PUNCT
ma-241	53	9	2	2	NUM
ma-241	53	10	=	=	SYM
ma-241	53	11	~f	~f	PUNCT
ma-241	53	12	in	in	ADP
ma-241	53	13	ω2	ω2	ADJ
ma-241	53	14	,	,	PUNCT
ma-241	53	15	d	d	X
ma-241	53	16	iv−→u2	iv−→u2	X
ma-241	53	17	(	(	PUNCT
ma-241	53	18	k	k	NOUN
ma-241	53	19	)	)	PUNCT
ma-241	53	20	=	=	SYM
ma-241	53	21	0	0	NUM
ma-241	53	22	in	in	ADP
ma-241	53	23	ω2	ω2	NUM
ma-241	53	24	,	,	PUNCT
ma-241	53	25	−→u2	−→u2	NOUN
ma-241	53	26	(	(	PUNCT
ma-241	53	27	k	k	NOUN
ma-241	53	28	)	)	PUNCT
ma-241	53	29	=	=	SYM
ma-241	53	30	−→u1	−→u1	PROPN
ma-241	53	31	(	(	PUNCT
ma-241	53	32	k−1)at	k−1)at	NOUN
ma-241	53	33	x	x	SYM
ma-241	53	34	=	=	SYM
ma-241	53	35	0	0	NUM
ma-241	53	36	,	,	PUNCT
ma-241	53	37	−→u2	−→u2	NOUN
ma-241	53	38	(	(	PUNCT
ma-241	53	39	k	k	NOUN
ma-241	53	40	)	)	PUNCT
ma-241	53	41	:	:	PUNCT
ma-241	53	42	bounded	bound	VERB
ma-241	53	43	at	at	ADP
ma-241	53	44	+	+	PROPN
ma-241	53	45	∞	∞	PROPN
ma-241	53	46	,	,	PUNCT
ma-241	53	47	p	p	X
ma-241	53	48	(	(	PUNCT
ma-241	53	49	k	k	NOUN
ma-241	53	50	)	)	PUNCT
ma-241	53	51	2	2	NUM
ma-241	53	52	:	:	PUNCT
ma-241	53	53	bounded	bound	VERB
ma-241	53	54	at	at	ADP
ma-241	53	55	+	+	PROPN
ma-241	53	56	∞	∞	PROPN
ma-241	53	57	,	,	PUNCT
ma-241	53	58	(	(	PUNCT
ma-241	53	59	4	4	X
ma-241	53	60	)	)	PUNCT
ma-241	53	61	where	where	SCONJ
ma-241	53	62	two	two	NUM
ma-241	53	63	initial	initial	ADJ
ma-241	53	64	guesses	guess	NOUN
ma-241	53	65	−→u1	−→u1	NOUN
ma-241	53	66	(	(	PUNCT
ma-241	53	67	0	0	NUM
ma-241	53	68	)	)	PUNCT
ma-241	53	69	,	,	PUNCT
ma-241	53	70	−→u2	−→u2	NOUN
ma-241	53	71	(	(	PUNCT
ma-241	53	72	0	0	NUM
ma-241	53	73	)	)	PUNCT
ma-241	53	74	are	be	AUX
ma-241	53	75	required	require	VERB
ma-241	53	76	to	to	PART
ma-241	53	77	start	start	VERB
ma-241	53	78	the	the	DET
ma-241	53	79	iterative	iterative	NOUN
ma-241	53	80	process	process	NOUN
ma-241	53	81	.	.	PUNCT
ma-241	54	1	theorem	theorem	NOUN
ma-241	54	2	1	1	NUM
ma-241	54	3	.	.	PUNCT
ma-241	55	1	the	the	DET
ma-241	55	2	convergence	convergence	NOUN
ma-241	55	3	factor	factor	NOUN
ma-241	55	4	of	of	ADP
ma-241	55	5	the	the	DET
ma-241	55	6	parallel	parallel	ADJ
ma-241	55	7	schwarz	schwarz	PROPN
ma-241	55	8	algorithm	algorithm	NOUN
ma-241	55	9	using	use	VERB
ma-241	55	10	dirichlet	dirichlet	PROPN
ma-241	55	11	transmission	transmission	NOUN
ma-241	55	12	conditions	condition	NOUN
ma-241	55	13	is	be	AUX
ma-241	55	14	given	give	VERB
ma-241	55	15	by	by	ADP
ma-241	55	16	the	the	DET
ma-241	55	17	formula	formula	NOUN
ma-241	55	18	below	below	ADP
ma-241	55	19	rpsm	rpsm	PROPN
ma-241	55	20	,	,	PUNCT
ma-241	55	21	d(ξ	d(ξ	PROPN
ma-241	55	22	,	,	PUNCT
ma-241	55	23	h	h	NOUN
ma-241	55	24	)	)	PUNCT
ma-241	55	25	=	=	PUNCT
ma-241	56	1	(	(	PUNCT
ma-241	56	2	1	1	NUM
ma-241	56	3	+	+	CCONJ
ma-241	56	4	2h2|ξ|2	2h2|ξ|2	NUM
ma-241	56	5	+	+	CCONJ
ma-241	56	6	2	2	NUM
ma-241	56	7	|ξ|	|ξ|	NOUN
ma-241	56	8	√	√	PROPN
ma-241	56	9	h2	h2	PROPN
ma-241	56	10	(	(	PUNCT
ma-241	56	11	1	1	NUM
ma-241	56	12	+	+	ADJ
ma-241	56	13	h2|ξ|2	h2|ξ|2	ADJ
ma-241	56	14	)	)	PUNCT
ma-241	56	15	)	)	PUNCT
ma-241	56	16	e−2|ξ|h	e−2|ξ|h	PROPN
ma-241	56	17	(	(	PUNCT
ma-241	56	18	5	5	NUM
ma-241	56	19	)	)	PUNCT
ma-241	56	20	where	where	SCONJ
ma-241	56	21	ξ	ξ	PROPN
ma-241	56	22	is	be	AUX
ma-241	56	23	the	the	DET
ma-241	56	24	fourier	fourier	ADJ
ma-241	56	25	frequency	frequency	NOUN
ma-241	56	26	and	and	CCONJ
ma-241	56	27	h	h	NOUN
ma-241	56	28	>	>	X
ma-241	56	29	0	0	PUNCT
ma-241	56	30	is	be	AUX
ma-241	56	31	the	the	DET
ma-241	56	32	size	size	NOUN
ma-241	56	33	of	of	ADP
ma-241	56	34	the	the	DET
ma-241	56	35	overlap	overlap	NOUN
ma-241	56	36	.	.	PUNCT
ma-241	57	1	proof	proof	NOUN
ma-241	57	2	.	.	PUNCT
ma-241	58	1	in	in	ADP
ma-241	58	2	order	order	NOUN
ma-241	58	3	to	to	PART
ma-241	58	4	study	study	VERB
ma-241	58	5	the	the	DET
ma-241	58	6	convergence	convergence	NOUN
ma-241	58	7	behavior	behavior	NOUN
ma-241	58	8	of	of	ADP
ma-241	58	9	the	the	DET
ma-241	58	10	method	method	NOUN
ma-241	58	11	,	,	PUNCT
ma-241	58	12	we	we	PRON
ma-241	58	13	go	go	VERB
ma-241	58	14	back	back	ADV
ma-241	58	15	to	to	ADP
ma-241	58	16	the	the	DET
ma-241	58	17	local	local	ADJ
ma-241	58	18	subproblemsin	subproblemsin	NOUN
ma-241	58	19	(	(	PUNCT
ma-241	58	20	4	4	NUM
ma-241	58	21	)	)	PUNCT
ma-241	58	22	and	and	CCONJ
ma-241	58	23	we	we	PRON
ma-241	58	24	consider	consider	VERB
ma-241	58	25	the	the	DET
ma-241	58	26	homogeneous	homogeneous	ADJ
ma-241	58	27	counterparts	counterpart	NOUN
ma-241	58	28	taking	take	VERB
ma-241	58	29	~f	~f	PUNCT
ma-241	58	30	=	=	SYM
ma-241	58	31	~0	~0	X
ma-241	58	32	.	.	PUNCT
ma-241	59	1	in	in	ADP
ma-241	59	2	addition	addition	NOUN
ma-241	59	3	,	,	PUNCT
ma-241	59	4	the	the	DET
ma-241	59	5	velocity	velocity	NOUN
ma-241	59	6	fieldsin	fieldsin	VERB
ma-241	59	7	the	the	DET
ma-241	59	8	two	two	NUM
ma-241	59	9	subdomains	subdomain	NOUN
ma-241	59	10	are	be	AUX
ma-241	59	11	−→u1	−→u1	NOUN
ma-241	59	12	(	(	PUNCT
ma-241	59	13	k	k	NOUN
ma-241	59	14	)	)	PUNCT
ma-241	59	15	=	=	SYM
ma-241	59	16	(	(	PUNCT
ma-241	59	17	u	u	X
ma-241	59	18	(	(	PUNCT
ma-241	59	19	k	k	NOUN
ma-241	59	20	)	)	PUNCT
ma-241	59	21	1,1	1,1	NUM
ma-241	59	22	,	,	PUNCT
ma-241	59	23	u	u	NOUN
ma-241	59	24	(	(	PUNCT
ma-241	59	25	k	k	NOUN
ma-241	59	26	)	)	PUNCT
ma-241	59	27	1,2	1,2	NUM
ma-241	59	28	)	)	PUNCT
ma-241	59	29	and	and	CCONJ
ma-241	59	30	−→u2	−→u2	NOUN
ma-241	59	31	(	(	PUNCT
ma-241	59	32	k	k	NOUN
ma-241	59	33	)	)	PUNCT
ma-241	60	1	=	=	SYM
ma-241	60	2	(	(	PUNCT
ma-241	60	3	u	u	X
ma-241	60	4	(	(	PUNCT
ma-241	60	5	k	k	PROPN
ma-241	60	6	)	)	PUNCT
ma-241	60	7	2,1	2,1	NUM
ma-241	60	8	,	,	PUNCT
ma-241	60	9	u	u	NOUN
ma-241	60	10	(	(	PUNCT
ma-241	60	11	k	k	NOUN
ma-241	60	12	)	)	PUNCT
ma-241	60	13	2,2	2,2	NUM
ma-241	60	14	)	)	PUNCT
ma-241	60	15	,	,	PUNCT
ma-241	60	16	where	where	SCONJ
ma-241	60	17	the	the	DET
ma-241	60	18	first	first	ADJ
ma-241	60	19	indicesdenote	indicesdenote	VERB
ma-241	60	20	the	the	DET
ma-241	60	21	subdomain	subdomain	NOUN
ma-241	60	22	and	and	CCONJ
ma-241	60	23	the	the	DET
ma-241	60	24	second	second	ADJ
ma-241	60	25	indices	index	NOUN
ma-241	60	26	denote	denote	VERB
ma-241	60	27	the	the	DET
ma-241	60	28	component	component	NOUN
ma-241	60	29	.	.	PUNCT
ma-241	61	1	consequently	consequently	ADV
ma-241	61	2	,	,	PUNCT
ma-241	61	3	the	the	DET
ma-241	61	4	parallelschwarz	parallelschwarz	ADJ
ma-241	61	5	method	method	NOUN
ma-241	61	6	prescribed	prescribe	VERB
ma-241	61	7	by	by	ADP
ma-241	61	8	(	(	PUNCT
ma-241	61	9	4	4	X
ma-241	61	10	)	)	PUNCT
ma-241	61	11	can	can	AUX
ma-241	61	12	be	be	AUX
ma-241	61	13	written	write	VERB
ma-241	61	14	in	in	ADP
ma-241	61	15	the	the	DET
ma-241	61	16	following	follow	VERB
ma-241	61	17	form	form	NOUN
ma-241	61	18	https://doi.org/10.28924/ada/ma.5.6	https://doi.org/10.28924/ada/ma.5.6	PROPN
ma-241	61	19	eur	eur	NOUN
ma-241	61	20	.	.	PUNCT
ma-241	62	1	j.	j.	PROPN
ma-241	62	2	math	math	PROPN
ma-241	62	3	.	.	PUNCT
ma-241	63	1	anal	anal	PROPN
ma-241	63	2	.	.	PUNCT
ma-241	64	1	10.28924	10.28924	NUM
ma-241	64	2	/	/	SYM
ma-241	64	3	ada	ada	PROPN
ma-241	64	4	/	/	SYM
ma-241	64	5	ma.5.6	ma.5.6	PROPN
ma-241	64	6	4	4	NUM
ma-241	64	7			NUM
ma-241	64	8	∂2u	∂2u	X
ma-241	64	9	(	(	PUNCT
ma-241	64	10	k	k	NOUN
ma-241	64	11	)	)	PUNCT
ma-241	64	12	1,1	1,1	NUM
ma-241	64	13	∂x2	∂x2	NOUN
ma-241	64	14	+	+	CCONJ
ma-241	64	15	∂2u	∂2u	X
ma-241	64	16	(	(	PUNCT
ma-241	64	17	k	k	X
ma-241	64	18	)	)	PUNCT
ma-241	64	19	1,1	1,1	NUM
ma-241	64	20	∂y2	∂y2	NOUN
ma-241	64	21	=	=	PUNCT
ma-241	64	22	1	1	NUM
ma-241	64	23	ν	ν	X
ma-241	64	24	∂p	∂p	PROPN
ma-241	64	25	(	(	PUNCT
ma-241	64	26	k	k	NOUN
ma-241	64	27	)	)	PUNCT
ma-241	64	28	1	1	NUM
ma-241	64	29	∂x	∂x	PROPN
ma-241	64	30	in	in	ADP
ma-241	64	31	ω1	ω1	PROPN
ma-241	64	32	,	,	PUNCT
ma-241	64	33	∂2u	∂2u	X
ma-241	64	34	(	(	PUNCT
ma-241	64	35	k	k	NOUN
ma-241	64	36	)	)	PUNCT
ma-241	64	37	1,2	1,2	NUM
ma-241	64	38	∂x2	∂x2	NOUN
ma-241	64	39	+	+	CCONJ
ma-241	64	40	∂2u	∂2u	X
ma-241	64	41	(	(	PUNCT
ma-241	64	42	k	k	X
ma-241	64	43	)	)	PUNCT
ma-241	64	44	1,2	1,2	NUM
ma-241	64	45	∂y2	∂y2	NOUN
ma-241	64	46	=	=	SYM
ma-241	65	1	1	1	NUM
ma-241	65	2	ν	ν	X
ma-241	65	3	∂p	∂p	PROPN
ma-241	65	4	(	(	PUNCT
ma-241	65	5	k	k	NOUN
ma-241	65	6	)	)	PUNCT
ma-241	65	7	1	1	NUM
ma-241	65	8	∂y	∂y	PROPN
ma-241	65	9	in	in	ADP
ma-241	65	10	ω1	ω1	PROPN
ma-241	65	11	,	,	PUNCT
ma-241	65	12	∂u	∂u	PROPN
ma-241	65	13	(	(	PUNCT
ma-241	65	14	k	k	NOUN
ma-241	65	15	)	)	PUNCT
ma-241	65	16	1,1	1,1	NUM
ma-241	65	17	∂x	∂x	PROPN
ma-241	65	18	+	+	CCONJ
ma-241	65	19	∂u	∂u	PROPN
ma-241	65	20	(	(	PUNCT
ma-241	65	21	k	k	NOUN
ma-241	65	22	)	)	PUNCT
ma-241	65	23	1,2	1,2	NUM
ma-241	65	24	∂y	∂y	X
ma-241	65	25	=	=	NOUN
ma-241	65	26	0	0	NUM
ma-241	65	27	in	in	ADP
ma-241	65	28	ω1	ω1	PROPN
ma-241	65	29	,	,	PUNCT
ma-241	65	30	u	u	NOUN
ma-241	65	31	(	(	PUNCT
ma-241	65	32	k	k	NOUN
ma-241	65	33	)	)	PUNCT
ma-241	65	34	1,1	1,1	NUM
ma-241	65	35	=	=	SYM
ma-241	65	36	u	u	PROPN
ma-241	65	37	(	(	PUNCT
ma-241	65	38	k−1	k−1	PROPN
ma-241	65	39	)	)	PUNCT
ma-241	65	40	2,1	2,1	NUM
ma-241	65	41	at	at	ADP
ma-241	65	42	x	x	X
ma-241	65	43	=	=	SYM
ma-241	65	44	h	h	NOUN
ma-241	65	45	,	,	PUNCT
ma-241	65	46	u	u	NOUN
ma-241	65	47	(	(	PUNCT
ma-241	65	48	k	k	NOUN
ma-241	65	49	)	)	PUNCT
ma-241	65	50	1,2	1,2	NUM
ma-241	65	51	=	=	SYM
ma-241	65	52	u	u	SYM
ma-241	65	53	(	(	PUNCT
ma-241	65	54	k−1	k−1	PROPN
ma-241	65	55	)	)	PUNCT
ma-241	65	56	2,2	2,2	NUM
ma-241	65	57	at	at	ADP
ma-241	65	58	x	x	X
ma-241	65	59	=	=	SYM
ma-241	65	60	h	h	NOUN
ma-241	65	61	,	,	PUNCT
ma-241	65	62	u	u	NOUN
ma-241	65	63	(	(	PUNCT
ma-241	65	64	k	k	NOUN
ma-241	65	65	)	)	PUNCT
ma-241	65	66	1,1	1,1	NUM
ma-241	65	67	:	:	PUNCT
ma-241	65	68	bounded	bound	VERB
ma-241	65	69	at	at	ADP
ma-241	65	70	−∞	−∞	PROPN
ma-241	65	71	,	,	PUNCT
ma-241	65	72	u	u	PROPN
ma-241	65	73	(	(	PUNCT
ma-241	65	74	k	k	NOUN
ma-241	65	75	)	)	PUNCT
ma-241	65	76	1,2	1,2	NUM
ma-241	65	77	:	:	PUNCT
ma-241	65	78	bounded	bound	VERB
ma-241	65	79	at	at	ADP
ma-241	65	80	−∞	−∞	PROPN
ma-241	65	81	,	,	PUNCT
ma-241	65	82	p	p	X
ma-241	65	83	(	(	PUNCT
ma-241	65	84	k	k	NOUN
ma-241	65	85	)	)	PUNCT
ma-241	65	86	1	1	NUM
ma-241	65	87	:	:	PUNCT
ma-241	65	88	bounded	bound	VERB
ma-241	65	89	at	at	ADP
ma-241	65	90	−∞	−∞	NOUN
ma-241	65	91	,	,	PUNCT
ma-241	65	92	,	,	PUNCT
ma-241	65	93	and	and	CCONJ
ma-241	65	94			NUM
ma-241	65	95	∂2u	∂2u	X
ma-241	65	96	(	(	PUNCT
ma-241	65	97	k	k	NOUN
ma-241	65	98	)	)	PUNCT
ma-241	65	99	2,1	2,1	NUM
ma-241	65	100	∂x2	∂x2	NOUN
ma-241	65	101	+	+	CCONJ
ma-241	65	102	∂2u	∂2u	X
ma-241	65	103	(	(	PUNCT
ma-241	65	104	k	k	X
ma-241	65	105	)	)	PUNCT
ma-241	65	106	2,1	2,1	NUM
ma-241	65	107	∂y2	∂y2	NOUN
ma-241	65	108	=	=	SYM
ma-241	65	109	1	1	NUM
ma-241	65	110	ν	ν	X
ma-241	65	111	∂p	∂p	PROPN
ma-241	65	112	(	(	PUNCT
ma-241	65	113	k	k	NOUN
ma-241	65	114	)	)	PUNCT
ma-241	65	115	2	2	NUM
ma-241	65	116	∂x	∂x	PROPN
ma-241	65	117	in	in	ADP
ma-241	65	118	ω2	ω2	ADJ
ma-241	65	119	,	,	PUNCT
ma-241	65	120	∂2u	∂2u	X
ma-241	65	121	(	(	PUNCT
ma-241	65	122	k	k	NOUN
ma-241	65	123	)	)	PUNCT
ma-241	65	124	2,2	2,2	NUM
ma-241	65	125	∂x2	∂x2	NOUN
ma-241	65	126	+	+	CCONJ
ma-241	65	127	∂2u	∂2u	X
ma-241	65	128	(	(	PUNCT
ma-241	65	129	k	k	NOUN
ma-241	65	130	)	)	PUNCT
ma-241	65	131	2,2	2,2	NUM
ma-241	65	132	∂y2	∂y2	NOUN
ma-241	65	133	=	=	NOUN
ma-241	65	134	1	1	NUM
ma-241	65	135	ν	ν	X
ma-241	65	136	∂p	∂p	PROPN
ma-241	65	137	(	(	PUNCT
ma-241	65	138	k	k	NOUN
ma-241	65	139	)	)	PUNCT
ma-241	65	140	2	2	NUM
ma-241	65	141	∂y	∂y	PROPN
ma-241	65	142	in	in	ADP
ma-241	65	143	ω2	ω2	PROPN
ma-241	65	144	,	,	PUNCT
ma-241	65	145	∂u	∂u	PROPN
ma-241	65	146	(	(	PUNCT
ma-241	65	147	k	k	NOUN
ma-241	65	148	)	)	PUNCT
ma-241	65	149	2,1	2,1	NUM
ma-241	66	1	∂x	∂x	PROPN
ma-241	66	2	+	+	CCONJ
ma-241	66	3	∂u	∂u	PROPN
ma-241	66	4	(	(	PUNCT
ma-241	66	5	k	k	NOUN
ma-241	66	6	)	)	PUNCT
ma-241	66	7	2,2	2,2	NUM
ma-241	66	8	∂y	∂y	SYM
ma-241	66	9	=	=	NOUN
ma-241	66	10	0	0	NUM
ma-241	66	11	in	in	ADP
ma-241	66	12	ω2	ω2	ADJ
ma-241	66	13	,	,	PUNCT
ma-241	66	14	u	u	NOUN
ma-241	66	15	(	(	PUNCT
ma-241	66	16	k	k	NOUN
ma-241	66	17	)	)	PUNCT
ma-241	66	18	2,1	2,1	NUM
ma-241	66	19	=	=	SYM
ma-241	66	20	u	u	PROPN
ma-241	66	21	(	(	PUNCT
ma-241	66	22	k−1	k−1	PROPN
ma-241	66	23	)	)	PUNCT
ma-241	66	24	1,1	1,1	NUM
ma-241	66	25	at	at	ADP
ma-241	66	26	x	x	X
ma-241	66	27	=	=	SYM
ma-241	66	28	0	0	NUM
ma-241	66	29	,	,	PUNCT
ma-241	66	30	u	u	NOUN
ma-241	66	31	(	(	PUNCT
ma-241	66	32	k	k	NOUN
ma-241	66	33	)	)	PUNCT
ma-241	66	34	2,2	2,2	PROPN
ma-241	66	35	=	=	SYM
ma-241	66	36	u	u	PROPN
ma-241	66	37	(	(	PUNCT
ma-241	66	38	k−1	k−1	PROPN
ma-241	66	39	)	)	PUNCT
ma-241	66	40	1,2	1,2	NUM
ma-241	66	41	at	at	ADP
ma-241	66	42	x	x	X
ma-241	66	43	=	=	SYM
ma-241	66	44	0	0	NUM
ma-241	66	45	,	,	PUNCT
ma-241	66	46	u	u	NOUN
ma-241	66	47	(	(	PUNCT
ma-241	66	48	k	k	NOUN
ma-241	66	49	)	)	PUNCT
ma-241	66	50	2,1	2,1	NUM
ma-241	66	51	:	:	PUNCT
ma-241	66	52	bounded	bound	VERB
ma-241	66	53	at	at	ADP
ma-241	66	54	+	+	PROPN
ma-241	66	55	∞	∞	PROPN
ma-241	66	56	,	,	PUNCT
ma-241	66	57	u	u	NOUN
ma-241	66	58	(	(	PUNCT
ma-241	66	59	k	k	NOUN
ma-241	66	60	)	)	PUNCT
ma-241	66	61	2,2	2,2	NUM
ma-241	66	62	:	:	PUNCT
ma-241	66	63	bounded	bound	VERB
ma-241	66	64	at	at	ADP
ma-241	66	65	+	+	PROPN
ma-241	66	66	∞	∞	PROPN
ma-241	66	67	,	,	PUNCT
ma-241	66	68	p	p	X
ma-241	66	69	(	(	PUNCT
ma-241	66	70	k	k	NOUN
ma-241	66	71	)	)	PUNCT
ma-241	66	72	2	2	NUM
ma-241	66	73	:	:	PUNCT
ma-241	66	74	bounded	bound	VERB
ma-241	66	75	at	at	ADP
ma-241	66	76	+	+	PROPN
ma-241	66	77	∞.	∞.	PROPN
ma-241	66	78	(	(	PUNCT
ma-241	66	79	6	6	NUM
ma-241	66	80	)	)	PUNCT
ma-241	66	81	going	go	VERB
ma-241	66	82	back	back	ADV
ma-241	66	83	to	to	ADP
ma-241	66	84	(	(	PUNCT
ma-241	66	85	4)1	4)1	NOUN
ma-241	66	86	,	,	PUNCT
ma-241	66	87	for	for	ADP
ma-241	66	88	~f	~f	NOUN
ma-241	66	89	=	=	SYM
ma-241	66	90	~0	~0	NOUN
ma-241	66	91	,	,	PUNCT
ma-241	66	92	taking	take	VERB
ma-241	66	93	the	the	DET
ma-241	66	94	divergence	divergence	NOUN
ma-241	66	95	on	on	ADP
ma-241	66	96	both	both	DET
ma-241	66	97	sides	side	NOUN
ma-241	66	98	for	for	ADP
ma-241	66	99	the	the	DET
ma-241	66	100	first	first	ADJ
ma-241	66	101	subproblem	subproblem	NOUN
ma-241	66	102	,	,	PUNCT
ma-241	66	103	weobtain	weobtain	NOUN
ma-241	66	104	div	div	X
ma-241	66	105	(	(	PUNCT
ma-241	66	106	∆−→u1	∆−→u1	NOUN
ma-241	66	107	(	(	PUNCT
ma-241	66	108	k	k	NOUN
ma-241	66	109	)	)	PUNCT
ma-241	66	110	)	)	PUNCT
ma-241	66	111	=	=	SYM
ma-241	66	112	1	1	NUM
ma-241	66	113	ν	ν	X
ma-241	66	114	∆p	∆p	PROPN
ma-241	66	115	(	(	PUNCT
ma-241	66	116	k	k	NOUN
ma-241	66	117	)	)	PUNCT
ma-241	66	118	1	1	NUM
ma-241	66	119	=	=	SYM
ma-241	66	120	(	(	PUNCT
ma-241	66	121	∂3u	∂3u	X
ma-241	66	122	(	(	PUNCT
ma-241	66	123	k	k	NOUN
ma-241	66	124	)	)	PUNCT
ma-241	66	125	1,1	1,1	NUM
ma-241	66	126	∂x3	∂x3	ADV
ma-241	66	127	+	+	CCONJ
ma-241	66	128	∂3u	∂3u	ADJ
ma-241	66	129	(	(	PUNCT
ma-241	66	130	k	k	NOUN
ma-241	66	131	)	)	PUNCT
ma-241	66	132	1,2	1,2	NUM
ma-241	66	133	∂y∂x2	∂y∂x2	NOUN
ma-241	66	134	)	)	PUNCT
ma-241	67	1	+	+	CCONJ
ma-241	67	2	(	(	PUNCT
ma-241	67	3	∂3u	∂3u	X
ma-241	67	4	(	(	PUNCT
ma-241	67	5	k	k	NOUN
ma-241	67	6	)	)	PUNCT
ma-241	67	7	1,2	1,2	NUM
ma-241	67	8	∂y3	∂y3	NOUN
ma-241	67	9	+	+	X
ma-241	67	10	∂3u	∂3u	ADJ
ma-241	67	11	(	(	PUNCT
ma-241	67	12	k	k	NOUN
ma-241	67	13	)	)	PUNCT
ma-241	67	14	1,1	1,1	NUM
ma-241	67	15	∂x∂y2	∂x∂y2	NUM
ma-241	67	16	)	)	PUNCT
ma-241	68	1	=	=	PUNCT
ma-241	68	2	0	0	NUM
ma-241	69	1	in	in	ADP
ma-241	69	2	ω1	ω1	PROPN
ma-241	69	3	exploiting	exploit	VERB
ma-241	69	4	the	the	DET
ma-241	69	5	equation	equation	NOUN
ma-241	69	6	(	(	PUNCT
ma-241	69	7	4)2	4)2	X
ma-241	69	8	(	(	PUNCT
ma-241	69	9	divergence	divergence	VERB
ma-241	69	10	free	free	ADJ
ma-241	69	11	velocity	velocity	NOUN
ma-241	69	12	in	in	ADP
ma-241	69	13	subdomain	subdomain	NOUN
ma-241	69	14	ω1	ω1	PROPN
ma-241	69	15	)	)	PUNCT
ma-241	69	16	.	.	PUNCT
ma-241	70	1	in	in	ADP
ma-241	70	2	the	the	DET
ma-241	70	3	same	same	ADJ
ma-241	70	4	fashion	fashion	NOUN
ma-241	70	5	weobtain	weobtain	NOUN
ma-241	70	6	that	that	PRON
ma-241	70	7	div	div	X
ma-241	70	8	(	(	PUNCT
ma-241	70	9	∆−→u2	∆−→u2	PROPN
ma-241	70	10	(	(	PUNCT
ma-241	70	11	k	k	NOUN
ma-241	70	12	)	)	PUNCT
ma-241	70	13	)	)	PUNCT
ma-241	70	14	=	=	SYM
ma-241	70	15	1	1	NUM
ma-241	70	16	ν	ν	X
ma-241	70	17	∆p	∆p	PROPN
ma-241	70	18	(	(	PUNCT
ma-241	70	19	k	k	NOUN
ma-241	70	20	)	)	PUNCT
ma-241	70	21	2	2	NUM
ma-241	70	22	=	=	SYM
ma-241	70	23	0	0	NUM
ma-241	70	24	in	in	ADP
ma-241	70	25	ω2	ω2	PROPN
ma-241	70	26	.	.	PUNCT
ma-241	71	1	as	as	ADP
ma-241	71	2	a	a	DET
ma-241	71	3	consequence	consequence	NOUN
ma-241	71	4	,	,	PUNCT
ma-241	71	5	we	we	PRON
ma-241	71	6	have	have	VERB
ma-241	71	7	to	to	PART
ma-241	71	8	solve	solve	VERB
ma-241	71	9	two	two	NUM
ma-241	71	10	laplaceproblems	laplaceproblem	NOUN
ma-241	71	11	in	in	ADP
ma-241	71	12	each	each	DET
ma-241	71	13	subdomain	subdomain	NOUN
ma-241	71	14	where	where	SCONJ
ma-241	71	15	the	the	DET
ma-241	71	16	unknown	unknown	NOUN
ma-241	71	17	is	be	AUX
ma-241	71	18	the	the	DET
ma-241	71	19	pressure	pressure	NOUN
ma-241	71	20	field	field	NOUN
ma-241	71	21	.	.	PUNCT
ma-241	72	1	we	we	PRON
ma-241	72	2	deal	deal	VERB
ma-241	72	3	with	with	ADP
ma-241	72	4	∆p	∆p	PROPN
ma-241	72	5	(	(	PUNCT
ma-241	72	6	k	k	NOUN
ma-241	72	7	)	)	PUNCT
ma-241	72	8	1	1	NUM
ma-241	73	1	=	=	SYM
ma-241	73	2	0	0	NUM
ma-241	73	3	in	in	ADP
ma-241	73	4	ω1	ω1	PROPN
ma-241	73	5	and	and	CCONJ
ma-241	73	6	by	by	ADP
ma-241	73	7	taking	take	VERB
ma-241	73	8	the	the	DET
ma-241	73	9	fourier	fourier	NOUN
ma-241	73	10	transform	transform	NOUN
ma-241	73	11	in	in	ADP
ma-241	73	12	the	the	DET
ma-241	73	13	y	y	PROPN
ma-241	73	14	direction	direction	NOUN
ma-241	73	15	we	we	PRON
ma-241	73	16	obtain	obtain	VERB
ma-241	73	17	the	the	DET
ma-241	73	18	homogeneous	homogeneous	ADJ
ma-241	73	19	equation	equation	NOUN
ma-241	73	20	∂2p̂	∂2p̂	PROPN
ma-241	73	21	(	(	PUNCT
ma-241	73	22	k	k	NOUN
ma-241	73	23	)	)	PUNCT
ma-241	73	24	1	1	NUM
ma-241	73	25	∂x2	∂x2	NOUN
ma-241	73	26	−	−	NOUN
ma-241	73	27	|ξ|2p̂(k	|ξ|2p̂(k	NOUN
ma-241	73	28	)	)	PUNCT
ma-241	73	29	1	1	NUM
ma-241	73	30	=	=	SYM
ma-241	73	31	0	0	NUM
ma-241	73	32	.	.	PUNCT
ma-241	74	1	the	the	DET
ma-241	74	2	general	general	ADJ
ma-241	74	3	solution	solution	NOUN
ma-241	74	4	of	of	ADP
ma-241	74	5	this	this	DET
ma-241	74	6	equation	equation	NOUN
ma-241	74	7	is	be	AUX
ma-241	74	8	p̂(k	p̂(k	NOUN
ma-241	74	9	)	)	PUNCT
ma-241	74	10	1	1	NUM
ma-241	74	11	=	=	SYM
ma-241	74	12	c(k	c(k	NOUN
ma-241	74	13	)	)	PUNCT
ma-241	74	14	1	1	NUM
ma-241	75	1	e−|ξ|x	e−|ξ|x	PROPN
ma-241	75	2	+	+	PROPN
ma-241	75	3	d(k	d(k	PROPN
ma-241	75	4	)	)	PUNCT
ma-241	76	1	1	1	NUM
ma-241	76	2	e	e	X
ma-241	76	3	|ξ|x	|ξ|x	PROPN
ma-241	76	4	.	.	PUNCT
ma-241	77	1	by	by	ADP
ma-241	77	2	theboundedness	theboundedness	ADJ
ma-241	77	3	assumption	assumption	NOUN
ma-241	77	4	of	of	ADP
ma-241	77	5	the	the	DET
ma-241	77	6	pressure	pressure	NOUN
ma-241	77	7	field	field	NOUN
ma-241	77	8	in	in	ADP
ma-241	77	9	ω1	ω1	PROPN
ma-241	77	10	as	as	SCONJ
ma-241	77	11	x	x	X
ma-241	77	12	→	→	SYM
ma-241	77	13	−∞	−∞	NOUN
ma-241	77	14	,	,	PUNCT
ma-241	77	15	we	we	PRON
ma-241	77	16	obtain	obtain	VERB
ma-241	77	17	that	that	SCONJ
ma-241	77	18	p̂(k	p̂(k	NOUN
ma-241	77	19	)	)	PUNCT
ma-241	77	20	1	1	NUM
ma-241	77	21	=	=	SYM
ma-241	77	22	d(k	d(k	PROPN
ma-241	77	23	)	)	PUNCT
ma-241	77	24	1	1	NUM
ma-241	77	25	e	e	X
ma-241	77	26	|ξ|x	|ξ|x	PROPN
ma-241	77	27	.we	.we	PUNCT
ma-241	77	28	proceed	proceed	VERB
ma-241	77	29	to	to	PART
ma-241	77	30	solve	solve	VERB
ma-241	77	31	the	the	DET
ma-241	77	32	equation	equation	NOUN
ma-241	77	33	∆p	∆p	PROPN
ma-241	77	34	(	(	PUNCT
ma-241	77	35	k	k	NOUN
ma-241	77	36	)	)	PUNCT
ma-241	77	37	2	2	NUM
ma-241	77	38	=	=	SYM
ma-241	77	39	0	0	NUM
ma-241	77	40	in	in	ADP
ma-241	77	41	ω2	ω2	ADJ
ma-241	77	42	,	,	PUNCT
ma-241	77	43	and	and	CCONJ
ma-241	77	44	the	the	DET
ma-241	77	45	first	first	ADJ
ma-241	77	46	step	step	NOUN
ma-241	77	47	is	be	AUX
ma-241	77	48	to	to	PART
ma-241	77	49	take	take	VERB
ma-241	77	50	the	the	DET
ma-241	77	51	fourier	fourier	NOUN
ma-241	77	52	transformin	transformin	NOUN
ma-241	77	53	the	the	DET
ma-241	77	54	y	y	PROPN
ma-241	77	55	direction	direction	NOUN
ma-241	77	56	.	.	PUNCT
ma-241	78	1	as	as	ADP
ma-241	78	2	a	a	DET
ma-241	78	3	result	result	NOUN
ma-241	78	4	,	,	PUNCT
ma-241	78	5	the	the	DET
ma-241	78	6	equation	equation	NOUN
ma-241	78	7	∂2p̂	∂2p̂	PROPN
ma-241	78	8	(	(	PUNCT
ma-241	78	9	k	k	NOUN
ma-241	78	10	)	)	PUNCT
ma-241	78	11	2	2	NUM
ma-241	78	12	∂x2	∂x2	NOUN
ma-241	78	13	−	−	NOUN
ma-241	78	14	|ξ|2p̂(k	|ξ|2p̂(k	NOUN
ma-241	78	15	)	)	PUNCT
ma-241	78	16	2	2	NUM
ma-241	78	17	=	=	SYM
ma-241	78	18	0	0	PROPN
ma-241	78	19	has	have	VERB
ma-241	78	20	a	a	DET
ma-241	78	21	general	general	ADJ
ma-241	78	22	solution	solution	NOUN
ma-241	78	23	of	of	ADP
ma-241	78	24	theform	theform	NOUN
ma-241	78	25	p̂	p̂	NOUN
ma-241	78	26	(	(	PUNCT
ma-241	78	27	k	k	NOUN
ma-241	78	28	)	)	PUNCT
ma-241	78	29	2	2	NUM
ma-241	78	30	=	=	SYM
ma-241	78	31	c(k	c(k	NOUN
ma-241	78	32	)	)	PUNCT
ma-241	78	33	2	2	NUM
ma-241	78	34	e−|ξ|x	e−|ξ|x	PROPN
ma-241	78	35	+	+	CCONJ
ma-241	78	36	d(k	d(k	PROPN
ma-241	78	37	)	)	PUNCT
ma-241	78	38	2	2	NUM
ma-241	78	39	e	e	SCONJ
ma-241	78	40	|ξ|x	|ξ|x	NOUN
ma-241	78	41	.by	.by	PUNCT
ma-241	78	42	exploiting	exploit	VERB
ma-241	78	43	the	the	DET
ma-241	78	44	property	property	NOUN
ma-241	78	45	that	that	PRON
ma-241	78	46	the	the	DET
ma-241	78	47	pressure	pressure	NOUN
ma-241	78	48	field	field	NOUN
ma-241	78	49	p̂(k	p̂(k	NOUN
ma-241	78	50	)	)	PUNCT
ma-241	78	51	2	2	NUM
ma-241	78	52	remainsbounded	remainsbounde	VERB
ma-241	78	53	as	as	ADP
ma-241	78	54	x	x	X
ma-241	78	55	→	→	SYM
ma-241	78	56	+	+	NOUN
ma-241	78	57	∞	∞	PROPN
ma-241	78	58	,	,	PUNCT
ma-241	78	59	we	we	PRON
ma-241	78	60	obtain	obtain	VERB
ma-241	78	61	that	that	SCONJ
ma-241	78	62	p̂(k	p̂(k	NOUN
ma-241	78	63	)	)	PUNCT
ma-241	78	64	2	2	NUM
ma-241	78	65	=	=	SYM
ma-241	78	66	c(k	c(k	NOUN
ma-241	78	67	)	)	PUNCT
ma-241	78	68	2	2	NUM
ma-241	78	69	e−|ξ|x	e−|ξ|x	ADV
ma-241	78	70	.	.	PUNCT
ma-241	79	1	the	the	DET
ma-241	79	2	next	next	ADJ
ma-241	79	3	move	move	NOUN
ma-241	79	4	is	be	AUX
ma-241	79	5	to	to	PART
ma-241	79	6	go	go	VERB
ma-241	79	7	to	to	ADP
ma-241	79	8	the	the	DET
ma-241	79	9	two	two	NUM
ma-241	79	10	localschwarz	localschwarz	NOUN
ma-241	79	11	subproblems	subproblem	VERB
ma-241	79	12	in	in	ADP
ma-241	79	13	(	(	PUNCT
ma-241	79	14	6)1	6)1	PROPN
ma-241	79	15	and	and	CCONJ
ma-241	79	16	to	to	PART
ma-241	79	17	take	take	VERB
ma-241	79	18	the	the	DET
ma-241	79	19	fourier	fourier	NOUN
ma-241	79	20	transform	transform	NOUN
ma-241	79	21	in	in	ADP
ma-241	79	22	the	the	DET
ma-241	79	23	y	y	PROPN
ma-241	79	24	direction	direction	NOUN
ma-241	79	25	.	.	PUNCT
ma-241	80	1	this	this	PRON
ma-241	80	2	will	will	AUX
ma-241	80	3	give	give	VERB
ma-241	80	4	∂2û	∂2û	PROPN
ma-241	80	5	(	(	PUNCT
ma-241	80	6	k	k	NOUN
ma-241	80	7	)	)	PUNCT
ma-241	80	8	1,1	1,1	NUM
ma-241	80	9	∂x2	∂x2	NOUN
ma-241	80	10	−	−	NOUN
ma-241	80	11	|ξ|2û(k	|ξ|2û(k	NOUN
ma-241	80	12	)	)	PUNCT
ma-241	80	13	1,1	1,1	NUM
ma-241	80	14	=	=	SYM
ma-241	80	15	|ξ|d(k	|ξ|d(k	NOUN
ma-241	80	16	)	)	PUNCT
ma-241	80	17	1	1	NUM
ma-241	80	18	e	e	X
ma-241	80	19	|ξ|x	|ξ|x	PROPN
ma-241	80	20	ν	ν	NOUN
ma-241	80	21	,	,	PUNCT
ma-241	80	22	(	(	PUNCT
ma-241	80	23	7	7	X
ma-241	80	24	)	)	PUNCT
ma-241	80	25	∂2û	∂2û	NOUN
ma-241	80	26	(	(	PUNCT
ma-241	80	27	k	k	NOUN
ma-241	80	28	)	)	PUNCT
ma-241	80	29	2,1	2,1	NUM
ma-241	80	30	∂x2	∂x2	NOUN
ma-241	80	31	−	−	NOUN
ma-241	80	32	|ξ|2û(k	|ξ|2û(k	NOUN
ma-241	80	33	)	)	PUNCT
ma-241	80	34	2,1	2,1	NUM
ma-241	80	35	=	=	SYM
ma-241	80	36	−|ξ|c(k	−|ξ|c(k	NUM
ma-241	80	37	)	)	PUNCT
ma-241	80	38	2	2	NUM
ma-241	80	39	e−|ξ|x	e−|ξ|x	NOUN
ma-241	80	40	ν	ν	NOUN
ma-241	80	41	.	.	PUNCT
ma-241	81	1	(	(	PUNCT
ma-241	81	2	8)	8)	NUM
ma-241	81	3	we	we	PRON
ma-241	81	4	solve	solve	VERB
ma-241	81	5	(	(	PUNCT
ma-241	81	6	7	7	NUM
ma-241	81	7	)	)	PUNCT
ma-241	81	8	,	,	PUNCT
ma-241	81	9	(	(	PUNCT
ma-241	81	10	8)	8)	NUM
ma-241	81	11	to	to	PART
ma-241	81	12	obtain	obtain	VERB
ma-241	81	13	the	the	DET
ma-241	81	14	two	two	NUM
ma-241	81	15	solutions	solution	NOUN
ma-241	81	16	in	in	ADP
ma-241	81	17	closed	closed	ADJ
ma-241	81	18	form	form	NOUN
ma-241	81	19	û	û	NUM
ma-241	81	20	(	(	PUNCT
ma-241	81	21	k	k	NOUN
ma-241	81	22	)	)	PUNCT
ma-241	81	23	1,1	1,1	NUM
ma-241	81	24	=	=	SYM
ma-241	81	25	(	(	PUNCT
ma-241	81	26	b(k	b(k	PROPN
ma-241	81	27	)	)	PUNCT
ma-241	81	28	1	1	NUM
ma-241	82	1	+	+	CCONJ
ma-241	82	2	x	x	SYM
ma-241	82	3	2ν	2ν	NUM
ma-241	82	4	d(k	d(k	PROPN
ma-241	82	5	)	)	PUNCT
ma-241	82	6	1	1	NUM
ma-241	82	7	)	)	PUNCT
ma-241	82	8	e	e	NOUN
ma-241	82	9	|ξ|x	|ξ|x	PROPN
ma-241	82	10	,	,	PUNCT
ma-241	82	11	(	(	PUNCT
ma-241	82	12	9	9	NUM
ma-241	82	13	)	)	PUNCT
ma-241	82	14	û	û	NUM
ma-241	82	15	(	(	PUNCT
ma-241	82	16	k	k	NOUN
ma-241	82	17	)	)	PUNCT
ma-241	82	18	2,1	2,1	NUM
ma-241	82	19	=	=	SYM
ma-241	82	20	(	(	PUNCT
ma-241	82	21	b(k	b(k	PROPN
ma-241	82	22	)	)	PUNCT
ma-241	82	23	2	2	NUM
ma-241	83	1	+	+	CCONJ
ma-241	83	2	x	x	SYM
ma-241	83	3	2ν	2ν	NUM
ma-241	83	4	c(k	c(k	NOUN
ma-241	83	5	)	)	PUNCT
ma-241	83	6	2	2	NUM
ma-241	83	7	)	)	PUNCT
ma-241	83	8	e−|ξ|x	e−|ξ|x	ADV
ma-241	83	9	.	.	PUNCT
ma-241	84	1	(	(	PUNCT
ma-241	84	2	10	10	NUM
ma-241	84	3	)	)	PUNCT
ma-241	84	4	https://doi.org/10.28924/ada/ma.5.6	https://doi.org/10.28924/ada/ma.5.6	PROPN
ma-241	84	5	eur	eur	PROPN
ma-241	84	6	.	.	PUNCT
ma-241	85	1	j.	j.	PROPN
ma-241	85	2	math	math	PROPN
ma-241	85	3	.	.	PUNCT
ma-241	86	1	anal	anal	PROPN
ma-241	86	2	.	.	PUNCT
ma-241	87	1	10.28924	10.28924	NUM
ma-241	87	2	/	/	SYM
ma-241	87	3	ada	ada	PROPN
ma-241	87	4	/	/	SYM
ma-241	87	5	ma.5.6	ma.5.6	PROPN
ma-241	87	6	5we	5we	NOUN
ma-241	87	7	go	go	VERB
ma-241	87	8	back	back	ADV
ma-241	87	9	to	to	ADP
ma-241	87	10	(	(	PUNCT
ma-241	87	11	6)3	6)3	NUM
ma-241	87	12	and	and	CCONJ
ma-241	87	13	by	by	ADP
ma-241	87	14	taking	take	VERB
ma-241	87	15	the	the	DET
ma-241	87	16	fourier	fourier	NOUN
ma-241	87	17	trasform	trasform	NOUN
ma-241	87	18	in	in	ADP
ma-241	87	19	the	the	DET
ma-241	87	20	y	y	PROPN
ma-241	87	21	direction	direction	NOUN
ma-241	87	22	and	and	CCONJ
ma-241	87	23	exploiting	exploit	VERB
ma-241	87	24	the	the	DET
ma-241	87	25	solutions(9	solutions(9	NOUN
ma-241	87	26	)	)	PUNCT
ma-241	87	27	,	,	PUNCT
ma-241	87	28	(	(	PUNCT
ma-241	87	29	10	10	NUM
ma-241	87	30	)	)	PUNCT
ma-241	87	31	we	we	PRON
ma-241	87	32	obtain	obtain	VERB
ma-241	88	1	û	û	NUM
ma-241	88	2	(	(	PUNCT
ma-241	88	3	k	k	NOUN
ma-241	88	4	)	)	PUNCT
ma-241	88	5	1,2	1,2	NUM
ma-241	89	1	=	=	SYM
ma-241	89	2	i	i	PRON
ma-241	89	3	ξ	ξ	PROPN
ma-241	89	4	(	(	PUNCT
ma-241	89	5	|ξ|b(k	|ξ|b(k	NOUN
ma-241	89	6	)	)	PUNCT
ma-241	89	7	1	1	NUM
ma-241	90	1	+	+	CCONJ
ma-241	90	2	(	(	PUNCT
ma-241	90	3	1	1	NUM
ma-241	90	4	+	+	CCONJ
ma-241	90	5	x	x	SYM
ma-241	90	6	|ξ|	|ξ|	PROPN
ma-241	90	7	2ν	2ν	NUM
ma-241	90	8	)	)	PUNCT
ma-241	90	9	d(k	d(k	PROPN
ma-241	90	10	)	)	PUNCT
ma-241	90	11	1	1	NUM
ma-241	90	12	)	)	PUNCT
ma-241	91	1	e	e	NOUN
ma-241	91	2	|ξ|x	|ξ|x	PROPN
ma-241	91	3	,	,	PUNCT
ma-241	91	4	(	(	PUNCT
ma-241	91	5	11	11	NUM
ma-241	91	6	)	)	PUNCT
ma-241	91	7	û	û	NUM
ma-241	91	8	(	(	PUNCT
ma-241	91	9	k	k	NOUN
ma-241	91	10	)	)	PUNCT
ma-241	91	11	2,2	2,2	NUM
ma-241	92	1	=	=	SYM
ma-241	92	2	i	i	PRON
ma-241	92	3	ξ	ξ	PROPN
ma-241	92	4	(	(	PUNCT
ma-241	92	5	−|ξ|b(k	−|ξ|b(k	NOUN
ma-241	92	6	)	)	PUNCT
ma-241	92	7	2	2	NUM
ma-241	93	1	+	+	CCONJ
ma-241	93	2	(	(	PUNCT
ma-241	93	3	1−	1−	NUM
ma-241	93	4	x	x	SYM
ma-241	93	5	|ξ|	|ξ|	PROPN
ma-241	93	6	2ν	2ν	NUM
ma-241	93	7	)	)	PUNCT
ma-241	93	8	c(k	c(k	NOUN
ma-241	93	9	)	)	PUNCT
ma-241	93	10	2	2	NUM
ma-241	93	11	)	)	PUNCT
ma-241	93	12	e−|ξ|x	e−|ξ|x	ADV
ma-241	93	13	.	.	PUNCT
ma-241	94	1	(	(	PUNCT
ma-241	94	2	12	12	NUM
ma-241	94	3	)	)	PUNCT
ma-241	94	4	we	we	PRON
ma-241	94	5	further	far	ADV
ma-241	94	6	proceed	proceed	VERB
ma-241	94	7	,	,	PUNCT
ma-241	94	8	substituting	substitute	VERB
ma-241	94	9	the	the	DET
ma-241	94	10	solutions	solution	NOUN
ma-241	94	11	(	(	PUNCT
ma-241	94	12	9	9	NUM
ma-241	94	13	)	)	PUNCT
ma-241	94	14	,	,	PUNCT
ma-241	94	15	(	(	PUNCT
ma-241	94	16	10	10	NUM
ma-241	94	17	)	)	PUNCT
ma-241	94	18	,	,	PUNCT
ma-241	94	19	(	(	PUNCT
ma-241	94	20	11	11	NUM
ma-241	94	21	)	)	PUNCT
ma-241	94	22	,	,	PUNCT
ma-241	94	23	(	(	PUNCT
ma-241	94	24	12	12	NUM
ma-241	94	25	)	)	PUNCT
ma-241	94	26	back	back	ADV
ma-241	94	27	to	to	ADP
ma-241	94	28	the	the	DET
ma-241	94	29	interface	interface	NOUN
ma-241	94	30	conditions(6)4	conditions(6)4	NOUN
ma-241	94	31	,	,	PUNCT
ma-241	94	32	(	(	PUNCT
ma-241	94	33	6)5	6)5	NOUN
ma-241	94	34	to	to	PART
ma-241	94	35	obtain	obtain	VERB
ma-241	94	36	the	the	DET
ma-241	94	37	following	follow	VERB
ma-241	94	38	equations	equation	NOUN
ma-241	94	39	b(k	b(k	PROPN
ma-241	94	40	)	)	PUNCT
ma-241	94	41	1	1	NUM
ma-241	95	1	+	+	NUM
ma-241	95	2	h	h	PROPN
ma-241	95	3	2ν	2ν	NOUN
ma-241	95	4	d(k	d(k	PROPN
ma-241	95	5	)	)	PUNCT
ma-241	96	1	1	1	NUM
ma-241	96	2	=	=	SYM
ma-241	96	3	(	(	PUNCT
ma-241	96	4	b(k−1	b(k−1	NOUN
ma-241	96	5	)	)	PUNCT
ma-241	96	6	2	2	NUM
ma-241	97	1	+	+	NUM
ma-241	97	2	h	h	PROPN
ma-241	97	3	2ν	2ν	NUM
ma-241	97	4	c(k−1	c(k−1	NOUN
ma-241	97	5	)	)	PUNCT
ma-241	97	6	2	2	NUM
ma-241	97	7	)	)	PUNCT
ma-241	97	8	e−2|ξ|h	e−2|ξ|h	PROPN
ma-241	97	9	,	,	PUNCT
ma-241	97	10	(	(	PUNCT
ma-241	97	11	13	13	NUM
ma-241	97	12	)	)	PUNCT
ma-241	97	13	|ξ|b(k	|ξ|b(k	NOUN
ma-241	97	14	)	)	PUNCT
ma-241	97	15	1	1	NUM
ma-241	98	1	+	+	CCONJ
ma-241	98	2	(	(	PUNCT
ma-241	98	3	1	1	NUM
ma-241	98	4	+	+	NOUN
ma-241	98	5	h|ξ|	h|ξ|	NOUN
ma-241	98	6	2ν	2ν	NOUN
ma-241	98	7	)	)	PUNCT
ma-241	98	8	d(k	d(k	PROPN
ma-241	98	9	)	)	PUNCT
ma-241	99	1	1	1	NUM
ma-241	99	2	=	=	SYM
ma-241	99	3	(	(	PUNCT
ma-241	99	4	−|ξ|b(k−1	−|ξ|b(k−1	ADJ
ma-241	99	5	)	)	PUNCT
ma-241	99	6	2	2	NUM
ma-241	100	1	+	+	CCONJ
ma-241	100	2	(	(	PUNCT
ma-241	100	3	1−h|ξ|	1−h|ξ|	NUM
ma-241	100	4	2ν	2ν	NOUN
ma-241	100	5	)	)	PUNCT
ma-241	100	6	c(k−1	c(k−1	X
ma-241	100	7	)	)	PUNCT
ma-241	100	8	2	2	NUM
ma-241	100	9	)	)	PUNCT
ma-241	100	10	e−2|ξ|h	e−2|ξ|h	PROPN
ma-241	100	11	,	,	PUNCT
ma-241	100	12	(	(	PUNCT
ma-241	100	13	14	14	NUM
ma-241	100	14	)	)	PUNCT
ma-241	100	15	b(k	b(k	PROPN
ma-241	100	16	)	)	PUNCT
ma-241	100	17	2	2	NUM
ma-241	100	18	=	=	SYM
ma-241	100	19	b(k−1	b(k−1	X
ma-241	100	20	)	)	PUNCT
ma-241	100	21	1	1	NUM
ma-241	100	22	,	,	PUNCT
ma-241	100	23	(	(	PUNCT
ma-241	100	24	15	15	NUM
ma-241	100	25	)	)	PUNCT
ma-241	100	26	−|ξ|b(k	−|ξ|b(k	NOUN
ma-241	100	27	)	)	PUNCT
ma-241	100	28	2	2	NUM
ma-241	101	1	+	+	CCONJ
ma-241	101	2	c(k	c(k	NOUN
ma-241	101	3	)	)	PUNCT
ma-241	101	4	2	2	NUM
ma-241	101	5	2ν	2ν	NOUN
ma-241	101	6	=	=	SYM
ma-241	101	7	|ξ|b(k−1	|ξ|b(k−1	PROPN
ma-241	101	8	)	)	PUNCT
ma-241	101	9	1	1	NUM
ma-241	101	10	+	+	SYM
ma-241	101	11	d(k−1	d(k−1	NOUN
ma-241	101	12	)	)	PUNCT
ma-241	101	13	1	1	NUM
ma-241	101	14	2ν	2ν	NOUN
ma-241	101	15	.	.	PUNCT
ma-241	102	1	(	(	PUNCT
ma-241	102	2	16	16	NUM
ma-241	102	3	)	)	PUNCT
ma-241	102	4	we	we	PRON
ma-241	102	5	combine	combine	VERB
ma-241	102	6	the	the	DET
ma-241	102	7	equations	equation	NOUN
ma-241	102	8	(	(	PUNCT
ma-241	102	9	15	15	NUM
ma-241	102	10	)	)	PUNCT
ma-241	102	11	,	,	PUNCT
ma-241	102	12	(	(	PUNCT
ma-241	102	13	16	16	NUM
ma-241	102	14	)	)	PUNCT
ma-241	102	15	to	to	PART
ma-241	102	16	obtain	obtain	VERB
ma-241	102	17	d(k	d(k	PROPN
ma-241	102	18	)	)	PUNCT
ma-241	102	19	1	1	NUM
ma-241	103	1	=	=	PUNCT
ma-241	103	2	c(k+1	c(k+1	X
ma-241	103	3	)	)	PUNCT
ma-241	103	4	2	2	NUM
ma-241	103	5	−	−	NOUN
ma-241	103	6	4|ξ|νb(k+1	4|ξ|νb(k+1	NUM
ma-241	103	7	)	)	PUNCT
ma-241	103	8	2	2	NUM
ma-241	103	9	.	.	PUNCT
ma-241	104	1	we	we	PRON
ma-241	104	2	substitute	substitute	VERB
ma-241	104	3	thecoefficients	thecoefficient	NOUN
ma-241	104	4	d(k	d(k	PROPN
ma-241	104	5	)	)	PUNCT
ma-241	104	6	1	1	NUM
ma-241	104	7	back	back	ADV
ma-241	104	8	to	to	ADP
ma-241	104	9	equation	equation	NOUN
ma-241	104	10	(	(	PUNCT
ma-241	104	11	13	13	NUM
ma-241	104	12	)	)	PUNCT
ma-241	104	13	to	to	PART
ma-241	104	14	obtain	obtain	VERB
ma-241	104	15	b(k+1	b(k+1	NOUN
ma-241	104	16	)	)	PUNCT
ma-241	104	17	2	2	NUM
ma-241	104	18	(	(	PUNCT
ma-241	104	19	2ν	2ν	NOUN
ma-241	104	20	−	−	PROPN
ma-241	104	21	4νh|ξ|	4νh|ξ|	NOUN
ma-241	104	22	)	)	PUNCT
ma-241	104	23	+	+	NOUN
ma-241	104	24	hc(k+1	hc(k+1	NOUN
ma-241	104	25	)	)	PUNCT
ma-241	104	26	2	2	NUM
ma-241	104	27	=	=	SYM
ma-241	104	28	b(k−1	b(k−1	X
ma-241	104	29	)	)	PUNCT
ma-241	104	30	2	2	NUM
ma-241	104	31	2νe−2|ξ|h	2νe−2|ξ|h	NUM
ma-241	104	32	+	+	NOUN
ma-241	104	33	hc(k−1	hc(k−1	NOUN
ma-241	104	34	)	)	PUNCT
ma-241	104	35	2	2	NUM
ma-241	104	36	e−2|ξ|h	e−2|ξ|h	NOUN
ma-241	104	37	.	.	PUNCT
ma-241	105	1	(	(	PUNCT
ma-241	105	2	17	17	NUM
ma-241	105	3	)	)	PUNCT
ma-241	105	4	in	in	ADP
ma-241	105	5	the	the	DET
ma-241	105	6	same	same	ADJ
ma-241	105	7	spirit	spirit	NOUN
ma-241	105	8	,	,	PUNCT
ma-241	105	9	we	we	PRON
ma-241	105	10	replace	replace	VERB
ma-241	105	11	the	the	DET
ma-241	105	12	iteration	iteration	NOUN
ma-241	105	13	coefficients	coefficient	NOUN
ma-241	105	14	d(k	d(k	PROPN
ma-241	105	15	)	)	PUNCT
ma-241	105	16	1	1	NUM
ma-241	105	17	back	back	ADV
ma-241	105	18	to	to	ADP
ma-241	105	19	(	(	PUNCT
ma-241	105	20	14	14	NUM
ma-241	105	21	)	)	PUNCT
ma-241	105	22	to	to	PART
ma-241	105	23	get	get	VERB
ma-241	105	24	b(k+1	b(k+1	NOUN
ma-241	105	25	)	)	PUNCT
ma-241	105	26	2	2	NUM
ma-241	105	27	(	(	PUNCT
ma-241	105	28	2ν|ξ|+	2ν|ξ|+	NUM
ma-241	105	29	4νh|ξ|2	4νh|ξ|2	NUM
ma-241	105	30	)	)	PUNCT
ma-241	105	31	−c(k+1	−c(k+1	NOUN
ma-241	105	32	)	)	PUNCT
ma-241	105	33	2	2	NUM
ma-241	105	34	(	(	PUNCT
ma-241	105	35	1+h|ξ|	1+h|ξ|	NUM
ma-241	105	36	)	)	PUNCT
ma-241	105	37	=	=	SYM
ma-241	105	38	2ν|ξ|b(k−1	2ν|ξ|b(k−1	PROPN
ma-241	105	39	)	)	PUNCT
ma-241	105	40	2	2	NUM
ma-241	105	41	e−2|ξ|h+(h|ξ|−1)c(k−1	e−2|ξ|h+(h|ξ|−1)c(k−1	PROPN
ma-241	105	42	)	)	PUNCT
ma-241	105	43	2	2	NUM
ma-241	105	44	e−2|ξ|h	e−2|ξ|h	PROPN
ma-241	105	45	.	.	PUNCT
ma-241	106	1	(	(	PUNCT
ma-241	106	2	18	18	NUM
ma-241	106	3	)	)	PUNCT
ma-241	106	4	we	we	PRON
ma-241	106	5	take	take	VERB
ma-241	106	6	the	the	DET
ma-241	106	7	two	two	NUM
ma-241	106	8	equations	equation	NOUN
ma-241	106	9	(	(	PUNCT
ma-241	106	10	17	17	NUM
ma-241	106	11	)	)	PUNCT
ma-241	106	12	,	,	PUNCT
ma-241	106	13	(	(	PUNCT
ma-241	106	14	18	18	NUM
ma-241	106	15	)	)	PUNCT
ma-241	106	16	and	and	CCONJ
ma-241	106	17	write	write	VERB
ma-241	106	18	them	they	PRON
ma-241	106	19	in	in	ADP
ma-241	106	20	matrix	matrix	NOUN
ma-241	106	21	form	form	NOUN
ma-241	106	22	[	[	PUNCT
ma-241	106	23	(	(	PUNCT
ma-241	106	24	2ν	2ν	NOUN
ma-241	106	25	−	−	PROPN
ma-241	106	26	4νh|ξ|	4νh|ξ|	NOUN
ma-241	106	27	)	)	PUNCT
ma-241	107	1	h	h	NOUN
ma-241	107	2	(	(	PUNCT
ma-241	107	3	2ν|ξ|+	2ν|ξ|+	NUM
ma-241	107	4	4νh|ξ|2	4νh|ξ|2	NUM
ma-241	107	5	)	)	PUNCT
ma-241	108	1	−(1	−(1	NOUN
ma-241	109	1	+	+	NOUN
ma-241	109	2	h|ξ|	h|ξ|	NOUN
ma-241	109	3	)	)	PUNCT
ma-241	109	4	]	]	PUNCT
ma-241	109	5	[	[	PUNCT
ma-241	109	6	b(k+1	b(k+1	NUM
ma-241	109	7	)	)	PUNCT
ma-241	109	8	2	2	NUM
ma-241	109	9	c(k+1	c(k+1	NOUN
ma-241	109	10	)	)	PUNCT
ma-241	109	11	2	2	NUM
ma-241	109	12	]	]	PUNCT
ma-241	109	13	=	=	PUNCT
ma-241	110	1	[	[	PUNCT
ma-241	110	2	2νe−2|ξ|h	2νe−2|ξ|h	NUM
ma-241	110	3	he−2|ξ|h	he−2|ξ|h	PROPN
ma-241	110	4	2ν|ξ|e−2|ξ|h	2ν|ξ|e−2|ξ|h	PROPN
ma-241	110	5	(	(	PUNCT
ma-241	110	6	h|ξ|	h|ξ|	NOUN
ma-241	110	7	−	−	NOUN
ma-241	110	8	1)e−2|ξ|h	1)e−2|ξ|h	NUM
ma-241	110	9	]	]	X
ma-241	110	10	[	[	PUNCT
ma-241	110	11	b(k−1	b(k−1	NOUN
ma-241	110	12	)	)	SYM
ma-241	110	13	2	2	NUM
ma-241	110	14	c(k−1	c(k−1	NOUN
ma-241	110	15	)	)	PUNCT
ma-241	110	16	2	2	NUM
ma-241	110	17	]	]	PUNCT
ma-241	110	18	.	.	PUNCT
ma-241	111	1	(	(	PUNCT
ma-241	111	2	19)we	19)we	NUM
ma-241	111	3	recast	recast	VERB
ma-241	111	4	the	the	DET
ma-241	111	5	equation	equation	NOUN
ma-241	111	6	(	(	PUNCT
ma-241	111	7	19	19	NUM
ma-241	111	8	)	)	PUNCT
ma-241	111	9	in	in	ADP
ma-241	111	10	the	the	DET
ma-241	111	11	form	form	NOUN
ma-241	111	12	[	[	PUNCT
ma-241	111	13	b(k+1	b(k+1	NOUN
ma-241	111	14	)	)	PUNCT
ma-241	111	15	2	2	NUM
ma-241	111	16	c(k+1	c(k+1	NOUN
ma-241	111	17	)	)	PUNCT
ma-241	111	18	2	2	NUM
ma-241	111	19	]	]	PUNCT
ma-241	111	20	=	=	PUNCT
ma-241	111	21	[	[	PUNCT
ma-241	111	22	(	(	PUNCT
ma-241	111	23	1	1	NUM
ma-241	111	24	+	+	NUM
ma-241	111	25	2h|ξ|)e−2|ξ|h	2h|ξ|)e−2|ξ|h	NUM
ma-241	111	26	h2|ξ|e−2|ξ|h	h2|ξ|e−2|ξ|h	NOUN
ma-241	111	27	ν	ν	X
ma-241	111	28	8νh|ξ|2e−2|ξ|h	8νh|ξ|2e−2|ξ|h	NOUN
ma-241	111	29	(	(	PUNCT
ma-241	111	30	4h2|ξ|2	4h2|ξ|2	NUM
ma-241	111	31	−	−	NOUN
ma-241	111	32	2h|ξ|+	2h|ξ|+	NUM
ma-241	111	33	1	1	NUM
ma-241	111	34	)	)	PUNCT
ma-241	111	35	e−2|ξ|h	e−2|ξ|h	PROPN
ma-241	111	36	]	]	PUNCT
ma-241	111	37	︸	︸	X
ma-241	111	38	︷︷	︷︷	PROPN
ma-241	111	39	︸	︸	X
ma-241	111	40	ψpsm	ψpsm	ADJ
ma-241	111	41	,	,	PUNCT
ma-241	111	42	d	d	X
ma-241	111	43	[	[	PUNCT
ma-241	111	44	b(k−1	b(k−1	NOUN
ma-241	111	45	)	)	SYM
ma-241	111	46	2	2	NUM
ma-241	111	47	c(k−1	c(k−1	NOUN
ma-241	111	48	)	)	PUNCT
ma-241	111	49	2	2	NUM
ma-241	111	50	]	]	PUNCT
ma-241	111	51	(	(	PUNCT
ma-241	111	52	20	20	NUM
ma-241	111	53	)	)	PUNCT
ma-241	111	54	where	where	SCONJ
ma-241	111	55	ψpsm	ψpsm	ADV
ma-241	111	56	,	,	PUNCT
ma-241	111	57	d	d	PROPN
ma-241	111	58	is	be	AUX
ma-241	111	59	the	the	DET
ma-241	111	60	schwarz	schwarz	PROPN
ma-241	111	61	iteration	iteration	NOUN
ma-241	111	62	matrix	matrix	NOUN
ma-241	111	63	.	.	PUNCT
ma-241	112	1	the	the	DET
ma-241	112	2	spectrum	spectrum	NOUN
ma-241	112	3	of	of	ADP
ma-241	112	4	ψpsm	ψpsm	ADJ
ma-241	112	5	,	,	PUNCT
ma-241	112	6	d	d	PROPN
ma-241	112	7	is	be	AUX
ma-241	112	8	σ(ψpsm	σ(ψpsm	ADJ
ma-241	112	9	,	,	PUNCT
ma-241	112	10	d	d	NOUN
ma-241	112	11	)	)	PUNCT
ma-241	112	12	=	=	NOUN
ma-241	112	13	{	{	PUNCT
ma-241	112	14	λ+	λ+	NOUN
ma-241	112	15	,	,	PUNCT
ma-241	112	16	λ−	λ−	PROPN
ma-241	112	17	}	}	PUNCT
ma-241	112	18	,	,	PUNCT
ma-241	112	19	where	where	SCONJ
ma-241	112	20	λ+	λ+	NUM
ma-241	112	21	and	and	CCONJ
ma-241	112	22	λ−	λ−	PROPN
ma-241	112	23	are	be	AUX
ma-241	112	24	the	the	DET
ma-241	112	25	corresponding	corresponding	ADJ
ma-241	112	26	eigenvalues	eigenvalue	NOUN
ma-241	112	27	given	give	VERB
ma-241	112	28	by	by	ADP
ma-241	112	29	the	the	DET
ma-241	112	30	formulas	formula	NOUN
ma-241	112	31	λ+	λ+	PUNCT
ma-241	112	32	=	=	SYM
ma-241	113	1	(	(	PUNCT
ma-241	113	2	1	1	NUM
ma-241	113	3	+	+	CCONJ
ma-241	113	4	2h2|ξ|2	2h2|ξ|2	NUM
ma-241	113	5	+	+	CCONJ
ma-241	113	6	2	2	NUM
ma-241	113	7	|ξ|	|ξ|	NOUN
ma-241	113	8	√	√	PROPN
ma-241	113	9	h2	h2	PROPN
ma-241	113	10	(	(	PUNCT
ma-241	113	11	1	1	NUM
ma-241	113	12	+	+	ADJ
ma-241	113	13	h2|ξ|2	h2|ξ|2	ADJ
ma-241	113	14	)	)	PUNCT
ma-241	113	15	)	)	PUNCT
ma-241	113	16	e−2|ξ|h	e−2|ξ|h	INTJ
ma-241	113	17	,	,	PUNCT
ma-241	113	18	λ−	λ−	PROPN
ma-241	113	19	=	=	PRON
ma-241	113	20	(	(	PUNCT
ma-241	113	21	1	1	NUM
ma-241	113	22	+	+	CCONJ
ma-241	113	23	2h2|ξ|2	2h2|ξ|2	NUM
ma-241	113	24	−	−	NUM
ma-241	113	25	2	2	NUM
ma-241	113	26	|ξ|	|ξ|	NOUN
ma-241	113	27	√	√	PROPN
ma-241	113	28	h2	h2	PROPN
ma-241	113	29	(	(	PUNCT
ma-241	113	30	1	1	NUM
ma-241	113	31	+	+	ADJ
ma-241	113	32	h2|ξ|2	h2|ξ|2	ADJ
ma-241	113	33	)	)	PUNCT
ma-241	113	34	)	)	PUNCT
ma-241	114	1	e−2|ξ|h	e−2|ξ|h	INTJ
ma-241	114	2	.	.	PUNCT
ma-241	115	1	https://doi.org/10.28924/ada/ma.5.6	https://doi.org/10.28924/ada/ma.5.6	PROPN
ma-241	115	2	eur	eur	PROPN
ma-241	115	3	.	.	PUNCT
ma-241	116	1	j.	j.	PROPN
ma-241	116	2	math	math	PROPN
ma-241	116	3	.	.	PUNCT
ma-241	117	1	anal	anal	PROPN
ma-241	117	2	.	.	PUNCT
ma-241	118	1	10.28924	10.28924	NUM
ma-241	118	2	/	/	SYM
ma-241	118	3	ada	ada	PROPN
ma-241	118	4	/	/	SYM
ma-241	118	5	ma.5.6	ma.5.6	PROPN
ma-241	118	6	6consequently	6consequently	ADV
ma-241	118	7	,	,	PUNCT
ma-241	118	8	the	the	DET
ma-241	118	9	convergence	convergence	NOUN
ma-241	118	10	factor	factor	NOUN
ma-241	118	11	of	of	ADP
ma-241	118	12	the	the	DET
ma-241	118	13	parallel	parallel	ADJ
ma-241	118	14	schwarz	schwarz	PROPN
ma-241	118	15	algorithm	algorithm	PROPN
ma-241	118	16	is	be	AUX
ma-241	118	17	rpsm	rpsm	ADJ
ma-241	118	18	,	,	PUNCT
ma-241	118	19	d	d	X
ma-241	118	20	=	=	PUNCT
ma-241	118	21	ρ(ψpsm	ρ(ψpsm	PROPN
ma-241	118	22	,	,	PUNCT
ma-241	118	23	d	d	NOUN
ma-241	118	24	)	)	PUNCT
ma-241	118	25	=	=	SYM
ma-241	118	26	max{|λ+|	max{|λ+|	NOUN
ma-241	118	27	,	,	PUNCT
ma-241	118	28	|λ−|	|λ−|	NOUN
ma-241	118	29	}	}	PUNCT
ma-241	118	30	=	=	SYM
ma-241	118	31	(	(	PUNCT
ma-241	118	32	1	1	NUM
ma-241	118	33	+	+	CCONJ
ma-241	118	34	2h2|ξ|2	2h2|ξ|2	NUM
ma-241	118	35	+	+	CCONJ
ma-241	118	36	2	2	NUM
ma-241	118	37	|ξ|	|ξ|	NOUN
ma-241	118	38	√	√	PROPN
ma-241	118	39	h2	h2	PROPN
ma-241	118	40	(	(	PUNCT
ma-241	118	41	1	1	NUM
ma-241	118	42	+	+	ADJ
ma-241	118	43	h2|ξ|2	h2|ξ|2	ADJ
ma-241	118	44	)	)	PUNCT
ma-241	118	45	)	)	PUNCT
ma-241	119	1	e−2|ξ|h	e−2|ξ|h	INTJ
ma-241	119	2	,	,	PUNCT
ma-241	119	3	where	where	SCONJ
ma-241	119	4	ρ(ψpsm	ρ(ψpsm	ADJ
ma-241	119	5	,	,	PUNCT
ma-241	119	6	d	d	NOUN
ma-241	119	7	)	)	PUNCT
ma-241	119	8	is	be	AUX
ma-241	119	9	the	the	DET
ma-241	119	10	spectral	spectral	ADJ
ma-241	119	11	radius	radius	NOUN
ma-241	119	12	of	of	ADP
ma-241	119	13	the	the	DET
ma-241	119	14	schwarz	schwarz	PROPN
ma-241	119	15	iteration	iteration	NOUN
ma-241	119	16	matrix	matrix	NOUN
ma-241	119	17	,	,	PUNCT
ma-241	119	18	h	h	NOUN
ma-241	119	19	is	be	AUX
ma-241	119	20	the	the	DET
ma-241	119	21	size	size	NOUN
ma-241	119	22	of	of	ADP
ma-241	119	23	theoverlap	theoverlap	NOUN
ma-241	119	24	between	between	ADP
ma-241	119	25	the	the	DET
ma-241	119	26	subdomains	subdomain	NOUN
ma-241	119	27	,	,	PUNCT
ma-241	119	28	ξ	ξ	X
ma-241	119	29	is	be	AUX
ma-241	119	30	the	the	DET
ma-241	119	31	fourier	fourier	ADJ
ma-241	119	32	frequency	frequency	NOUN
ma-241	119	33	.	.	PUNCT
ma-241	120	1	�	�	PROPN
ma-241	120	2	3	3	NUM
ma-241	120	3	.	.	PUNCT
ma-241	120	4	alternating	alternate	VERB
ma-241	120	5	schwarz	schwarz	PROPN
ma-241	120	6	method	method	PROPN
ma-241	120	7	-	-	PUNCT
ma-241	120	8	neumann	neumann	PROPN
ma-241	120	9	ic	ic	PROPN
ma-241	121	1	the	the	DET
ma-241	121	2	interface	interface	NOUN
ma-241	121	3	conditions	condition	NOUN
ma-241	121	4	play	play	VERB
ma-241	121	5	critical	critical	ADJ
ma-241	121	6	role	role	NOUN
ma-241	121	7	on	on	ADP
ma-241	121	8	the	the	DET
ma-241	121	9	convergence	convergence	NOUN
ma-241	121	10	of	of	ADP
ma-241	121	11	the	the	DET
ma-241	121	12	schwarz	schwarz	PROPN
ma-241	121	13	method	method	NOUN
ma-241	121	14	.	.	PUNCT
ma-241	122	1	in	in	ADP
ma-241	122	2	thissection	thissection	NOUN
ma-241	122	3	,	,	PUNCT
ma-241	122	4	we	we	PRON
ma-241	122	5	introduce	introduce	VERB
ma-241	122	6	the	the	DET
ma-241	122	7	alternating	alternate	VERB
ma-241	122	8	schwarz	schwarz	PROPN
ma-241	122	9	algorithm	algorithm	NOUN
ma-241	122	10	employing	employ	VERB
ma-241	122	11	neumann	neumann	PROPN
ma-241	122	12	interface	interface	NOUN
ma-241	122	13	conditions.we	conditions.we	PRON
ma-241	122	14	go	go	VERB
ma-241	122	15	back	back	ADV
ma-241	122	16	to	to	ADP
ma-241	122	17	the	the	DET
ma-241	122	18	iterative	iterative	NOUN
ma-241	122	19	scheme	scheme	NOUN
ma-241	122	20	prescribed	prescribe	VERB
ma-241	122	21	by	by	ADP
ma-241	122	22	(	(	PUNCT
ma-241	122	23	4	4	NUM
ma-241	122	24	)	)	PUNCT
ma-241	122	25	and	and	CCONJ
ma-241	122	26	we	we	PRON
ma-241	122	27	modify	modify	VERB
ma-241	122	28	the	the	DET
ma-241	122	29	transmission	transmission	NOUN
ma-241	122	30	conditions	condition	NOUN
ma-241	122	31	in(4)3	in(4)3	NOUN
ma-241	122	32	.	.	PROPN
ma-241	122	33	as	as	ADP
ma-241	122	34	a	a	DET
ma-241	122	35	consequence	consequence	NOUN
ma-241	122	36	,	,	PUNCT
ma-241	122	37	the	the	DET
ma-241	122	38	schwarz	schwarz	PROPN
ma-241	122	39	method	method	NOUN
ma-241	122	40	in	in	ADP
ma-241	122	41	strong	strong	ADJ
ma-241	122	42	form	form	NOUN
ma-241	122	43	reads	reads	NOUN
ma-241	122	44	−ν∆−→u1	−ν∆−→u1	NOUN
ma-241	122	45	(	(	PUNCT
ma-241	122	46	k	k	NOUN
ma-241	122	47	)	)	PUNCT
ma-241	122	48	+	+	NUM
ma-241	122	49	op(k	op(k	X
ma-241	122	50	)	)	PUNCT
ma-241	122	51	1	1	NUM
ma-241	123	1	=	=	SYM
ma-241	123	2	~f	~f	PUNCT
ma-241	123	3	in	in	ADP
ma-241	123	4	ω1	ω1	PROPN
ma-241	123	5	,	,	PUNCT
ma-241	123	6	d	d	NOUN
ma-241	123	7	iv−→u1	iv−→u1	NOUN
ma-241	123	8	(	(	PUNCT
ma-241	123	9	k	k	NOUN
ma-241	123	10	)	)	PUNCT
ma-241	123	11	=	=	SYM
ma-241	123	12	0	0	NUM
ma-241	123	13	in	in	ADP
ma-241	123	14	ω1	ω1	PROPN
ma-241	123	15	,	,	PUNCT
ma-241	123	16	νo−→u1	νo−→u1	NOUN
ma-241	123	17	(	(	PUNCT
ma-241	123	18	k)~n	k)~n	VERB
ma-241	123	19	−	−	NOUN
ma-241	123	20	p(k	p(k	NOUN
ma-241	123	21	)	)	PUNCT
ma-241	123	22	1	1	NUM
ma-241	123	23	~n	~n	NUM
ma-241	123	24	=	=	SYM
ma-241	123	25	νo−→u2	νo−→u2	NOUN
ma-241	123	26	(	(	PUNCT
ma-241	123	27	k−1)~n	k−1)~n	ADJ
ma-241	123	28	−	−	NOUN
ma-241	123	29	p(k−1	p(k−1	NOUN
ma-241	123	30	)	)	PUNCT
ma-241	123	31	2	2	NUM
ma-241	123	32	~n	~n	PUNCT
ma-241	123	33	at	at	ADP
ma-241	123	34	x	x	X
ma-241	123	35	=	=	SYM
ma-241	123	36	h	h	NOUN
ma-241	123	37	,	,	PUNCT
ma-241	123	38	−→u1	−→u1	PROPN
ma-241	123	39	(	(	PUNCT
ma-241	123	40	k	k	NOUN
ma-241	123	41	)	)	PUNCT
ma-241	123	42	:	:	PUNCT
ma-241	123	43	bounded	bound	VERB
ma-241	123	44	at	at	ADP
ma-241	123	45	−∞	−∞	PROPN
ma-241	123	46	,	,	PUNCT
ma-241	123	47	p	p	X
ma-241	123	48	(	(	PUNCT
ma-241	123	49	k	k	NOUN
ma-241	123	50	)	)	PUNCT
ma-241	123	51	1	1	NUM
ma-241	123	52	:	:	PUNCT
ma-241	123	53	bounded	bound	VERB
ma-241	123	54	at	at	ADP
ma-241	123	55	−∞	−∞	NOUN
ma-241	123	56	,	,	PUNCT
ma-241	123	57			PROPN
ma-241	123	58	−ν∆−→u2	−ν∆−→u2	PROPN
ma-241	123	59	(	(	PUNCT
ma-241	123	60	k	k	NOUN
ma-241	123	61	)	)	PUNCT
ma-241	123	62	+	+	NUM
ma-241	123	63	op(k	op(k	X
ma-241	123	64	)	)	PUNCT
ma-241	123	65	2	2	NUM
ma-241	123	66	=	=	SYM
ma-241	123	67	~f	~f	PUNCT
ma-241	123	68	in	in	ADP
ma-241	123	69	ω2	ω2	ADJ
ma-241	123	70	,	,	PUNCT
ma-241	123	71	d	d	X
ma-241	123	72	iv−→u2	iv−→u2	X
ma-241	123	73	(	(	PUNCT
ma-241	123	74	k	k	NOUN
ma-241	123	75	)	)	PUNCT
ma-241	123	76	=	=	SYM
ma-241	123	77	0	0	NUM
ma-241	123	78	in	in	ADP
ma-241	123	79	ω2	ω2	NUM
ma-241	123	80	,	,	PUNCT
ma-241	123	81	νo−→u2	νo−→u2	X
ma-241	123	82	(	(	PUNCT
ma-241	123	83	k)~n	k)~n	VERB
ma-241	123	84	−	−	NOUN
ma-241	123	85	p(k	p(k	NOUN
ma-241	123	86	)	)	PUNCT
ma-241	123	87	2	2	NUM
ma-241	123	88	~n	~n	NUM
ma-241	123	89	=	=	SYM
ma-241	123	90	νo−→u1	νo−→u1	NOUN
ma-241	123	91	(	(	PUNCT
ma-241	123	92	k)~n	k)~n	VERB
ma-241	123	93	−	−	NOUN
ma-241	123	94	p(k	p(k	NOUN
ma-241	123	95	)	)	PUNCT
ma-241	123	96	1	1	NUM
ma-241	123	97	~n	~n	PUNCT
ma-241	123	98	at	at	ADP
ma-241	123	99	x	x	X
ma-241	123	100	=	=	SYM
ma-241	123	101	0	0	NUM
ma-241	123	102	,	,	PUNCT
ma-241	123	103	−→u2	−→u2	NOUN
ma-241	123	104	(	(	PUNCT
ma-241	123	105	k	k	NOUN
ma-241	123	106	)	)	PUNCT
ma-241	123	107	:	:	PUNCT
ma-241	123	108	bounded	bound	VERB
ma-241	123	109	at	at	ADP
ma-241	123	110	+	+	PROPN
ma-241	123	111	∞	∞	PROPN
ma-241	123	112	,	,	PUNCT
ma-241	123	113	p	p	X
ma-241	123	114	(	(	PUNCT
ma-241	123	115	k	k	NOUN
ma-241	123	116	)	)	PUNCT
ma-241	123	117	2	2	NUM
ma-241	123	118	:	:	PUNCT
ma-241	123	119	bounded	bound	VERB
ma-241	123	120	at	at	ADP
ma-241	123	121	+	+	PROPN
ma-241	123	122	∞	∞	PROPN
ma-241	123	123	,	,	PUNCT
ma-241	123	124	(	(	PUNCT
ma-241	123	125	21)where	21)where	NUM
ma-241	123	126	~n	~n	NUM
ma-241	123	127	is	be	AUX
ma-241	123	128	the	the	DET
ma-241	123	129	outward	outward	ADJ
ma-241	123	130	normal	normal	ADJ
ma-241	123	131	vector	vector	NOUN
ma-241	123	132	.	.	PUNCT
ma-241	124	1	the	the	DET
ma-241	124	2	initial	initial	ADJ
ma-241	124	3	guess	guess	NOUN
ma-241	124	4	νo−→u2	νo−→u2	NOUN
ma-241	124	5	(	(	PUNCT
ma-241	124	6	0)~n	0)~n	INTJ
ma-241	124	7	−	−	PROPN
ma-241	124	8	p(0	p(0	NOUN
ma-241	124	9	)	)	PUNCT
ma-241	124	10	2	2	NUM
ma-241	124	11	~n	~n	NUM
ma-241	124	12	is	be	AUX
ma-241	124	13	required	require	VERB
ma-241	124	14	to	to	PART
ma-241	124	15	start	start	VERB
ma-241	124	16	theiterative	theiterative	ADJ
ma-241	124	17	procedure	procedure	NOUN
ma-241	124	18	.	.	PUNCT
ma-241	125	1	theorem	theorem	NOUN
ma-241	125	2	2	2	NUM
ma-241	125	3	.	.	PUNCT
ma-241	126	1	the	the	DET
ma-241	126	2	convergence	convergence	NOUN
ma-241	126	3	factor	factor	NOUN
ma-241	126	4	of	of	ADP
ma-241	126	5	the	the	DET
ma-241	126	6	schwarz	schwarz	PROPN
ma-241	126	7	algorithm	algorithm	PROPN
ma-241	126	8	using	use	VERB
ma-241	126	9	neumann	neumann	PROPN
ma-241	126	10	transmission	transmission	NOUN
ma-241	126	11	conditions	condition	NOUN
ma-241	126	12	is	be	AUX
ma-241	126	13	given	give	VERB
ma-241	126	14	by	by	ADP
ma-241	126	15	the	the	DET
ma-241	126	16	formula	formula	NOUN
ma-241	126	17	below	below	ADP
ma-241	126	18	rasm	rasm	NOUN
ma-241	126	19	,	,	PUNCT
ma-241	126	20	n(ξ	n(ξ	PROPN
ma-241	126	21	,	,	PUNCT
ma-241	126	22	h	h	NOUN
ma-241	126	23	)	)	PUNCT
ma-241	126	24	=	=	PUNCT
ma-241	127	1	∣∣∣(2|ξ|2h2	∣∣∣(2|ξ|2h2	ADP
ma-241	127	2	9	9	NUM
ma-241	127	3	−	−	NUM
ma-241	127	4	2|ξ|h	2|ξ|h	NUM
ma-241	127	5	9	9	NUM
ma-241	127	6	+	+	CCONJ
ma-241	127	7	1	1	NUM
ma-241	127	8	+	+	NUM
ma-241	127	9	2	2	NUM
ma-241	127	10	√	√	NUM
ma-241	127	11	|ξ|4h4	|ξ|4h4	PROPN
ma-241	127	12	+	+	CCONJ
ma-241	127	13	2|ξ|3h3	2|ξ|3h3	PROPN
ma-241	127	14	+	+	CCONJ
ma-241	127	15	8	8	NUM
ma-241	127	16	|ξ|2h2	|ξ|2h2	NOUN
ma-241	127	17	9	9	NUM
ma-241	127	18	)	)	PUNCT
ma-241	127	19	∣∣∣e−2|ξ|h	∣∣∣e−2|ξ|h	NOUN
ma-241	127	20	(	(	PUNCT
ma-241	127	21	22	22	NUM
ma-241	127	22	)	)	PUNCT
ma-241	127	23	where	where	SCONJ
ma-241	127	24	ξ	ξ	PROPN
ma-241	127	25	is	be	AUX
ma-241	127	26	the	the	DET
ma-241	127	27	fourier	fourier	ADJ
ma-241	127	28	frequency	frequency	NOUN
ma-241	127	29	and	and	CCONJ
ma-241	127	30	h	h	NOUN
ma-241	127	31	>	>	X
ma-241	127	32	0	0	PUNCT
ma-241	127	33	is	be	AUX
ma-241	127	34	the	the	DET
ma-241	127	35	size	size	NOUN
ma-241	127	36	of	of	ADP
ma-241	127	37	the	the	DET
ma-241	127	38	overlap	overlap	NOUN
ma-241	127	39	.	.	PUNCT
ma-241	128	1	proof	proof	NOUN
ma-241	128	2	.	.	PUNCT
ma-241	129	1	as	as	ADP
ma-241	129	2	a	a	DET
ma-241	129	3	first	first	ADJ
ma-241	129	4	step	step	NOUN
ma-241	129	5	,	,	PUNCT
ma-241	129	6	we	we	PRON
ma-241	129	7	go	go	VERB
ma-241	129	8	back	back	ADV
ma-241	129	9	to	to	ADP
ma-241	129	10	the	the	DET
ma-241	129	11	local	local	ADJ
ma-241	129	12	subproblems	subproblem	NOUN
ma-241	129	13	in	in	ADP
ma-241	129	14	(	(	PUNCT
ma-241	129	15	21	21	NUM
ma-241	129	16	)	)	PUNCT
ma-241	129	17	and	and	CCONJ
ma-241	129	18	we	we	PRON
ma-241	129	19	consider	consider	VERB
ma-241	129	20	the	the	DET
ma-241	129	21	homogeneouscounterparts	homogeneouscounterpart	NOUN
ma-241	129	22	taking	take	VERB
ma-241	129	23	~f	~f	PUNCT
ma-241	129	24	=	=	SYM
ma-241	129	25	~0	~0	X
ma-241	129	26	.	.	PUNCT
ma-241	130	1	we	we	PRON
ma-241	130	2	recast	recast	VERB
ma-241	130	3	the	the	DET
ma-241	130	4	method	method	NOUN
ma-241	130	5	prescribed	prescribe	VERB
ma-241	130	6	by	by	ADP
ma-241	130	7	(	(	PUNCT
ma-241	130	8	21	21	NUM
ma-241	130	9	)	)	PUNCT
ma-241	130	10	in	in	ADP
ma-241	130	11	the	the	DET
ma-241	130	12	following	follow	VERB
ma-241	130	13	form	form	PROPN
ma-241	130	14	∂2u	∂2u	PROPN
ma-241	130	15	(	(	PUNCT
ma-241	130	16	k	k	NOUN
ma-241	130	17	)	)	PUNCT
ma-241	130	18	1,1	1,1	NUM
ma-241	130	19	∂x2	∂x2	NOUN
ma-241	130	20	+	+	CCONJ
ma-241	130	21	∂2u	∂2u	X
ma-241	130	22	(	(	PUNCT
ma-241	130	23	k	k	X
ma-241	130	24	)	)	PUNCT
ma-241	130	25	1,1	1,1	NUM
ma-241	130	26	∂y2	∂y2	NOUN
ma-241	130	27	=	=	PUNCT
ma-241	130	28	1	1	NUM
ma-241	130	29	ν	ν	X
ma-241	130	30	∂p	∂p	PROPN
ma-241	130	31	(	(	PUNCT
ma-241	130	32	k	k	NOUN
ma-241	130	33	)	)	PUNCT
ma-241	130	34	1	1	NUM
ma-241	130	35	∂x	∂x	PROPN
ma-241	130	36	in	in	ADP
ma-241	130	37	ω1	ω1	PROPN
ma-241	130	38	,	,	PUNCT
ma-241	130	39	∂2u	∂2u	X
ma-241	130	40	(	(	PUNCT
ma-241	130	41	k	k	NOUN
ma-241	130	42	)	)	PUNCT
ma-241	130	43	1,2	1,2	NUM
ma-241	130	44	∂x2	∂x2	NOUN
ma-241	130	45	+	+	CCONJ
ma-241	130	46	∂2u	∂2u	X
ma-241	130	47	(	(	PUNCT
ma-241	130	48	k	k	X
ma-241	130	49	)	)	PUNCT
ma-241	130	50	1,2	1,2	NUM
ma-241	130	51	∂y2	∂y2	NOUN
ma-241	130	52	=	=	SYM
ma-241	130	53	1	1	NUM
ma-241	130	54	ν	ν	X
ma-241	130	55	∂p	∂p	PROPN
ma-241	130	56	(	(	PUNCT
ma-241	130	57	k	k	NOUN
ma-241	130	58	)	)	PUNCT
ma-241	130	59	1	1	NUM
ma-241	130	60	∂y	∂y	PROPN
ma-241	130	61	in	in	ADP
ma-241	130	62	ω1	ω1	PROPN
ma-241	130	63	,	,	PUNCT
ma-241	130	64	∂u	∂u	PROPN
ma-241	130	65	(	(	PUNCT
ma-241	130	66	k	k	NOUN
ma-241	130	67	)	)	PUNCT
ma-241	130	68	1,1	1,1	NUM
ma-241	130	69	∂x	∂x	PROPN
ma-241	130	70	+	+	CCONJ
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ma-241	130	80	ω1	ω1	PROPN
ma-241	130	81	,	,	PUNCT
ma-241	130	82	ν	ν	X
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ma-241	130	92	(	(	PUNCT
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ma-241	130	94	)	)	PUNCT
ma-241	130	95	1	1	NUM
ma-241	130	96	=	=	SYM
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ma-241	130	127	)	)	PUNCT
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ma-241	130	137	)	)	PUNCT
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ma-241	130	155	(	(	PUNCT
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ma-241	130	157	)	)	PUNCT
ma-241	130	158	1	1	NUM
ma-241	130	159	:	:	PUNCT
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ma-241	130	161	at	at	ADP
ma-241	130	162	−∞	−∞	NOUN
ma-241	130	163	,	,	PUNCT
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ma-241	130	165	∂2u	∂2u	X
ma-241	130	166	(	(	PUNCT
ma-241	130	167	k	k	NOUN
ma-241	130	168	)	)	PUNCT
ma-241	130	169	2,1	2,1	NUM
ma-241	130	170	∂x2	∂x2	NOUN
ma-241	130	171	+	+	CCONJ
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ma-241	130	173	(	(	PUNCT
ma-241	130	174	k	k	X
ma-241	130	175	)	)	PUNCT
ma-241	130	176	2,1	2,1	NUM
ma-241	130	177	∂y2	∂y2	NOUN
ma-241	130	178	=	=	SYM
ma-241	130	179	1	1	NUM
ma-241	130	180	ν	ν	X
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ma-241	130	182	(	(	PUNCT
ma-241	130	183	k	k	NOUN
ma-241	130	184	)	)	PUNCT
ma-241	130	185	2	2	NUM
ma-241	130	186	∂x	∂x	PROPN
ma-241	130	187	in	in	ADP
ma-241	130	188	ω2	ω2	ADJ
ma-241	130	189	,	,	PUNCT
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ma-241	130	191	(	(	PUNCT
ma-241	130	192	k	k	NOUN
ma-241	130	193	)	)	PUNCT
ma-241	130	194	2,2	2,2	NUM
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ma-241	130	198	(	(	PUNCT
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ma-241	130	200	)	)	PUNCT
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ma-241	130	203	=	=	NOUN
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ma-241	130	205	ν	ν	X
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ma-241	130	213	ω2	ω2	PROPN
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ma-241	130	218	)	)	PUNCT
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ma-241	131	1	p	p	X
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ma-241	132	4	)	)	PUNCT
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ma-241	132	22	(	(	PUNCT
ma-241	132	23	k	k	NOUN
ma-241	132	24	)	)	PUNCT
ma-241	132	25	1,2	1,2	NUM
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ma-241	132	35	2,1	2,1	NUM
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ma-241	132	54	(	(	PUNCT
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ma-241	132	56	)	)	PUNCT
ma-241	132	57	2	2	NUM
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ma-241	132	60	at	at	ADP
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ma-241	132	65	)	)	PUNCT
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ma-241	132	68	.	.	PUNCT
ma-241	133	1	j.	j.	PROPN
ma-241	133	2	math	math	PROPN
ma-241	133	3	.	.	PUNCT
ma-241	134	1	anal	anal	PROPN
ma-241	134	2	.	.	PUNCT
ma-241	135	1	10.28924	10.28924	NUM
ma-241	135	2	/	/	SYM
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ma-241	135	4	/	/	SYM
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ma-241	135	6	7we	7we	NOUN
ma-241	135	7	apply	apply	VERB
ma-241	135	8	the	the	DET
ma-241	135	9	fourier	fourier	NOUN
ma-241	135	10	transform	transform	NOUN
ma-241	135	11	in	in	ADP
ma-241	135	12	the	the	DET
ma-241	135	13	y	y	PROPN
ma-241	135	14	direction	direction	NOUN
ma-241	135	15	to	to	ADP
ma-241	135	16	the	the	DET
ma-241	135	17	schwarz	schwarz	PROPN
ma-241	135	18	subproblems	subproblem	NOUN
ma-241	135	19	prescribed	prescribe	VERB
ma-241	135	20	by	by	ADP
ma-241	135	21	(	(	PUNCT
ma-241	135	22	23).the	23).the	DET
ma-241	135	23	fourier	fourier	NOUN
ma-241	135	24	transformed	transform	VERB
ma-241	135	25	velocity	velocity	NOUN
ma-241	135	26	components	component	NOUN
ma-241	135	27	are	be	AUX
ma-241	135	28	given	give	VERB
ma-241	135	29	by	by	ADP
ma-241	135	30	the	the	DET
ma-241	135	31	formulas	formula	NOUN
ma-241	135	32	(	(	PUNCT
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ma-241	135	34	)	)	PUNCT
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ma-241	135	36	(	(	PUNCT
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ma-241	135	38	)	)	PUNCT
ma-241	135	39	,	,	PUNCT
ma-241	135	40	(	(	PUNCT
ma-241	135	41	11	11	NUM
ma-241	135	42	)	)	PUNCT
ma-241	135	43	,	,	PUNCT
ma-241	135	44	(	(	PUNCT
ma-241	135	45	12	12	NUM
ma-241	135	46	)	)	PUNCT
ma-241	135	47	.	.	PUNCT
ma-241	136	1	thefourier	thefourier	PROPN
ma-241	136	2	transformed	transform	VERB
ma-241	136	3	pressure	pressure	NOUN
ma-241	136	4	fields	field	NOUN
ma-241	136	5	are	be	AUX
ma-241	136	6	given	give	VERB
ma-241	136	7	by	by	ADP
ma-241	136	8	the	the	DET
ma-241	136	9	relations	relation	NOUN
ma-241	136	10	:	:	PUNCT
ma-241	136	11	p̂(k	p̂(k	X
ma-241	136	12	)	)	PUNCT
ma-241	136	13	1	1	NUM
ma-241	136	14	=	=	SYM
ma-241	136	15	d(k	d(k	PROPN
ma-241	136	16	)	)	PUNCT
ma-241	136	17	1	1	NUM
ma-241	136	18	e	e	X
ma-241	136	19	|ξ|x	|ξ|x	PROPN
ma-241	136	20	,	,	PUNCT
ma-241	136	21	p̂(k	p̂(k	NOUN
ma-241	136	22	)	)	PUNCT
ma-241	136	23	2	2	NUM
ma-241	136	24	=	=	SYM
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ma-241	136	26	)	)	PUNCT
ma-241	136	27	2	2	NUM
ma-241	136	28	e−|ξ|x	e−|ξ|x	ADV
ma-241	136	29	.we	.we	PUNCT
ma-241	136	30	plug	plug	NOUN
ma-241	136	31	in	in	ADP
ma-241	136	32	the	the	DET
ma-241	136	33	fourier	fourier	NOUN
ma-241	136	34	transformed	transform	VERB
ma-241	136	35	velocities	velocity	NOUN
ma-241	136	36	and	and	CCONJ
ma-241	136	37	pressure	pressure	NOUN
ma-241	136	38	fields	field	NOUN
ma-241	136	39	back	back	ADV
ma-241	136	40	to	to	ADP
ma-241	136	41	the	the	DET
ma-241	136	42	interface	interface	NOUN
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ma-241	136	46	23)5	23)5	NUM
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ma-241	136	53	we	we	PRON
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ma-241	136	56	|ξ|hb(k	|ξ|hb(k	NOUN
ma-241	136	57	)	)	PUNCT
ma-241	136	58	1	1	NUM
ma-241	137	1	+	+	NOUN
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ma-241	137	3	)	)	PUNCT
ma-241	137	4	1	1	NUM
ma-241	137	5	(	(	PUNCT
ma-241	137	6	h|ξ|	h|ξ|	NOUN
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ma-241	137	8	1)e	1)e	NUM
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ma-241	137	12	)	)	PUNCT
ma-241	137	13	2	2	NUM
ma-241	137	14	e−|ξ|h	e−|ξ|h	PROPN
ma-241	137	15	−	−	PROPN
ma-241	137	16	c(k−1	c(k−1	NOUN
ma-241	137	17	)	)	PUNCT
ma-241	137	18	2	2	NUM
ma-241	137	19	e−|ξ|h(1	e−|ξ|h(1	PROPN
ma-241	137	20	+	+	NOUN
ma-241	137	21	h|ξ|	h|ξ|	NOUN
ma-241	137	22	)	)	PUNCT
ma-241	137	23	,	,	PUNCT
ma-241	137	24	(	(	PUNCT
ma-241	137	25	24	24	NUM
ma-241	137	26	)	)	PUNCT
ma-241	137	27	2νb(k	2νb(k	NUM
ma-241	137	28	)	)	PUNCT
ma-241	137	29	1	1	NUM
ma-241	137	30	|ξ|	|ξ|	PROPN
ma-241	137	31	2e	2e	PROPN
ma-241	137	32	|ξ|h	|ξ|h	PROPN
ma-241	137	33	+	+	PROPN
ma-241	137	34	d(k	d(k	PROPN
ma-241	137	35	)	)	PUNCT
ma-241	137	36	1	1	NUM
ma-241	137	37	e	e	NOUN
ma-241	137	38	|ξ|h	|ξ|h	PROPN
ma-241	137	39	(	(	PUNCT
ma-241	137	40	2|ξ|+h	2|ξ|+h	NUM
ma-241	137	41	|ξ|2	|ξ|2	ADJ
ma-241	137	42	)	)	PUNCT
ma-241	137	43	=	=	SYM
ma-241	137	44	2ν|ξ|2b(k−1	2ν|ξ|2b(k−1	NUM
ma-241	137	45	)	)	PUNCT
ma-241	137	46	2	2	NUM
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ma-241	137	56	2|ξ|	2|ξ|	NUM
ma-241	137	57	)	)	PUNCT
ma-241	137	58	,	,	PUNCT
ma-241	137	59	(	(	PUNCT
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ma-241	137	61	)	)	PUNCT
ma-241	137	62	2ν|ξ|b(k	2ν|ξ|b(k	NUM
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ma-241	137	64	2	2	NUM
ma-241	137	65	+	+	CCONJ
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ma-241	137	70	2	2	NUM
ma-241	137	71	=	=	SYM
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ma-241	137	73	)	)	PUNCT
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ma-241	137	75	+	+	NOUN
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ma-241	137	85	2	2	NUM
ma-241	137	86	−	−	NOUN
ma-241	137	87	|ξ|c(k	|ξ|c(k	NOUN
ma-241	137	88	)	)	PUNCT
ma-241	137	89	2	2	NUM
ma-241	137	90	=	=	SYM
ma-241	137	91	νb(k	νb(k	NUM
ma-241	137	92	)	)	PUNCT
ma-241	137	93	1	1	NUM
ma-241	137	94	|ξ|	|ξ|	NOUN
ma-241	137	95	2	2	NUM
ma-241	137	96	+	+	CCONJ
ma-241	137	97	|ξ|d(k	|ξ|d(k	NOUN
ma-241	137	98	)	)	PUNCT
ma-241	137	99	1	1	NUM
ma-241	137	100	.	.	PUNCT
ma-241	138	1	(	(	PUNCT
ma-241	138	2	27	27	NUM
ma-241	138	3	)	)	PUNCT
ma-241	138	4	we	we	PRON
ma-241	138	5	multiply	multiply	VERB
ma-241	138	6	(	(	PUNCT
ma-241	138	7	26	26	NUM
ma-241	138	8	)	)	PUNCT
ma-241	138	9	by	by	ADP
ma-241	138	10	−|ξ|	−|ξ|	NOUN
ma-241	138	11	then	then	ADV
ma-241	138	12	add	add	VERB
ma-241	138	13	(	(	PUNCT
ma-241	138	14	27	27	NUM
ma-241	138	15	)	)	PUNCT
ma-241	138	16	,	,	PUNCT
ma-241	138	17	and	and	CCONJ
ma-241	138	18	solve	solve	VERB
ma-241	138	19	with	with	ADP
ma-241	138	20	respect	respect	NOUN
ma-241	138	21	to	to	ADP
ma-241	138	22	the	the	DET
ma-241	138	23	coefficient	coefficient	NOUN
ma-241	138	24	b(k	b(k	PROPN
ma-241	138	25	)	)	PUNCT
ma-241	138	26	1	1	NUM
ma-241	138	27	obtaining	obtain	VERB
ma-241	138	28	b(k	b(k	PROPN
ma-241	138	29	)	)	PUNCT
ma-241	138	30	1	1	NUM
ma-241	139	1	=	=	SYM
ma-241	139	2	−	−	NUM
ma-241	139	3	1	1	NUM
ma-241	139	4	3	3	NUM
ma-241	139	5	b(k	b(k	PROPN
ma-241	139	6	)	)	PUNCT
ma-241	139	7	2	2	NUM
ma-241	139	8	−	−	NOUN
ma-241	139	9	2	2	NUM
ma-241	139	10	3	3	NUM
ma-241	139	11	1	1	NUM
ma-241	139	12	ν|ξ|c	ν|ξ|c	NOUN
ma-241	139	13	(	(	PUNCT
ma-241	139	14	k	k	NOUN
ma-241	139	15	)	)	PUNCT
ma-241	139	16	2	2	NUM
ma-241	139	17	.	.	PUNCT
ma-241	140	1	(	(	PUNCT
ma-241	140	2	28	28	NUM
ma-241	140	3	)	)	PUNCT
ma-241	140	4	the	the	DET
ma-241	140	5	next	next	ADJ
ma-241	140	6	step	step	NOUN
ma-241	140	7	is	be	AUX
ma-241	140	8	to	to	PART
ma-241	140	9	obtain	obtain	VERB
ma-241	140	10	a	a	DET
ma-241	140	11	formula	formula	NOUN
ma-241	140	12	for	for	ADP
ma-241	140	13	the	the	DET
ma-241	140	14	coefficient	coefficient	NOUN
ma-241	140	15	d(k	d(k	PROPN
ma-241	140	16	)	)	PUNCT
ma-241	140	17	1	1	NUM
ma-241	140	18	.	.	PUNCT
ma-241	141	1	in	in	ADP
ma-241	141	2	order	order	NOUN
ma-241	141	3	to	to	PART
ma-241	141	4	achieve	achieve	VERB
ma-241	141	5	that	that	PRON
ma-241	141	6	,	,	PUNCT
ma-241	141	7	we	we	PRON
ma-241	141	8	multiply(26	multiply(26	VERB
ma-241	141	9	)	)	PUNCT
ma-241	141	10	by	by	ADP
ma-241	141	11	|ξ|	|ξ|	PROPN
ma-241	141	12	then	then	ADV
ma-241	141	13	add	add	VERB
ma-241	141	14	(	(	PUNCT
ma-241	141	15	27	27	NUM
ma-241	141	16	)	)	PUNCT
ma-241	141	17	to	to	PART
ma-241	141	18	obtain	obtain	VERB
ma-241	141	19	d(k	d(k	PROPN
ma-241	141	20	)	)	PUNCT
ma-241	141	21	1	1	NUM
ma-241	141	22	=	=	SYM
ma-241	141	23	4	4	NUM
ma-241	141	24	3	3	NUM
ma-241	141	25	ν|ξ|b(k	ν|ξ|b(k	NOUN
ma-241	141	26	)	)	PUNCT
ma-241	141	27	2	2	NUM
ma-241	141	28	−	−	NOUN
ma-241	141	29	1	1	NUM
ma-241	141	30	3	3	NUM
ma-241	141	31	c(k	c(k	NOUN
ma-241	141	32	)	)	PUNCT
ma-241	141	33	2	2	NUM
ma-241	141	34	.	.	PUNCT
ma-241	142	1	(	(	PUNCT
ma-241	142	2	29	29	NUM
ma-241	142	3	)	)	PUNCT
ma-241	142	4	we	we	PRON
ma-241	142	5	substitute	substitute	VERB
ma-241	142	6	the	the	DET
ma-241	142	7	expressions	expression	NOUN
ma-241	142	8	(	(	PUNCT
ma-241	142	9	28	28	NUM
ma-241	142	10	)	)	PUNCT
ma-241	142	11	,	,	PUNCT
ma-241	142	12	(	(	PUNCT
ma-241	142	13	29	29	NUM
ma-241	142	14	)	)	PUNCT
ma-241	142	15	back	back	ADV
ma-241	142	16	to	to	ADP
ma-241	142	17	(	(	PUNCT
ma-241	142	18	24	24	NUM
ma-241	142	19	)	)	PUNCT
ma-241	142	20	and	and	CCONJ
ma-241	142	21	(	(	PUNCT
ma-241	142	22	25	25	NUM
ma-241	142	23	)	)	PUNCT
ma-241	142	24	and	and	CCONJ
ma-241	142	25	this	this	DET
ma-241	142	26	yields	yield	NOUN
ma-241	142	27	b(k	b(k	PROPN
ma-241	142	28	)	)	PUNCT
ma-241	142	29	2	2	NUM
ma-241	142	30	e	e	NOUN
ma-241	142	31	|ξ|h	|ξ|h	PROPN
ma-241	142	32	(	(	PUNCT
ma-241	142	33	6ν|ξ|	6ν|ξ|	NUM
ma-241	142	34	−	−	PROPN
ma-241	142	35	4νh|ξ|2	4νh|ξ|2	NUM
ma-241	142	36	)	)	PUNCT
ma-241	143	1	+	+	CCONJ
ma-241	143	2	c(k	c(k	NOUN
ma-241	143	3	)	)	PUNCT
ma-241	143	4	2	2	NUM
ma-241	143	5	e	e	NOUN
ma-241	143	6	|ξ|h(3	|ξ|h(3	X
ma-241	144	1	+	+	ADJ
ma-241	144	2	h|ξ|	h|ξ|	NOUN
ma-241	144	3	)	)	PUNCT
ma-241	144	4	=	=	PUNCT
ma-241	144	5	6ν|ξ|b(k−1	6ν|ξ|b(k−1	NOUN
ma-241	144	6	)	)	PUNCT
ma-241	144	7	2	2	NUM
ma-241	144	8	e−|ξ|h	e−|ξ|h	NOUN
ma-241	144	9	+	+	CCONJ
ma-241	144	10	3c(k−1	3c(k−1	NUM
ma-241	144	11	)	)	PUNCT
ma-241	144	12	2	2	NUM
ma-241	144	13	e−|ξ|h(1	e−|ξ|h(1	PROPN
ma-241	144	14	+	+	NOUN
ma-241	144	15	h|ξ|	h|ξ|	NOUN
ma-241	144	16	)	)	PUNCT
ma-241	144	17	,	,	PUNCT
ma-241	144	18	b(k	b(k	PROPN
ma-241	144	19	)	)	PUNCT
ma-241	144	20	2	2	NUM
ma-241	144	21	e	e	NOUN
ma-241	144	22	|ξ|h	|ξ|h	PROPN
ma-241	144	23	(	(	PUNCT
ma-241	144	24	6ν|ξ|2	6ν|ξ|2	PROPN
ma-241	144	25	+	+	CCONJ
ma-241	144	26	4νh|ξ|3	4νh|ξ|3	NUM
ma-241	144	27	)	)	PUNCT
ma-241	144	28	−	−	PRON
ma-241	144	29	c(k	c(k	NOUN
ma-241	144	30	)	)	PUNCT
ma-241	144	31	2	2	NUM
ma-241	144	32	e	e	NOUN
ma-241	144	33	|ξ|h	|ξ|h	PROPN
ma-241	144	34	(	(	PUNCT
ma-241	144	35	6|ξ|+h|ξ|2	6|ξ|+h|ξ|2	NUM
ma-241	144	36	)	)	PUNCT
ma-241	144	37	=	=	SYM
ma-241	144	38	6ν|ξ|2b(k−1	6ν|ξ|2b(k−1	NUM
ma-241	144	39	)	)	PUNCT
ma-241	144	40	2	2	NUM
ma-241	144	41	e−|ξ|h	e−|ξ|h	NOUN
ma-241	144	42	+	+	CCONJ
ma-241	144	43	3c(k−1	3c(k−1	NUM
ma-241	144	44	)	)	PUNCT
ma-241	144	45	2	2	NUM
ma-241	144	46	e−|ξ|h	e−|ξ|h	NOUN
ma-241	144	47	(	(	PUNCT
ma-241	144	48	h|ξ|2	h|ξ|2	ADJ
ma-241	144	49	−	−	PROPN
ma-241	144	50	2|ξ|	2|ξ|	NUM
ma-241	144	51	)	)	PUNCT
ma-241	144	52	.	.	PUNCT
ma-241	145	1	we	we	PRON
ma-241	145	2	write	write	VERB
ma-241	145	3	the	the	DET
ma-241	145	4	above	above	ADJ
ma-241	145	5	equations	equation	NOUN
ma-241	145	6	in	in	ADP
ma-241	145	7	matrix	matrix	NOUN
ma-241	145	8	form	form	NOUN
ma-241	145	9	and	and	CCONJ
ma-241	145	10	by	by	ADP
ma-241	145	11	doing	do	VERB
ma-241	145	12	some	some	DET
ma-241	145	13	algebraic	algebraic	ADJ
ma-241	145	14	manipulations	manipulation	NOUN
ma-241	145	15	we	we	PRON
ma-241	145	16	derivethe	derivethe	VERB
ma-241	145	17	stationary	stationary	ADJ
ma-241	145	18	iteration	iteration	NOUN
ma-241	145	19	[	[	PUNCT
ma-241	145	20	b(k	b(k	NOUN
ma-241	145	21	)	)	PUNCT
ma-241	145	22	2	2	NUM
ma-241	145	23	c	c	X
ma-241	145	24	(	(	PUNCT
ma-241	145	25	k	k	NOUN
ma-241	145	26	)	)	PUNCT
ma-241	145	27	2	2	NUM
ma-241	145	28	]	]	PUNCT
ma-241	145	29	=	=	SYM
ma-241	145	30	−12νh|ξ|3−54ν|ξ|2	−12νh|ξ|3−54ν|ξ|2	PROPN
ma-241	145	31	54e2|ξ|h	54e2|ξ|h	NUM
ma-241	145	32	|ξ|2ν	|ξ|2ν	NOUN
ma-241	145	33	h(h|ξ|+4	h(h|ξ|+4	NOUN
ma-241	145	34	)	)	PUNCT
ma-241	145	35	9e2|ξ|hν	9e2|ξ|hν	PROPN
ma-241	145	36	8|ξ|2νh	8|ξ|2νh	NUM
ma-241	145	37	9e2|ξ|h	9e2|ξ|h	NUM
ma-241	145	38	4|ξ|2h2−2|ξ|h+9	4|ξ|2h2−2|ξ|h+9	NUM
ma-241	145	39	9e2|ξ|h	9e2|ξ|h	NUM
ma-241	145	40			NOUN
ma-241	145	41	︸	︸	ADP
ma-241	145	42	︷︷	︷︷	NOUN
ma-241	145	43	︸	︸	ADP
ma-241	145	44	ψasm	ψasm	NOUN
ma-241	145	45	,	,	PUNCT
ma-241	145	46	n	n	CCONJ
ma-241	145	47	[	[	PUNCT
ma-241	145	48	b(k−1	b(k−1	X
ma-241	145	49	)	)	PUNCT
ma-241	145	50	2	2	NUM
ma-241	145	51	c	c	NOUN
ma-241	145	52	(	(	PUNCT
ma-241	145	53	k−1	k−1	PROPN
ma-241	145	54	)	)	PUNCT
ma-241	145	55	2	2	NUM
ma-241	145	56	]	]	PUNCT
ma-241	145	57	(	(	PUNCT
ma-241	145	58	30	30	NUM
ma-241	145	59	)	)	PUNCT
ma-241	145	60	where	where	SCONJ
ma-241	145	61	ψasm	ψasm	NOUN
ma-241	145	62	,	,	PUNCT
ma-241	145	63	n	n	PRON
ma-241	145	64	is	be	AUX
ma-241	145	65	the	the	DET
ma-241	145	66	schwarz	schwarz	PROPN
ma-241	145	67	iteration	iteration	NOUN
ma-241	145	68	matrix	matrix	NOUN
ma-241	145	69	.	.	PUNCT
ma-241	146	1	the	the	DET
ma-241	146	2	spectrum	spectrum	NOUN
ma-241	146	3	of	of	ADP
ma-241	146	4	ψasm	ψasm	NOUN
ma-241	146	5	,	,	PUNCT
ma-241	146	6	n	n	PRON
ma-241	146	7	is	be	AUX
ma-241	146	8	σ(ψasm	σ(ψasm	NOUN
ma-241	146	9	,	,	PUNCT
ma-241	146	10	n	n	CCONJ
ma-241	146	11	)	)	PUNCT
ma-241	146	12	=	=	PRON
ma-241	146	13	{	{	PUNCT
ma-241	146	14	µ+	µ+	NOUN
ma-241	146	15	,	,	PUNCT
ma-241	146	16	µ−},where	µ−},where	NOUN
ma-241	146	17	µ+	µ+	X
ma-241	146	18	and	and	CCONJ
ma-241	146	19	µ−	µ−	PROPN
ma-241	146	20	are	be	AUX
ma-241	146	21	the	the	DET
ma-241	146	22	eigenvalues	eigenvalue	NOUN
ma-241	146	23	of	of	ADP
ma-241	146	24	the	the	DET
ma-241	146	25	schwarz	schwarz	PROPN
ma-241	146	26	iteration	iteration	NOUN
ma-241	146	27	matrix	matrix	NOUN
ma-241	146	28	provided	provide	VERB
ma-241	146	29	by	by	ADP
ma-241	146	30	the	the	DET
ma-241	146	31	formulas	formula	NOUN
ma-241	147	1	µ+	µ+	X
ma-241	147	2	=	=	PUNCT
ma-241	147	3	(	(	PUNCT
ma-241	147	4	2|ξ|2h2	2|ξ|2h2	NUM
ma-241	147	5	9	9	NUM
ma-241	147	6	−	−	NUM
ma-241	147	7	2|ξ|h	2|ξ|h	NUM
ma-241	147	8	9	9	NUM
ma-241	147	9	+	+	CCONJ
ma-241	147	10	1	1	NUM
ma-241	147	11	+	+	NUM
ma-241	147	12	2	2	NUM
ma-241	147	13	√	√	NUM
ma-241	147	14	|ξ|4h4	|ξ|4h4	PROPN
ma-241	147	15	+	+	CCONJ
ma-241	147	16	2|ξ|3h3	2|ξ|3h3	PROPN
ma-241	147	17	+	+	CCONJ
ma-241	147	18	8	8	NUM
ma-241	147	19	|ξ|2h2	|ξ|2h2	NOUN
ma-241	147	20	9	9	NUM
ma-241	147	21	)	)	PUNCT
ma-241	147	22	e−2|ξ|h	e−2|ξ|h	PROPN
ma-241	147	23	,	,	PUNCT
ma-241	147	24	µ−	µ−	PROPN
ma-241	147	25	=	=	PUNCT
ma-241	147	26	(	(	PUNCT
ma-241	147	27	2|ξ|2h2	2|ξ|2h2	NUM
ma-241	147	28	9	9	NUM
ma-241	147	29	−	−	NOUN
ma-241	147	30	2|ξ|h	2|ξ|h	NUM
ma-241	147	31	9	9	NUM
ma-241	147	32	+	+	CCONJ
ma-241	147	33	1−	1−	NUM
ma-241	147	34	2	2	NUM
ma-241	147	35	√	√	NOUN
ma-241	147	36	|ξ|4h4	|ξ|4h4	PROPN
ma-241	147	37	+	+	CCONJ
ma-241	147	38	2|ξ|3h3	2|ξ|3h3	PROPN
ma-241	147	39	+	+	CCONJ
ma-241	147	40	8	8	NUM
ma-241	147	41	|ξ|2h2	|ξ|2h2	NOUN
ma-241	147	42	9	9	NUM
ma-241	147	43	)	)	PUNCT
ma-241	147	44	e−2|ξ|h	e−2|ξ|h	PROPN
ma-241	147	45	.	.	PUNCT
ma-241	148	1	https://doi.org/10.28924/ada/ma.5.6	https://doi.org/10.28924/ada/ma.5.6	PROPN
ma-241	148	2	eur	eur	PROPN
ma-241	148	3	.	.	PUNCT
ma-241	149	1	j.	j.	PROPN
ma-241	149	2	math	math	PROPN
ma-241	149	3	.	.	PUNCT
ma-241	150	1	anal	anal	PROPN
ma-241	150	2	.	.	PUNCT
ma-241	151	1	10.28924	10.28924	NUM
ma-241	151	2	/	/	SYM
ma-241	151	3	ada	ada	PROPN
ma-241	151	4	/	/	SYM
ma-241	151	5	ma.5.6	ma.5.6	PROPN
ma-241	151	6	8as	8as	NOUN
ma-241	151	7	a	a	DET
ma-241	151	8	result	result	NOUN
ma-241	151	9	,	,	PUNCT
ma-241	151	10	the	the	DET
ma-241	151	11	reduction	reduction	NOUN
ma-241	151	12	factor	factor	NOUN
ma-241	151	13	of	of	ADP
ma-241	151	14	the	the	DET
ma-241	151	15	schwarz	schwarz	PROPN
ma-241	151	16	method	method	NOUN
ma-241	151	17	(	(	PUNCT
ma-241	151	18	neumann	neumann	PROPN
ma-241	151	19	interface	interface	NOUN
ma-241	151	20	conditions	condition	NOUN
ma-241	151	21	)	)	PUNCT
ma-241	151	22	is	be	AUX
ma-241	151	23	given	give	VERB
ma-241	151	24	by	by	ADP
ma-241	151	25	rasm	rasm	NOUN
ma-241	151	26	,	,	PUNCT
ma-241	151	27	n	n	NOUN
ma-241	151	28	=	=	SYM
ma-241	151	29	ρ(ψasm	ρ(ψasm	NOUN
ma-241	151	30	,	,	PUNCT
ma-241	151	31	n	n	CCONJ
ma-241	151	32	)	)	PUNCT
ma-241	151	33	=	=	SYM
ma-241	151	34	max{|µ+|	max{|µ+|	NOUN
ma-241	151	35	,	,	PUNCT
ma-241	151	36	|µ−|	|µ−|	NOUN
ma-241	151	37	}	}	PUNCT
ma-241	151	38	=	=	PUNCT
ma-241	151	39	∣∣∣(2|ξ|2h2	∣∣∣(2|ξ|2h2	ADP
ma-241	151	40	9	9	NUM
ma-241	151	41	−	−	NUM
ma-241	151	42	2|ξ|h	2|ξ|h	NUM
ma-241	151	43	9	9	NUM
ma-241	151	44	+	+	CCONJ
ma-241	151	45	1	1	NUM
ma-241	151	46	+	+	NUM
ma-241	151	47	2	2	NUM
ma-241	151	48	√	√	NUM
ma-241	151	49	|ξ|4h4	|ξ|4h4	PROPN
ma-241	151	50	+	+	CCONJ
ma-241	151	51	2|ξ|3h3	2|ξ|3h3	PROPN
ma-241	151	52	+	+	CCONJ
ma-241	151	53	8	8	NUM
ma-241	151	54	|ξ|2h2	|ξ|2h2	NOUN
ma-241	151	55	9	9	NUM
ma-241	151	56	)	)	PUNCT
ma-241	151	57	∣∣∣e−2|ξ|h	∣∣∣e−2|ξ|h	PROPN
ma-241	151	58	.	.	PUNCT
ma-241	151	59	�	�	PROPN
ma-241	151	60	4	4	NUM
ma-241	151	61	.	.	PUNCT
ma-241	152	1	non	non	ADJ
ma-241	152	2	-	-	ADJ
ma-241	152	3	overlapping	overlapping	ADJ
ma-241	152	4	optimized	optimize	VERB
ma-241	152	5	schwarz	schwarz	PROPN
ma-241	152	6	algorithm	algorithm	PROPN
ma-241	152	7	-	-	PUNCT
ma-241	152	8	robin	robin	PROPN
ma-241	152	9	ic	ic	PROPN
ma-241	152	10	the	the	DET
ma-241	152	11	domain	domain	NOUN
ma-241	152	12	ω	ω	NOUN
ma-241	152	13	=	=	NOUN
ma-241	152	14	r2	r2	PROPN
ma-241	152	15	is	be	AUX
ma-241	152	16	decomposed	decompose	VERB
ma-241	152	17	into	into	ADP
ma-241	152	18	two	two	NUM
ma-241	152	19	non	non	ADJ
ma-241	152	20	-	-	ADJ
ma-241	152	21	overlapping	overlapping	ADJ
ma-241	152	22	subdomains	subdomain	NOUN
ma-241	152	23	ω1	ω1	X
ma-241	152	24	=	=	SYM
ma-241	152	25	(	(	PUNCT
ma-241	152	26	−∞	−∞	NOUN
ma-241	152	27	,	,	PUNCT
ma-241	152	28	0	0	NUM
ma-241	152	29	)	)	PUNCT
ma-241	152	30	×	×	NOUN
ma-241	152	31	(	(	PUNCT
ma-241	152	32	−∞,+∞	−∞,+∞	NUM
ma-241	152	33	)	)	PUNCT
ma-241	152	34	and	and	CCONJ
ma-241	153	1	ω2	ω2	NOUN
ma-241	153	2	=	=	SYM
ma-241	153	3	(	(	PUNCT
ma-241	153	4	0,+∞	0,+∞	NUM
ma-241	153	5	)	)	PUNCT
ma-241	153	6	×	×	NOUN
ma-241	153	7	(	(	PUNCT
ma-241	153	8	−∞,+∞).the	−∞,+∞).the	DET
ma-241	153	9	optimized	optimize	VERB
ma-241	153	10	schwarz	schwarz	PROPN
ma-241	153	11	methods	method	NOUN
ma-241	153	12	employ	employ	VERB
ma-241	153	13	mixed	mixed	ADJ
ma-241	153	14	in	in	ADP
ma-241	153	15	-	-	PUNCT
ma-241	153	16	terface	terface	NOUN
ma-241	153	17	boundary	boundary	ADJ
ma-241	153	18	conditions	condition	NOUN
ma-241	153	19	,	,	PUNCT
ma-241	153	20	and	and	CCONJ
ma-241	153	21	more	more	ADV
ma-241	153	22	precisely	precisely	ADV
ma-241	153	23	robin	robin	PROPN
ma-241	153	24	.	.	PUNCT
ma-241	154	1	in	in	ADP
ma-241	154	2	this	this	DET
ma-241	154	3	way	way	NOUN
ma-241	154	4	,	,	PUNCT
ma-241	154	5	they	they	PRON
ma-241	154	6	facilitate	facilitate	VERB
ma-241	154	7	both	both	DET
ma-241	154	8	neumannand	neumannand	NOUN
ma-241	154	9	dirichlet	dirichlet	PROPN
ma-241	154	10	conditions	condition	NOUN
ma-241	154	11	and	and	CCONJ
ma-241	154	12	there	there	PRON
ma-241	154	13	is	be	VERB
ma-241	154	14	a	a	DET
ma-241	154	15	tuning	tuning	NOUN
ma-241	154	16	parameter	parameter	NOUN
ma-241	154	17	to	to	PART
ma-241	154	18	tune	tune	VERB
ma-241	154	19	the	the	DET
ma-241	154	20	method	method	NOUN
ma-241	154	21	accordingly	accordingly	ADV
ma-241	154	22	.	.	PUNCT
ma-241	155	1	theoptimized	theoptimize	VERB
ma-241	155	2	schwarz	schwarz	PROPN
ma-241	155	3	iterative	iterative	NOUN
ma-241	155	4	scheme	scheme	NOUN
ma-241	155	5	is	be	AUX
ma-241	155	6	given	give	VERB
ma-241	155	7	in	in	ADP
ma-241	155	8	strong	strong	ADJ
ma-241	155	9	form	form	NOUN
ma-241	155	10	−ν∆−→u1	−ν∆−→u1	NOUN
ma-241	155	11	(	(	PUNCT
ma-241	155	12	k	k	NOUN
ma-241	155	13	)	)	PUNCT
ma-241	156	1	+	+	NUM
ma-241	156	2	op(k	op(k	X
ma-241	156	3	)	)	PUNCT
ma-241	156	4	1	1	NUM
ma-241	156	5	=	=	SYM
ma-241	156	6	~f	~f	PUNCT
ma-241	156	7	in	in	ADP
ma-241	156	8	ω1	ω1	PROPN
ma-241	156	9	,	,	PUNCT
ma-241	156	10	d	d	NOUN
ma-241	156	11	iv−→u1	iv−→u1	NOUN
ma-241	156	12	(	(	PUNCT
ma-241	156	13	k	k	NOUN
ma-241	156	14	)	)	PUNCT
ma-241	156	15	=	=	SYM
ma-241	156	16	0	0	NUM
ma-241	156	17	in	in	ADP
ma-241	156	18	ω1	ω1	PROPN
ma-241	156	19	,	,	PUNCT
ma-241	156	20	νo−→u1	νo−→u1	NOUN
ma-241	156	21	(	(	PUNCT
ma-241	156	22	k)~n	k)~n	VERB
ma-241	156	23	−	−	NOUN
ma-241	156	24	p(k	p(k	NOUN
ma-241	156	25	)	)	PUNCT
ma-241	156	26	1	1	NUM
ma-241	156	27	~n	~n	NUM
ma-241	156	28	+	+	CCONJ
ma-241	157	1	γ−→u1	γ−→u1	NOUN
ma-241	157	2	(	(	PUNCT
ma-241	157	3	k	k	NOUN
ma-241	157	4	)	)	PUNCT
ma-241	157	5	=	=	SYM
ma-241	157	6	νo−→u2	νo−→u2	NOUN
ma-241	157	7	(	(	PUNCT
ma-241	157	8	k−1)~n	k−1)~n	ADJ
ma-241	157	9	−	−	NOUN
ma-241	157	10	p(k−1	p(k−1	NOUN
ma-241	157	11	)	)	PUNCT
ma-241	157	12	2	2	NUM
ma-241	157	13	~n	~n	NUM
ma-241	157	14	+	+	CCONJ
ma-241	157	15	γ−→u2	γ−→u2	NOUN
ma-241	157	16	(	(	PUNCT
ma-241	157	17	k−1	k−1	PROPN
ma-241	157	18	)	)	PUNCT
ma-241	157	19	at	at	ADP
ma-241	157	20	x	x	X
ma-241	157	21	=	=	SYM
ma-241	157	22	0	0	NUM
ma-241	157	23	,	,	PUNCT
ma-241	157	24	−→u1	−→u1	NOUN
ma-241	157	25	(	(	PUNCT
ma-241	157	26	k	k	NOUN
ma-241	157	27	)	)	PUNCT
ma-241	157	28	:	:	PUNCT
ma-241	157	29	bounded	bound	VERB
ma-241	157	30	at	at	ADP
ma-241	157	31	−∞	−∞	PROPN
ma-241	157	32	,	,	PUNCT
ma-241	157	33	p	p	X
ma-241	157	34	(	(	PUNCT
ma-241	157	35	k	k	NOUN
ma-241	157	36	)	)	PUNCT
ma-241	157	37	1	1	NUM
ma-241	157	38	:	:	PUNCT
ma-241	157	39	bounded	bound	VERB
ma-241	157	40	at	at	ADP
ma-241	157	41	−∞	−∞	NOUN
ma-241	157	42	,	,	PUNCT
ma-241	157	43	(	(	PUNCT
ma-241	157	44	31	31	NUM
ma-241	157	45	)	)	PUNCT
ma-241	157	46			X
ma-241	158	1	−ν∆−→u2	−ν∆−→u2	PROPN
ma-241	158	2	(	(	PUNCT
ma-241	158	3	k	k	NOUN
ma-241	158	4	)	)	PUNCT
ma-241	158	5	+	+	NUM
ma-241	158	6	op(k	op(k	X
ma-241	158	7	)	)	PUNCT
ma-241	158	8	2	2	NUM
ma-241	158	9	=	=	SYM
ma-241	158	10	~f	~f	PUNCT
ma-241	158	11	in	in	ADP
ma-241	158	12	ω2	ω2	ADJ
ma-241	158	13	,	,	PUNCT
ma-241	158	14	d	d	X
ma-241	158	15	iv−→u2	iv−→u2	X
ma-241	158	16	(	(	PUNCT
ma-241	158	17	k	k	NOUN
ma-241	158	18	)	)	PUNCT
ma-241	158	19	=	=	SYM
ma-241	158	20	0	0	NUM
ma-241	158	21	in	in	ADP
ma-241	158	22	ω2	ω2	NUM
ma-241	158	23	,	,	PUNCT
ma-241	158	24	νo−→u2	νo−→u2	X
ma-241	158	25	(	(	PUNCT
ma-241	158	26	k)~n	k)~n	VERB
ma-241	158	27	−	−	NOUN
ma-241	158	28	p(k	p(k	NOUN
ma-241	158	29	)	)	PUNCT
ma-241	158	30	2	2	NUM
ma-241	158	31	~n	~n	NUM
ma-241	158	32	+	+	CCONJ
ma-241	158	33	γ−→u2	γ−→u2	NOUN
ma-241	158	34	(	(	PUNCT
ma-241	158	35	k	k	NOUN
ma-241	158	36	)	)	PUNCT
ma-241	158	37	=	=	SYM
ma-241	158	38	νo−→u1	νo−→u1	NOUN
ma-241	158	39	(	(	PUNCT
ma-241	158	40	k−1)~n	k−1)~n	ADJ
ma-241	158	41	−	−	NOUN
ma-241	158	42	p(k−1	p(k−1	NOUN
ma-241	158	43	)	)	PUNCT
ma-241	158	44	1	1	NUM
ma-241	158	45	~n	~n	NUM
ma-241	158	46	+	+	CCONJ
ma-241	158	47	γ−→u1	γ−→u1	NOUN
ma-241	158	48	(	(	PUNCT
ma-241	158	49	k−1	k−1	PROPN
ma-241	158	50	)	)	PUNCT
ma-241	158	51	at	at	ADP
ma-241	158	52	x	x	X
ma-241	158	53	=	=	SYM
ma-241	158	54	0	0	NUM
ma-241	158	55	,	,	PUNCT
ma-241	158	56	−→u2	−→u2	NOUN
ma-241	158	57	(	(	PUNCT
ma-241	158	58	k	k	NOUN
ma-241	158	59	)	)	PUNCT
ma-241	158	60	:	:	PUNCT
ma-241	158	61	bounded	bound	VERB
ma-241	158	62	at	at	ADP
ma-241	158	63	+	+	PROPN
ma-241	158	64	∞	∞	PROPN
ma-241	158	65	,	,	PUNCT
ma-241	158	66	p	p	X
ma-241	158	67	(	(	PUNCT
ma-241	158	68	k	k	NOUN
ma-241	158	69	)	)	PUNCT
ma-241	158	70	2	2	NUM
ma-241	158	71	:	:	PUNCT
ma-241	158	72	bounded	bound	VERB
ma-241	158	73	at	at	ADP
ma-241	158	74	+	+	PROPN
ma-241	158	75	∞	∞	PROPN
ma-241	158	76	,	,	PUNCT
ma-241	158	77	(	(	PUNCT
ma-241	158	78	32	32	NUM
ma-241	158	79	)	)	PUNCT
ma-241	158	80	where	where	SCONJ
ma-241	158	81	γ	γ	PROPN
ma-241	158	82	is	be	AUX
ma-241	158	83	the	the	DET
ma-241	158	84	tuning	tuning	NOUN
ma-241	158	85	parameter	parameter	NOUN
ma-241	158	86	of	of	ADP
ma-241	158	87	the	the	DET
ma-241	158	88	method	method	NOUN
ma-241	158	89	.	.	PUNCT
ma-241	159	1	two	two	NUM
ma-241	159	2	initial	initial	ADJ
ma-241	159	3	guesses	guess	NOUN
ma-241	159	4	are	be	AUX
ma-241	159	5	needed	need	VERB
ma-241	159	6	for	for	ADP
ma-241	159	7	the	the	DET
ma-241	159	8	iterativemethod	iterativemethod	PROPN
ma-241	159	9	.	.	PUNCT
ma-241	160	1	theorem	theorem	NOUN
ma-241	160	2	3	3	NUM
ma-241	160	3	.	.	PUNCT
ma-241	161	1	the	the	DET
ma-241	161	2	contraction	contraction	NOUN
ma-241	161	3	factor	factor	NOUN
ma-241	161	4	of	of	ADP
ma-241	161	5	the	the	DET
ma-241	161	6	non	non	ADJ
ma-241	161	7	-	-	ADJ
ma-241	161	8	overlapping	overlapping	ADJ
ma-241	161	9	schwarz	schwarz	PROPN
ma-241	161	10	algorithm	algorithm	NOUN
ma-241	161	11	is	be	AUX
ma-241	161	12	given	give	VERB
ma-241	161	13	by	by	ADP
ma-241	161	14	the	the	DET
ma-241	161	15	mathematical	mathematical	ADJ
ma-241	161	16	expression	expression	NOUN
ma-241	161	17	r2	r2	PROPN
ma-241	161	18	osm(ξ	osm(ξ	PROPN
ma-241	161	19	,	,	PUNCT
ma-241	161	20	ν	ν	PROPN
ma-241	161	21	,	,	PUNCT
ma-241	161	22	γ	γ	NOUN
ma-241	161	23	)	)	PUNCT
ma-241	161	24	=	=	SYM
ma-241	161	25	|3ν2|ξ|2	|3ν2|ξ|2	NUM
ma-241	161	26	−	−	NUM
ma-241	161	27	4ν|ξ|γ	4ν|ξ|γ	NUM
ma-241	162	1	+	+	CCONJ
ma-241	162	2	γ2|2	γ2|2	PROPN
ma-241	162	3	|3ν2|ξ|2	|3ν2|ξ|2	AUX
ma-241	162	4	+	+	CCONJ
ma-241	162	5	4ν|ξ|γ	4ν|ξ|γ	NUM
ma-241	162	6	+	+	CCONJ
ma-241	162	7	γ2|2	γ2|2	PROPN
ma-241	162	8	.	.	PUNCT
ma-241	163	1	(	(	PUNCT
ma-241	163	2	33	33	NUM
ma-241	163	3	)	)	PUNCT
ma-241	163	4	https://doi.org/10.28924/ada/ma.5.6	https://doi.org/10.28924/ada/ma.5.6	PROPN
ma-241	163	5	eur	eur	PROPN
ma-241	163	6	.	.	PUNCT
ma-241	164	1	j.	j.	PROPN
ma-241	164	2	math	math	PROPN
ma-241	164	3	.	.	PUNCT
ma-241	165	1	anal	anal	PROPN
ma-241	165	2	.	.	PUNCT
ma-241	166	1	10.28924	10.28924	NUM
ma-241	166	2	/	/	SYM
ma-241	166	3	ada	ada	PROPN
ma-241	166	4	/	/	SYM
ma-241	166	5	ma.5.6	ma.5.6	ADJ
ma-241	166	6	9	9	NUM
ma-241	166	7	proof	proof	NOUN
ma-241	166	8	.	.	PUNCT
ma-241	167	1	we	we	PRON
ma-241	167	2	recast	recast	VERB
ma-241	167	3	the	the	DET
ma-241	167	4	local	local	ADJ
ma-241	167	5	schwarz	schwarz	PROPN
ma-241	167	6	subproblems	subproblem	NOUN
ma-241	167	7	(	(	PUNCT
ma-241	167	8	31	31	NUM
ma-241	167	9	)	)	PUNCT
ma-241	167	10	,	,	PUNCT
ma-241	167	11	(	(	PUNCT
ma-241	167	12	32	32	NUM
ma-241	167	13	)	)	PUNCT
ma-241	167	14	in	in	ADP
ma-241	167	15	the	the	DET
ma-241	167	16	form	form	PROPN
ma-241	167	17	∂2u	∂2u	PROPN
ma-241	167	18	(	(	PUNCT
ma-241	167	19	k	k	NOUN
ma-241	167	20	)	)	PUNCT
ma-241	167	21	1,1	1,1	NUM
ma-241	167	22	∂x2	∂x2	NOUN
ma-241	167	23	+	+	CCONJ
ma-241	167	24	∂2u	∂2u	X
ma-241	167	25	(	(	PUNCT
ma-241	167	26	k	k	X
ma-241	167	27	)	)	PUNCT
ma-241	167	28	1,1	1,1	NUM
ma-241	167	29	∂y2	∂y2	NOUN
ma-241	167	30	=	=	PUNCT
ma-241	167	31	1	1	NUM
ma-241	167	32	ν	ν	X
ma-241	167	33	∂p	∂p	PROPN
ma-241	167	34	(	(	PUNCT
ma-241	167	35	k	k	NOUN
ma-241	167	36	)	)	PUNCT
ma-241	167	37	1	1	NUM
ma-241	167	38	∂x	∂x	PROPN
ma-241	167	39	in	in	ADP
ma-241	167	40	ω1	ω1	PROPN
ma-241	167	41	,	,	PUNCT
ma-241	167	42	∂2u	∂2u	X
ma-241	167	43	(	(	PUNCT
ma-241	167	44	k	k	NOUN
ma-241	167	45	)	)	PUNCT
ma-241	167	46	1,2	1,2	NUM
ma-241	167	47	∂x2	∂x2	NOUN
ma-241	167	48	+	+	CCONJ
ma-241	167	49	∂2u	∂2u	X
ma-241	167	50	(	(	PUNCT
ma-241	167	51	k	k	X
ma-241	167	52	)	)	PUNCT
ma-241	167	53	1,2	1,2	NUM
ma-241	167	54	∂y2	∂y2	NOUN
ma-241	167	55	=	=	SYM
ma-241	167	56	1	1	NUM
ma-241	167	57	ν	ν	X
ma-241	167	58	∂p	∂p	PROPN
ma-241	167	59	(	(	PUNCT
ma-241	167	60	k	k	NOUN
ma-241	167	61	)	)	PUNCT
ma-241	167	62	1	1	NUM
ma-241	167	63	∂y	∂y	PROPN
ma-241	167	64	in	in	ADP
ma-241	167	65	ω1	ω1	PROPN
ma-241	167	66	,	,	PUNCT
ma-241	167	67	∂u	∂u	PROPN
ma-241	167	68	(	(	PUNCT
ma-241	167	69	k	k	NOUN
ma-241	167	70	)	)	PUNCT
ma-241	167	71	1,1	1,1	NUM
ma-241	167	72	∂x	∂x	PROPN
ma-241	167	73	+	+	CCONJ
ma-241	167	74	∂u	∂u	PROPN
ma-241	167	75	(	(	PUNCT
ma-241	167	76	k	k	NOUN
ma-241	167	77	)	)	PUNCT
ma-241	167	78	1,2	1,2	NUM
ma-241	167	79	∂y	∂y	X
ma-241	167	80	=	=	NOUN
ma-241	167	81	0	0	NUM
ma-241	167	82	in	in	ADP
ma-241	167	83	ω1	ω1	PROPN
ma-241	167	84	,	,	PUNCT
ma-241	167	85	ν	ν	X
ma-241	167	86	∂	∂	NOUN
ma-241	167	87	∂x	∂x	PROPN
ma-241	167	88	u	u	NOUN
ma-241	167	89	(	(	PUNCT
ma-241	167	90	k	k	NOUN
ma-241	167	91	)	)	PUNCT
ma-241	167	92	1,1	1,1	NUM
ma-241	167	93	−	−	NOUN
ma-241	168	1	p	p	X
ma-241	168	2	(	(	PUNCT
ma-241	168	3	k	k	NOUN
ma-241	168	4	)	)	PUNCT
ma-241	168	5	1	1	NUM
ma-241	169	1	+	+	NUM
ma-241	169	2	γu	γu	INTJ
ma-241	169	3	(	(	PUNCT
ma-241	169	4	k	k	NOUN
ma-241	169	5	)	)	PUNCT
ma-241	169	6	1,1	1,1	NUM
ma-241	169	7	=	=	SYM
ma-241	169	8	ν	ν	NOUN
ma-241	169	9	∂	∂	NOUN
ma-241	169	10	∂x	∂x	PROPN
ma-241	169	11	u	u	NOUN
ma-241	169	12	(	(	PUNCT
ma-241	169	13	k−1	k−1	PROPN
ma-241	169	14	)	)	PUNCT
ma-241	169	15	2,1	2,1	NUM
ma-241	169	16	−	−	NOUN
ma-241	169	17	p(k−1	p(k−1	NOUN
ma-241	169	18	)	)	PUNCT
ma-241	169	19	2	2	NUM
ma-241	170	1	+	+	NUM
ma-241	170	2	γu	γu	NOUN
ma-241	170	3	(	(	PUNCT
ma-241	170	4	k−1	k−1	PROPN
ma-241	170	5	)	)	PUNCT
ma-241	170	6	2,1	2,1	NUM
ma-241	170	7	at	at	ADP
ma-241	170	8	x	x	X
ma-241	170	9	=	=	SYM
ma-241	170	10	0	0	NUM
ma-241	170	11	,	,	PUNCT
ma-241	170	12	ν	ν	NOUN
ma-241	170	13	∂	∂	NOUN
ma-241	170	14	∂x	∂x	PROPN
ma-241	170	15	u	u	NOUN
ma-241	170	16	(	(	PUNCT
ma-241	170	17	k	k	NOUN
ma-241	170	18	)	)	PUNCT
ma-241	170	19	1,2	1,2	NUM
ma-241	170	20	+	+	NUM
ma-241	170	21	γu	γu	INTJ
ma-241	170	22	(	(	PUNCT
ma-241	170	23	k	k	NOUN
ma-241	170	24	)	)	PUNCT
ma-241	170	25	1,2	1,2	NUM
ma-241	170	26	=	=	SYM
ma-241	170	27	ν	ν	NOUN
ma-241	170	28	∂	∂	NUM
ma-241	170	29	∂x	∂x	PROPN
ma-241	170	30	u	u	NOUN
ma-241	170	31	(	(	PUNCT
ma-241	170	32	k−1	k−1	PROPN
ma-241	170	33	)	)	PUNCT
ma-241	170	34	2,2	2,2	PROPN
ma-241	170	35	+	+	NUM
ma-241	170	36	γu	γu	PROPN
ma-241	170	37	(	(	PUNCT
ma-241	170	38	k−1	k−1	PROPN
ma-241	170	39	)	)	PUNCT
ma-241	170	40	2,2	2,2	NUM
ma-241	170	41	at	at	ADP
ma-241	170	42	x	x	X
ma-241	170	43	=	=	SYM
ma-241	170	44	0	0	NUM
ma-241	170	45	,	,	PUNCT
ma-241	170	46	u	u	NOUN
ma-241	170	47	(	(	PUNCT
ma-241	170	48	k	k	NOUN
ma-241	170	49	)	)	PUNCT
ma-241	170	50	1,1	1,1	NUM
ma-241	170	51	:	:	PUNCT
ma-241	170	52	bounded	bound	VERB
ma-241	170	53	at	at	ADP
ma-241	170	54	−∞	−∞	PROPN
ma-241	170	55	,	,	PUNCT
ma-241	170	56	u	u	PROPN
ma-241	170	57	(	(	PUNCT
ma-241	170	58	k	k	NOUN
ma-241	170	59	)	)	PUNCT
ma-241	170	60	1,2	1,2	NUM
ma-241	170	61	:	:	PUNCT
ma-241	170	62	bounded	bound	VERB
ma-241	170	63	at	at	ADP
ma-241	170	64	−∞	−∞	PROPN
ma-241	170	65	,	,	PUNCT
ma-241	170	66	p	p	X
ma-241	170	67	(	(	PUNCT
ma-241	170	68	k	k	NOUN
ma-241	170	69	)	)	PUNCT
ma-241	170	70	1	1	NUM
ma-241	170	71	:	:	PUNCT
ma-241	170	72	bounded	bound	VERB
ma-241	170	73	at	at	ADP
ma-241	170	74	−∞	−∞	NOUN
ma-241	170	75	,	,	PUNCT
ma-241	170	76	(	(	PUNCT
ma-241	170	77	34	34	NUM
ma-241	170	78	)	)	PUNCT
ma-241	170	79			NUM
ma-241	170	80	∂2u	∂2u	X
ma-241	170	81	(	(	PUNCT
ma-241	170	82	k	k	NOUN
ma-241	170	83	)	)	PUNCT
ma-241	170	84	2,1	2,1	NUM
ma-241	170	85	∂x2	∂x2	NOUN
ma-241	170	86	+	+	CCONJ
ma-241	170	87	∂2u	∂2u	X
ma-241	170	88	(	(	PUNCT
ma-241	170	89	k	k	X
ma-241	170	90	)	)	PUNCT
ma-241	170	91	2,1	2,1	NUM
ma-241	170	92	∂y2	∂y2	NOUN
ma-241	170	93	=	=	SYM
ma-241	170	94	1	1	NUM
ma-241	170	95	ν	ν	X
ma-241	170	96	∂p	∂p	PROPN
ma-241	170	97	(	(	PUNCT
ma-241	170	98	k	k	NOUN
ma-241	170	99	)	)	PUNCT
ma-241	170	100	2	2	NUM
ma-241	170	101	∂x	∂x	PROPN
ma-241	170	102	in	in	ADP
ma-241	170	103	ω2	ω2	ADJ
ma-241	170	104	,	,	PUNCT
ma-241	170	105	∂2u	∂2u	X
ma-241	170	106	(	(	PUNCT
ma-241	170	107	k	k	NOUN
ma-241	170	108	)	)	PUNCT
ma-241	170	109	2,2	2,2	NUM
ma-241	170	110	∂x2	∂x2	NOUN
ma-241	170	111	+	+	CCONJ
ma-241	170	112	∂2u	∂2u	X
ma-241	170	113	(	(	PUNCT
ma-241	170	114	k	k	NOUN
ma-241	170	115	)	)	PUNCT
ma-241	170	116	2,2	2,2	NUM
ma-241	170	117	∂y2	∂y2	NOUN
ma-241	170	118	=	=	NOUN
ma-241	170	119	1	1	NUM
ma-241	170	120	ν	ν	X
ma-241	170	121	∂p	∂p	PROPN
ma-241	170	122	(	(	PUNCT
ma-241	170	123	k	k	NOUN
ma-241	170	124	)	)	PUNCT
ma-241	170	125	2	2	NUM
ma-241	170	126	∂y	∂y	PROPN
ma-241	170	127	in	in	ADP
ma-241	170	128	ω2	ω2	PROPN
ma-241	170	129	,	,	PUNCT
ma-241	170	130	∂u	∂u	PROPN
ma-241	170	131	(	(	PUNCT
ma-241	170	132	k	k	NOUN
ma-241	170	133	)	)	PUNCT
ma-241	170	134	2,1	2,1	NUM
ma-241	170	135	∂x	∂x	PROPN
ma-241	171	1	+	+	CCONJ
ma-241	171	2	∂u	∂u	PROPN
ma-241	171	3	(	(	PUNCT
ma-241	171	4	k	k	NOUN
ma-241	171	5	)	)	PUNCT
ma-241	171	6	2,2	2,2	NUM
ma-241	172	1	∂y	∂y	SYM
ma-241	172	2	=	=	NOUN
ma-241	172	3	0	0	NUM
ma-241	172	4	in	in	ADP
ma-241	172	5	ω2	ω2	NUM
ma-241	172	6	,	,	PUNCT
ma-241	172	7	ν	ν	X
ma-241	172	8	∂	∂	NUM
ma-241	172	9	∂x	∂x	PROPN
ma-241	172	10	u	u	NOUN
ma-241	172	11	(	(	PUNCT
ma-241	172	12	k	k	NOUN
ma-241	172	13	)	)	PUNCT
ma-241	172	14	2,1	2,1	NUM
ma-241	172	15	−	−	NOUN
ma-241	173	1	p	p	X
ma-241	173	2	(	(	PUNCT
ma-241	173	3	k	k	NOUN
ma-241	173	4	)	)	PUNCT
ma-241	173	5	2	2	NUM
ma-241	173	6	−	−	NOUN
ma-241	173	7	γu(k	γu(k	NUM
ma-241	173	8	)	)	PUNCT
ma-241	173	9	2,1	2,1	NUM
ma-241	173	10	=	=	SYM
ma-241	173	11	ν	ν	NOUN
ma-241	173	12	∂	∂	NOUN
ma-241	173	13	∂x	∂x	PROPN
ma-241	173	14	u	u	NOUN
ma-241	173	15	(	(	PUNCT
ma-241	173	16	k−1	k−1	PROPN
ma-241	173	17	)	)	PUNCT
ma-241	173	18	1,1	1,1	NUM
ma-241	173	19	−	−	NOUN
ma-241	173	20	p(k−1	p(k−1	NOUN
ma-241	173	21	)	)	PUNCT
ma-241	173	22	1	1	NUM
ma-241	173	23	−	−	NOUN
ma-241	173	24	γu(k−1	γu(k−1	NOUN
ma-241	173	25	)	)	PUNCT
ma-241	173	26	1,1	1,1	NUM
ma-241	173	27	at	at	ADP
ma-241	173	28	x	x	X
ma-241	173	29	=	=	SYM
ma-241	173	30	0	0	NUM
ma-241	173	31	,	,	PUNCT
ma-241	173	32	ν	ν	NOUN
ma-241	173	33	∂	∂	NOUN
ma-241	173	34	∂x	∂x	PROPN
ma-241	173	35	u	u	NOUN
ma-241	173	36	(	(	PUNCT
ma-241	173	37	k	k	NOUN
ma-241	173	38	)	)	PUNCT
ma-241	173	39	2,2	2,2	NUM
ma-241	173	40	−	−	PROPN
ma-241	173	41	γu	γu	NOUN
ma-241	173	42	(	(	PUNCT
ma-241	173	43	k	k	NOUN
ma-241	173	44	)	)	PUNCT
ma-241	173	45	2,2	2,2	NUM
ma-241	173	46	=	=	SYM
ma-241	173	47	ν	ν	NOUN
ma-241	173	48	∂	∂	NUM
ma-241	173	49	∂x	∂x	PROPN
ma-241	173	50	u	u	NOUN
ma-241	173	51	(	(	PUNCT
ma-241	173	52	k−1	k−1	PROPN
ma-241	173	53	)	)	PUNCT
ma-241	173	54	1,2	1,2	NUM
ma-241	173	55	−	−	NOUN
ma-241	173	56	γu(k−1	γu(k−1	NOUN
ma-241	173	57	)	)	PUNCT
ma-241	173	58	1,2	1,2	NUM
ma-241	173	59	at	at	ADP
ma-241	173	60	x	x	X
ma-241	174	1	=	=	SYM
ma-241	174	2	0	0	NUM
ma-241	174	3	,	,	PUNCT
ma-241	174	4	u	u	NOUN
ma-241	174	5	(	(	PUNCT
ma-241	174	6	k	k	NOUN
ma-241	174	7	)	)	PUNCT
ma-241	174	8	2,1	2,1	NUM
ma-241	174	9	:	:	PUNCT
ma-241	174	10	bounded	bound	VERB
ma-241	174	11	at	at	ADP
ma-241	174	12	+	+	PROPN
ma-241	174	13	∞	∞	PROPN
ma-241	174	14	,	,	PUNCT
ma-241	174	15	u	u	NOUN
ma-241	174	16	(	(	PUNCT
ma-241	174	17	k	k	NOUN
ma-241	174	18	)	)	PUNCT
ma-241	174	19	2,2	2,2	NUM
ma-241	174	20	:	:	PUNCT
ma-241	174	21	bounded	bound	VERB
ma-241	174	22	at	at	ADP
ma-241	174	23	+	+	PROPN
ma-241	174	24	∞	∞	PROPN
ma-241	174	25	,	,	PUNCT
ma-241	174	26	p	p	X
ma-241	174	27	(	(	PUNCT
ma-241	174	28	k	k	NOUN
ma-241	174	29	)	)	PUNCT
ma-241	174	30	2	2	NUM
ma-241	174	31	:	:	PUNCT
ma-241	174	32	bounded	bound	VERB
ma-241	174	33	at	at	ADP
ma-241	174	34	+	+	PROPN
ma-241	174	35	∞.	∞.	PROPN
ma-241	174	36	(	(	PUNCT
ma-241	174	37	35	35	NUM
ma-241	174	38	)	)	PUNCT
ma-241	174	39	we	we	PRON
ma-241	174	40	employ	employ	VERB
ma-241	174	41	the	the	DET
ma-241	174	42	fourier	fourier	NOUN
ma-241	174	43	transform	transform	NOUN
ma-241	174	44	for	for	ADP
ma-241	174	45	the	the	DET
ma-241	174	46	local	local	ADJ
ma-241	174	47	schwarz	schwarz	PROPN
ma-241	174	48	subproblems	subproblem	NOUN
ma-241	174	49	(	(	PUNCT
ma-241	174	50	34	34	NUM
ma-241	174	51	)	)	PUNCT
ma-241	174	52	,	,	PUNCT
ma-241	174	53	(	(	PUNCT
ma-241	174	54	35	35	NUM
ma-241	174	55	)	)	PUNCT
ma-241	174	56	.	.	PUNCT
ma-241	175	1	the	the	DET
ma-241	175	2	fourier	fourier	NOUN
ma-241	175	3	trans	trans	PROPN
ma-241	175	4	-	-	ADJ
ma-241	175	5	formed	form	VERB
ma-241	175	6	velocity	velocity	NOUN
ma-241	175	7	components	component	NOUN
ma-241	175	8	are	be	AUX
ma-241	175	9	given	give	VERB
ma-241	175	10	by	by	ADP
ma-241	175	11	the	the	DET
ma-241	175	12	mathematical	mathematical	ADJ
ma-241	175	13	expressions	expression	NOUN
ma-241	175	14	(	(	PUNCT
ma-241	175	15	9	9	NUM
ma-241	175	16	)	)	PUNCT
ma-241	175	17	,	,	PUNCT
ma-241	175	18	(	(	PUNCT
ma-241	175	19	10	10	NUM
ma-241	175	20	)	)	PUNCT
ma-241	175	21	,	,	PUNCT
ma-241	175	22	(	(	PUNCT
ma-241	175	23	11	11	NUM
ma-241	175	24	)	)	PUNCT
ma-241	175	25	,	,	PUNCT
ma-241	175	26	(	(	PUNCT
ma-241	175	27	12	12	NUM
ma-241	175	28	)	)	PUNCT
ma-241	175	29	.	.	PUNCT
ma-241	176	1	thefourier	thefourier	PROPN
ma-241	176	2	transformed	transform	VERB
ma-241	176	3	pressure	pressure	NOUN
ma-241	176	4	fields	field	NOUN
ma-241	176	5	are	be	AUX
ma-241	176	6	given	give	VERB
ma-241	176	7	by	by	ADP
ma-241	176	8	p̂(k	p̂(k	NOUN
ma-241	176	9	)	)	PUNCT
ma-241	176	10	1	1	NUM
ma-241	176	11	=	=	SYM
ma-241	176	12	d(k	d(k	PROPN
ma-241	176	13	)	)	PUNCT
ma-241	176	14	1	1	NUM
ma-241	176	15	e	e	X
ma-241	176	16	|ξ|x	|ξ|x	PROPN
ma-241	176	17	,	,	PUNCT
ma-241	176	18	p̂(k	p̂(k	NOUN
ma-241	176	19	)	)	PUNCT
ma-241	176	20	2	2	NUM
ma-241	176	21	=	=	SYM
ma-241	176	22	c(k	c(k	NOUN
ma-241	176	23	)	)	PUNCT
ma-241	176	24	2	2	NUM
ma-241	176	25	e−|ξ|x	e−|ξ|x	ADV
ma-241	176	26	.	.	PUNCT
ma-241	177	1	we	we	PRON
ma-241	177	2	substitutethe	substitutethe	VERB
ma-241	177	3	velocities	velocity	NOUN
ma-241	177	4	and	and	CCONJ
ma-241	177	5	pressure	pressure	NOUN
ma-241	177	6	fields	field	NOUN
ma-241	177	7	back	back	ADV
ma-241	177	8	to	to	ADP
ma-241	177	9	the	the	DET
ma-241	177	10	transmission	transmission	NOUN
ma-241	177	11	conditions	condition	NOUN
ma-241	177	12	(	(	PUNCT
ma-241	177	13	34)4	34)4	NUM
ma-241	177	14	,	,	PUNCT
ma-241	177	15	(	(	PUNCT
ma-241	177	16	34)5	34)5	NUM
ma-241	177	17	,	,	PUNCT
ma-241	177	18	(	(	PUNCT
ma-241	177	19	35)4	35)4	NUM
ma-241	177	20	,	,	PUNCT
ma-241	177	21	(	(	PUNCT
ma-241	177	22	35)5	35)5	PRON
ma-241	177	23	,	,	PUNCT
ma-241	177	24	andby	andby	NOUN
ma-241	177	25	doing	do	VERB
ma-241	177	26	some	some	DET
ma-241	177	27	algebraic	algebraic	ADJ
ma-241	177	28	manipulations	manipulation	NOUN
ma-241	177	29	we	we	PRON
ma-241	177	30	obtain	obtain	VERB
ma-241	177	31	b(k	b(k	PROPN
ma-241	177	32	)	)	PUNCT
ma-241	177	33	1	1	NUM
ma-241	177	34	(	(	PUNCT
ma-241	177	35	2γ	2γ	NOUN
ma-241	177	36	+	+	X
ma-241	177	37	2ν|ξ|)−d(k	2ν|ξ|)−d(k	NUM
ma-241	177	38	)	)	PUNCT
ma-241	177	39	1	1	NUM
ma-241	177	40	=	=	SYM
ma-241	177	41	b(k−1	b(k−1	X
ma-241	177	42	)	)	PUNCT
ma-241	177	43	2	2	NUM
ma-241	177	44	(	(	PUNCT
ma-241	177	45	2γ	2γ	VERB
ma-241	177	46	−	−	PROPN
ma-241	177	47	2ν|ξ|	2ν|ξ|	NUM
ma-241	177	48	)	)	PUNCT
ma-241	177	49	−	−	NOUN
ma-241	177	50	c(k−1	c(k−1	NOUN
ma-241	177	51	)	)	PUNCT
ma-241	177	52	2	2	NUM
ma-241	177	53	,	,	PUNCT
ma-241	177	54	(	(	PUNCT
ma-241	177	55	36	36	NUM
ma-241	177	56	)	)	PUNCT
ma-241	177	57	b(k	b(k	PROPN
ma-241	177	58	)	)	PUNCT
ma-241	177	59	1	1	NUM
ma-241	178	1	(	(	PUNCT
ma-241	178	2	2ν2|ξ|2	2ν2|ξ|2	NUM
ma-241	178	3	+	+	CCONJ
ma-241	178	4	2νγ|ξ|	2νγ|ξ|	NOUN
ma-241	178	5	)	)	PUNCT
ma-241	179	1	+	+	PROPN
ma-241	179	2	d(k	d(k	PROPN
ma-241	179	3	)	)	PUNCT
ma-241	179	4	1	1	NUM
ma-241	179	5	(	(	PUNCT
ma-241	179	6	2ν|ξ|	2ν|ξ|	NUM
ma-241	179	7	+	+	CCONJ
ma-241	179	8	γ	γ	X
ma-241	179	9	)	)	PUNCT
ma-241	179	10	=	=	PUNCT
ma-241	179	11	b(k−1	b(k−1	X
ma-241	179	12	)	)	PUNCT
ma-241	179	13	2	2	NUM
ma-241	179	14	(	(	PUNCT
ma-241	179	15	2ν2|ξ|2	2ν2|ξ|2	NUM
ma-241	179	16	−	−	PROPN
ma-241	179	17	2νγ|ξ|	2νγ|ξ|	PROPN
ma-241	179	18	)	)	PUNCT
ma-241	180	1	+	+	CCONJ
ma-241	180	2	c(k−1	c(k−1	X
ma-241	180	3	)	)	PUNCT
ma-241	180	4	2	2	NUM
ma-241	180	5	(	(	PUNCT
ma-241	180	6	γ	γ	PROPN
ma-241	180	7	−	−	PROPN
ma-241	180	8	2ν|ξ|),(37	2ν|ξ|),(37	NUM
ma-241	180	9	)	)	PUNCT
ma-241	180	10	b(k	b(k	PROPN
ma-241	180	11	)	)	PUNCT
ma-241	180	12	2	2	NUM
ma-241	180	13	(	(	PUNCT
ma-241	180	14	2γ	2γ	NOUN
ma-241	180	15	+	+	X
ma-241	180	16	2ν|ξ|	2ν|ξ|	NUM
ma-241	180	17	)	)	PUNCT
ma-241	181	1	+	+	CCONJ
ma-241	181	2	c(k	c(k	NOUN
ma-241	181	3	)	)	PUNCT
ma-241	181	4	2	2	NUM
ma-241	181	5	=	=	SYM
ma-241	181	6	b(k−1	b(k−1	X
ma-241	181	7	)	)	PUNCT
ma-241	181	8	1	1	NUM
ma-241	181	9	(	(	PUNCT
ma-241	181	10	2γ	2γ	VERB
ma-241	181	11	−	−	PROPN
ma-241	181	12	2ν|ξ|	2ν|ξ|	NUM
ma-241	181	13	)	)	PUNCT
ma-241	181	14	+	+	NOUN
ma-241	181	15	d(k−1	d(k−1	NOUN
ma-241	181	16	)	)	PUNCT
ma-241	181	17	1	1	NUM
ma-241	181	18	,	,	PUNCT
ma-241	181	19	(	(	PUNCT
ma-241	181	20	38	38	NUM
ma-241	181	21	)	)	PUNCT
ma-241	181	22	b(k	b(k	PROPN
ma-241	181	23	)	)	PUNCT
ma-241	181	24	2	2	NUM
ma-241	181	25	(	(	PUNCT
ma-241	181	26	2νγ|ξ|+	2νγ|ξ|+	NUM
ma-241	181	27	2ν2|ξ|2	2ν2|ξ|2	NUM
ma-241	181	28	)	)	PUNCT
ma-241	181	29	−	−	PRON
ma-241	181	30	c(k	c(k	NOUN
ma-241	181	31	)	)	PUNCT
ma-241	181	32	2	2	NUM
ma-241	181	33	(	(	PUNCT
ma-241	181	34	2ν|ξ|+	2ν|ξ|+	NUM
ma-241	181	35	γ	γ	NOUN
ma-241	181	36	)	)	PUNCT
ma-241	181	37	=	=	PUNCT
ma-241	181	38	b(k−1	b(k−1	X
ma-241	181	39	)	)	PUNCT
ma-241	181	40	1	1	NUM
ma-241	181	41	(	(	PUNCT
ma-241	181	42	2ν2|ξ|2	2ν2|ξ|2	NUM
ma-241	181	43	−	−	PROPN
ma-241	181	44	2νγ|ξ|	2νγ|ξ|	NOUN
ma-241	181	45	)	)	PUNCT
ma-241	182	1	+	+	NOUN
ma-241	182	2	d(k−1	d(k−1	X
ma-241	182	3	)	)	PUNCT
ma-241	182	4	1	1	NUM
ma-241	182	5	(	(	PUNCT
ma-241	182	6	2ν|ξ|	2ν|ξ|	NUM
ma-241	182	7	−	−	NUM
ma-241	182	8	γ).(39	γ).(39	NOUN
ma-241	182	9	)	)	PUNCT
ma-241	182	10	we	we	PRON
ma-241	182	11	pick	pick	VERB
ma-241	182	12	(	(	PUNCT
ma-241	182	13	38	38	NUM
ma-241	182	14	)	)	PUNCT
ma-241	182	15	and	and	CCONJ
ma-241	182	16	we	we	PRON
ma-241	182	17	obtain	obtain	VERB
ma-241	182	18	the	the	DET
ma-241	182	19	coefficients	coefficient	NOUN
ma-241	182	20	d(k	d(k	PROPN
ma-241	182	21	)	)	PUNCT
ma-241	182	22	1	1	NUM
ma-241	182	23	=	=	SYM
ma-241	182	24	b(k+1	b(k+1	PROPN
ma-241	182	25	)	)	PUNCT
ma-241	182	26	2	2	NUM
ma-241	182	27	(	(	PUNCT
ma-241	182	28	2γ	2γ	X
ma-241	182	29	+	+	X
ma-241	182	30	2ν|ξ|	2ν|ξ|	NUM
ma-241	182	31	)	)	PUNCT
ma-241	182	32	+	+	NUM
ma-241	182	33	c(k+1	c(k+1	NOUN
ma-241	182	34	)	)	PUNCT
ma-241	182	35	2	2	NUM
ma-241	182	36	−	−	PROPN
ma-241	182	37	b(k	b(k	PROPN
ma-241	182	38	)	)	PUNCT
ma-241	182	39	1	1	NUM
ma-241	182	40	(	(	PUNCT
ma-241	182	41	2γ	2γ	VERB
ma-241	182	42	−	−	PROPN
ma-241	182	43	2ν|ξ|	2ν|ξ|	NUM
ma-241	182	44	)	)	PUNCT
ma-241	182	45	.	.	PUNCT
ma-241	183	1	(	(	PUNCT
ma-241	183	2	40	40	NUM
ma-241	183	3	)	)	PUNCT
ma-241	183	4	https://doi.org/10.28924/ada/ma.5.6	https://doi.org/10.28924/ada/ma.5.6	PROPN
ma-241	183	5	eur	eur	PROPN
ma-241	183	6	.	.	PUNCT
ma-241	184	1	j.	j.	PROPN
ma-241	184	2	math	math	PROPN
ma-241	184	3	.	.	PUNCT
ma-241	185	1	anal	anal	PROPN
ma-241	185	2	.	.	PUNCT
ma-241	186	1	10.28924	10.28924	NUM
ma-241	186	2	/	/	SYM
ma-241	186	3	ada	ada	PROPN
ma-241	186	4	/	/	SYM
ma-241	186	5	ma.5.6	ma.5.6	PROPN
ma-241	186	6	10we	10we	NOUN
ma-241	186	7	substitiute	substitiute	NOUN
ma-241	186	8	the	the	DET
ma-241	186	9	coefficients	coefficient	NOUN
ma-241	186	10	(	(	PUNCT
ma-241	186	11	40	40	NUM
ma-241	186	12	)	)	PUNCT
ma-241	186	13	back	back	ADV
ma-241	186	14	to	to	ADP
ma-241	186	15	(	(	PUNCT
ma-241	186	16	36	36	NUM
ma-241	186	17	)	)	PUNCT
ma-241	186	18	and	and	CCONJ
ma-241	186	19	we	we	PRON
ma-241	186	20	obtain	obtain	VERB
ma-241	186	21	4	4	NUM
ma-241	186	22	©	©	PROPN
ma-241	186	23	b(k	b(k	PROPN
ma-241	186	24	)	)	PUNCT
ma-241	186	25	1	1	NUM
ma-241	186	26	=	=	SYM
ma-241	186	27	b(k+1	b(k+1	PROPN
ma-241	186	28	)	)	PUNCT
ma-241	186	29	2	2	NUM
ma-241	186	30	(	(	PUNCT
ma-241	186	31	2γ	2γ	X
ma-241	186	32	+	+	X
ma-241	186	33	2ν|ξ|	2ν|ξ|	NUM
ma-241	186	34	)	)	PUNCT
ma-241	186	35	+	+	NUM
ma-241	186	36	c(k+1	c(k+1	NOUN
ma-241	186	37	)	)	PUNCT
ma-241	186	38	2	2	NUM
ma-241	186	39	+	+	CCONJ
ma-241	186	40	b(k−1	b(k−1	X
ma-241	186	41	)	)	PUNCT
ma-241	186	42	2	2	NUM
ma-241	186	43	(	(	PUNCT
ma-241	186	44	2γ	2γ	NOUN
ma-241	186	45	−	−	PROPN
ma-241	186	46	2ν|ξ|)−	2ν|ξ|)−	PROPN
ma-241	186	47	c(k−1	c(k−1	PROPN
ma-241	186	48	)	)	PUNCT
ma-241	186	49	2	2	NUM
ma-241	186	50	.	.	PUNCT
ma-241	187	1	(	(	PUNCT
ma-241	187	2	41)the	41)the	DET
ma-241	187	3	equation	equation	NOUN
ma-241	187	4	(	(	PUNCT
ma-241	187	5	40	40	NUM
ma-241	187	6	)	)	PUNCT
ma-241	187	7	can	can	AUX
ma-241	187	8	take	take	VERB
ma-241	187	9	the	the	DET
ma-241	187	10	following	follow	VERB
ma-241	187	11	form	form	NOUN
ma-241	187	12	4	4	NUM
ma-241	187	13	©	©	PROPN
ma-241	187	14	d(k	d(k	PROPN
ma-241	187	15	)	)	PUNCT
ma-241	187	16	1	1	NUM
ma-241	187	17	=	=	SYM
ma-241	187	18	b(k+1	b(k+1	PROPN
ma-241	187	19	)	)	PUNCT
ma-241	187	20	2	2	NUM
ma-241	187	21	(	(	PUNCT
ma-241	187	22	2γ+2ν|ξ|)2+c(k+1	2γ+2ν|ξ|)2+c(k+1	NUM
ma-241	187	23	)	)	PUNCT
ma-241	187	24	2	2	NUM
ma-241	187	25	(	(	PUNCT
ma-241	187	26	2γ+2ν|ξ|)−b(k−1	2γ+2ν|ξ|)−b(k−1	NUM
ma-241	187	27	)	)	PUNCT
ma-241	187	28	2	2	NUM
ma-241	187	29	(	(	PUNCT
ma-241	187	30	2γ−2ν|ξ|)2+c(k−1	2γ−2ν|ξ|)2+c(k−1	NOUN
ma-241	187	31	)	)	PUNCT
ma-241	187	32	2	2	NUM
ma-241	187	33	(	(	PUNCT
ma-241	187	34	2γ−2ν|ξ|	2γ−2ν|ξ|	NUM
ma-241	187	35	)	)	PUNCT
ma-241	187	36	(	(	PUNCT
ma-241	187	37	42	42	NUM
ma-241	187	38	)	)	PUNCT
ma-241	187	39	by	by	ADP
ma-241	187	40	employing	employ	VERB
ma-241	187	41	(	(	PUNCT
ma-241	187	42	41	41	NUM
ma-241	187	43	)	)	PUNCT
ma-241	187	44	.	.	PUNCT
ma-241	188	1	we	we	PRON
ma-241	188	2	take	take	VERB
ma-241	188	3	the	the	DET
ma-241	188	4	relation	relation	NOUN
ma-241	188	5	(	(	PUNCT
ma-241	188	6	37	37	NUM
ma-241	188	7	)	)	PUNCT
ma-241	188	8	,	,	PUNCT
ma-241	188	9	multiply	multiply	ADP
ma-241	188	10	with	with	ADP
ma-241	188	11	4γ	4γ	NOUN
ma-241	188	12	,	,	PUNCT
ma-241	188	13	and	and	CCONJ
ma-241	188	14	then	then	ADV
ma-241	188	15	plug	plug	VERB
ma-241	188	16	in	in	ADP
ma-241	188	17	(	(	PUNCT
ma-241	188	18	41	41	NUM
ma-241	188	19	)	)	PUNCT
ma-241	188	20	,	,	PUNCT
ma-241	188	21	(	(	PUNCT
ma-241	188	22	42	42	NUM
ma-241	188	23	)	)	PUNCT
ma-241	188	24	to	to	PART
ma-241	188	25	obtain	obtain	VERB
ma-241	188	26	k1b(k+1	k1b(k+1	NOUN
ma-241	188	27	)	)	PUNCT
ma-241	188	28	2	2	NUM
ma-241	188	29	+	+	CCONJ
ma-241	188	30	k2c(k+1	k2c(k+1	NOUN
ma-241	188	31	)	)	PUNCT
ma-241	188	32	2	2	NUM
ma-241	188	33	=	=	SYM
ma-241	188	34	k3b(k−1	k3b(k−1	PROPN
ma-241	188	35	)	)	PUNCT
ma-241	188	36	2	2	NUM
ma-241	188	37	+	+	NUM
ma-241	188	38	k4c(k−1	k4c(k−1	NOUN
ma-241	188	39	)	)	PUNCT
ma-241	188	40	2	2	NUM
ma-241	188	41	(	(	PUNCT
ma-241	188	42	43	43	NUM
ma-241	188	43	)	)	PUNCT
ma-241	188	44	where	where	SCONJ
ma-241	188	45	k1	k1	NOUN
ma-241	188	46	,	,	PUNCT
ma-241	188	47	k2	k2	PROPN
ma-241	188	48	,	,	PUNCT
ma-241	188	49	k3	k3	PROPN
ma-241	188	50	,	,	PUNCT
ma-241	188	51	k4	k4	PROPN
ma-241	188	52	are	be	AUX
ma-241	188	53	given	give	VERB
ma-241	188	54	by	by	ADP
ma-241	188	55	the	the	DET
ma-241	188	56	relations	relation	NOUN
ma-241	188	57	below	below	ADP
ma-241	188	58	k1	k1	NOUN
ma-241	188	59	=	=	SYM
ma-241	188	60	12	12	NUM
ma-241	188	61	(	(	PUNCT
ma-241	188	62	ν|ξ|+	ν|ξ|+	PROPN
ma-241	188	63	γ	γ	X
ma-241	188	64	3	3	NUM
ma-241	188	65	)	)	PUNCT
ma-241	188	66	(	(	PUNCT
ma-241	188	67	ν|ξ|+	ν|ξ|+	PROPN
ma-241	188	68	γ)2	γ)2	PROPN
ma-241	188	69	,	,	PUNCT
ma-241	188	70	k2	k2	NOUN
ma-241	188	71	=	=	PROPN
ma-241	188	72	6ν2|ξ|2	6ν2|ξ|2	NUM
ma-241	188	73	+	+	NUM
ma-241	188	74	8ν|ξ|γ	8ν|ξ|γ	NUM
ma-241	189	1	+	+	CCONJ
ma-241	189	2	2γ2	2γ2	NUM
ma-241	189	3	,	,	PUNCT
ma-241	189	4	k3	k3	ADJ
ma-241	189	5	=	=	PROPN
ma-241	189	6	12|ξ|3ν3	12|ξ|3ν3	PROPN
ma-241	189	7	−	−	NOUN
ma-241	189	8	4|ξ|2γν2	4|ξ|2γν2	NUM
ma-241	190	1	−	−	PROPN
ma-241	190	2	12|ξ|γ2ν	12|ξ|γ2ν	PROPN
ma-241	190	3	+	+	CCONJ
ma-241	190	4	4γ3	4γ3	NUM
ma-241	190	5	,	,	PUNCT
ma-241	190	6	k4	k4	NOUN
ma-241	190	7	=	=	SYM
ma-241	191	1	6ν2|ξ|2	6ν2|ξ|2	NUM
ma-241	191	2	−	−	PROPN
ma-241	191	3	8ν|ξ|γ	8ν|ξ|γ	NUM
ma-241	192	1	+	+	CCONJ
ma-241	192	2	2γ2	2γ2	X
ma-241	192	3	.	.	PUNCT
ma-241	193	1	in	in	ADP
ma-241	193	2	the	the	DET
ma-241	193	3	same	same	ADJ
ma-241	193	4	fashion	fashion	NOUN
ma-241	193	5	,	,	PUNCT
ma-241	193	6	we	we	PRON
ma-241	193	7	pick	pick	VERB
ma-241	193	8	(	(	PUNCT
ma-241	193	9	39	39	NUM
ma-241	193	10	)	)	PUNCT
ma-241	193	11	,	,	PUNCT
ma-241	193	12	multiply	multiply	ADP
ma-241	193	13	with	with	ADP
ma-241	193	14	4γ	4γ	NOUN
ma-241	193	15	,	,	PUNCT
ma-241	193	16	and	and	CCONJ
ma-241	193	17	then	then	ADV
ma-241	193	18	exploit	exploit	VERB
ma-241	193	19	the	the	DET
ma-241	193	20	expressions	expression	NOUN
ma-241	193	21	(	(	PUNCT
ma-241	193	22	41	41	NUM
ma-241	193	23	)	)	PUNCT
ma-241	193	24	,	,	PUNCT
ma-241	193	25	(	(	PUNCT
ma-241	193	26	42	42	X
ma-241	193	27	)	)	PUNCT
ma-241	193	28	toderive	toderive	NOUN
ma-241	193	29	the	the	DET
ma-241	193	30	equation	equation	NOUN
ma-241	193	31	q1b(k+1	q1b(k+1	VERB
ma-241	193	32	)	)	PUNCT
ma-241	193	33	2	2	NUM
ma-241	193	34	+	+	NUM
ma-241	193	35	q2c(k+1	q2c(k+1	NOUN
ma-241	193	36	)	)	PUNCT
ma-241	193	37	2	2	NUM
ma-241	193	38	=	=	SYM
ma-241	193	39	q3b(k−1	q3b(k−1	NOUN
ma-241	193	40	)	)	PUNCT
ma-241	193	41	2	2	NUM
ma-241	194	1	+	+	NUM
ma-241	194	2	q4c(k−1	q4c(k−1	NOUN
ma-241	194	3	)	)	PUNCT
ma-241	194	4	2	2	NUM
ma-241	195	1	(	(	PUNCT
ma-241	195	2	44)where	44)where	PROPN
ma-241	195	3	q1	q1	PROPN
ma-241	195	4	,	,	PUNCT
ma-241	195	5	q2	q2	PROPN
ma-241	195	6	,	,	PUNCT
ma-241	195	7	q3	q3	PROPN
ma-241	195	8	,	,	PUNCT
ma-241	195	9	q4	q4	PROPN
ma-241	195	10	are	be	AUX
ma-241	195	11	provided	provide	VERB
ma-241	195	12	by	by	ADP
ma-241	195	13	the	the	DET
ma-241	195	14	expressions	expression	NOUN
ma-241	195	15	q1	q1	NOUN
ma-241	195	16	=	=	NOUN
ma-241	195	17	12|ξ|3ν2	12|ξ|3ν2	NUM
ma-241	196	1	+	+	CCONJ
ma-241	197	1	4|ξ|2γν2	4|ξ|2γν2	NUM
ma-241	197	2	−	−	NUM
ma-241	198	1	12|ξ|γ2ν	12|ξ|γ2ν	NUM
ma-241	198	2	−	−	PROPN
ma-241	198	3	4γ3	4γ3	NUM
ma-241	198	4	,	,	PUNCT
ma-241	198	5	q2	q2	NOUN
ma-241	198	6	=	=	PUNCT
ma-241	199	1	6ν2|ξ|2	6ν2|ξ|2	NUM
ma-241	199	2	+	+	NUM
ma-241	199	3	8νγ|ξ|+	8νγ|ξ|+	NUM
ma-241	199	4	2γ2	2γ2	NUM
ma-241	199	5	,	,	PUNCT
ma-241	199	6	q3	q3	NOUN
ma-241	199	7	=	=	PROPN
ma-241	199	8	12	12	NUM
ma-241	199	9	(	(	PUNCT
ma-241	199	10	ν|ξ|	ν|ξ|	NOUN
ma-241	199	11	−	−	PROPN
ma-241	199	12	γ	γ	NOUN
ma-241	199	13	3	3	NUM
ma-241	199	14	)	)	PUNCT
ma-241	199	15	(	(	PUNCT
ma-241	199	16	ν|ξ|	ν|ξ|	NOUN
ma-241	199	17	−	−	PROPN
ma-241	199	18	γ)2	γ)2	NOUN
ma-241	199	19	,	,	PUNCT
ma-241	199	20	q4	q4	PROPN
ma-241	199	21	=	=	PROPN
ma-241	200	1	6ν2|ξ|2	6ν2|ξ|2	NUM
ma-241	200	2	−	−	PROPN
ma-241	200	3	8νγ|ξ|+	8νγ|ξ|+	NUM
ma-241	200	4	2γ2	2γ2	NUM
ma-241	200	5	.	.	PUNCT
ma-241	201	1	we	we	PRON
ma-241	201	2	take	take	VERB
ma-241	201	3	(	(	PUNCT
ma-241	201	4	43	43	NUM
ma-241	201	5	)	)	PUNCT
ma-241	201	6	,	,	PUNCT
ma-241	201	7	(	(	PUNCT
ma-241	201	8	44	44	NUM
ma-241	201	9	)	)	PUNCT
ma-241	201	10	and	and	CCONJ
ma-241	201	11	after	after	ADP
ma-241	201	12	some	some	DET
ma-241	201	13	algebraic	algebraic	ADJ
ma-241	201	14	manipulations	manipulation	NOUN
ma-241	201	15	we	we	PRON
ma-241	201	16	obtain	obtain	VERB
ma-241	201	17	a	a	DET
ma-241	201	18	stationary	stationary	ADJ
ma-241	201	19	iteration	iteration	NOUN
ma-241	201	20	[	[	PUNCT
ma-241	201	21	b(k+1	b(k+1	NOUN
ma-241	201	22	)	)	PUNCT
ma-241	201	23	2	2	NUM
ma-241	201	24	c	c	NOUN
ma-241	201	25	(	(	PUNCT
ma-241	201	26	k+1	k+1	NOUN
ma-241	201	27	)	)	PUNCT
ma-241	201	28	2	2	NUM
ma-241	201	29	]	]	PUNCT
ma-241	201	30	=	=	PUNCT
ma-241	201	31	[	[	PUNCT
ma-241	201	32	3ν2|ξ|2−4ν|ξ|γ+γ2	3ν2|ξ|2−4ν|ξ|γ+γ2	NUM
ma-241	201	33	3ν2|ξ|2	3ν2|ξ|2	NUM
ma-241	201	34	+	+	PROPN
ma-241	201	35	4ν|ξ|γ+γ2	4ν|ξ|γ+γ2	NUM
ma-241	201	36	0	0	NUM
ma-241	201	37	0	0	NUM
ma-241	201	38	3ν2|ξ|2−4ν|ξ|γ+γ2	3ν2|ξ|2−4ν|ξ|γ+γ2	NUM
ma-241	201	39	3ν2|ξ|2	3ν2|ξ|2	NUM
ma-241	201	40	+	+	PROPN
ma-241	201	41	4ν|ξ|γ+γ2	4ν|ξ|γ+γ2	NOUN
ma-241	201	42	]	]	PUNCT
ma-241	201	43	︸	︸	X
ma-241	202	1	︷︷	︷︷	PROPN
ma-241	202	2	︸	︸	X
ma-241	202	3	ψosm	ψosm	NOUN
ma-241	202	4	[	[	PUNCT
ma-241	202	5	b(k−1	b(k−1	NOUN
ma-241	202	6	)	)	PUNCT
ma-241	202	7	2	2	NUM
ma-241	202	8	c	c	NOUN
ma-241	202	9	(	(	PUNCT
ma-241	202	10	k−1	k−1	PROPN
ma-241	202	11	)	)	PUNCT
ma-241	202	12	2	2	NUM
ma-241	202	13	]	]	PUNCT
ma-241	202	14	.	.	PUNCT
ma-241	203	1	(	(	PUNCT
ma-241	203	2	45	45	NUM
ma-241	203	3	)	)	PUNCT
ma-241	203	4	the	the	DET
ma-241	203	5	eigenvalue	eigenvalue	NOUN
ma-241	203	6	of	of	ADP
ma-241	203	7	the	the	DET
ma-241	203	8	schwarz	schwarz	PROPN
ma-241	203	9	iteration	iteration	NOUN
ma-241	203	10	matrix	matrix	NOUN
ma-241	203	11	ψosm	ψosm	NOUN
ma-241	203	12	of	of	ADP
ma-241	203	13	multiplicity	multiplicity	NOUN
ma-241	203	14	two	two	NUM
ma-241	203	15	is	be	AUX
ma-241	203	16	provided	provide	VERB
ma-241	203	17	by	by	ADP
ma-241	203	18	the	the	DET
ma-241	203	19	formula	formula	NOUN
ma-241	203	20	µd	µd	NOUN
ma-241	203	21	=	=	SYM
ma-241	203	22	3ν2|ξ|2	3ν2|ξ|2	NUM
ma-241	203	23	−	−	PROPN
ma-241	203	24	4ν|ξ|γ	4ν|ξ|γ	NUM
ma-241	204	1	+	+	CCONJ
ma-241	204	2	γ2	γ2	PROPN
ma-241	204	3	3ν2|ξ|2	3ν2|ξ|2	PROPN
ma-241	204	4	+	+	CCONJ
ma-241	204	5	4ν|ξ|γ	4ν|ξ|γ	NUM
ma-241	205	1	+	+	CCONJ
ma-241	205	2	γ2	γ2	ADJ
ma-241	205	3	.	.	PUNCT
ma-241	206	1	as	as	ADP
ma-241	206	2	a	a	DET
ma-241	206	3	consequence	consequence	NOUN
ma-241	206	4	,	,	PUNCT
ma-241	206	5	the	the	DET
ma-241	206	6	contraction	contraction	NOUN
ma-241	206	7	factor	factor	NOUN
ma-241	206	8	is	be	AUX
ma-241	206	9	r2	r2	PROPN
ma-241	206	10	osm	osm	PROPN
ma-241	206	11	=	=	SYM
ma-241	206	12	|µd	|µd	NOUN
ma-241	206	13	|2	|2	NUM
ma-241	206	14	=	=	SYM
ma-241	206	15	|3ν2|ξ|2	|3ν2|ξ|2	NUM
ma-241	206	16	−	−	NUM
ma-241	206	17	4ν|ξ|γ	4ν|ξ|γ	NUM
ma-241	207	1	+	+	CCONJ
ma-241	207	2	γ2|2	γ2|2	PROPN
ma-241	207	3	|3ν2|ξ|2	|3ν2|ξ|2	AUX
ma-241	207	4	+	+	CCONJ
ma-241	207	5	4ν|ξ|γ	4ν|ξ|γ	NUM
ma-241	207	6	+	+	CCONJ
ma-241	207	7	γ2|2	γ2|2	PROPN
ma-241	207	8	.	.	PUNCT
ma-241	208	1	�	�	PROPN
ma-241	208	2	https://doi.org/10.28924/ada/ma.5.6	https://doi.org/10.28924/ada/ma.5.6	PROPN
ma-241	208	3	eur	eur	PROPN
ma-241	208	4	.	.	PUNCT
ma-241	209	1	j.	j.	PROPN
ma-241	209	2	math	math	PROPN
ma-241	209	3	.	.	PUNCT
ma-241	210	1	anal	anal	PROPN
ma-241	210	2	.	.	PUNCT
ma-241	211	1	10.28924	10.28924	NUM
ma-241	211	2	/	/	SYM
ma-241	211	3	ada	ada	PROPN
ma-241	211	4	/	/	SYM
ma-241	211	5	ma.5.6	ma.5.6	PROPN
ma-241	211	6	115	115	NUM
ma-241	211	7	.	.	PUNCT
ma-241	212	1	non	non	ADJ
ma-241	212	2	-	-	ADJ
ma-241	212	3	overlapping	overlapping	ADJ
ma-241	212	4	optimized	optimize	VERB
ma-241	212	5	schwarz	schwarz	PROPN
ma-241	212	6	algorithm	algorithm	NOUN
ma-241	212	7	-	-	PUNCT
ma-241	212	8	second	second	NOUN
ma-241	212	9	order	order	NOUN
ma-241	212	10	ic	ic	X
ma-241	212	11	more	more	ADV
ma-241	212	12	sophisticated	sophisticated	ADJ
ma-241	212	13	schwarz	schwarz	PROPN
ma-241	212	14	methods	method	NOUN
ma-241	212	15	arise	arise	VERB
ma-241	212	16	by	by	ADP
ma-241	212	17	the	the	DET
ma-241	212	18	appropriate	appropriate	ADJ
ma-241	212	19	modification	modification	NOUN
ma-241	212	20	of	of	ADP
ma-241	212	21	the	the	DET
ma-241	212	22	interfaceconditions	interfacecondition	NOUN
ma-241	212	23	.	.	PUNCT
ma-241	213	1	we	we	PRON
ma-241	213	2	can	can	AUX
ma-241	213	3	employ	employ	VERB
ma-241	213	4	the	the	DET
ma-241	213	5	optimized	optimize	VERB
ma-241	213	6	schwarz	schwarz	PROPN
ma-241	213	7	algorithms	algorithm	NOUN
ma-241	213	8	imposing	impose	VERB
ma-241	213	9	second	second	ADJ
ma-241	213	10	order	order	NOUN
ma-241	213	11	transmissionconditions	transmissioncondition	NOUN
ma-241	213	12	.	.	PUNCT
ma-241	214	1	more	more	ADV
ma-241	214	2	precisely	precisely	ADV
ma-241	214	3	,	,	PUNCT
ma-241	214	4	we	we	PRON
ma-241	214	5	go	go	VERB
ma-241	214	6	back	back	ADV
ma-241	214	7	to	to	ADP
ma-241	214	8	the	the	DET
ma-241	214	9	algorithm	algorithm	NOUN
ma-241	214	10	prescribed	prescribe	VERB
ma-241	214	11	by	by	ADP
ma-241	214	12	(	(	PUNCT
ma-241	214	13	31	31	NUM
ma-241	214	14	)	)	PUNCT
ma-241	214	15	,	,	PUNCT
ma-241	214	16	(	(	PUNCT
ma-241	214	17	32	32	NUM
ma-241	214	18	)	)	PUNCT
ma-241	214	19	,	,	PUNCT
ma-241	214	20	go	go	VERB
ma-241	214	21	to	to	ADP
ma-241	214	22	the	the	DET
ma-241	214	23	interfaceconditions	interfacecondition	NOUN
ma-241	214	24	and	and	CCONJ
ma-241	214	25	instead	instead	ADV
ma-241	214	26	of	of	ADP
ma-241	214	27	γ	γ	NOUN
ma-241	214	28	we	we	PRON
ma-241	214	29	use	use	VERB
ma-241	214	30	the	the	DET
ma-241	214	31	symbol	symbol	NOUN
ma-241	214	32	s	s	NOUN
ma-241	214	33	,	,	PUNCT
ma-241	214	34	where	where	SCONJ
ma-241	214	35	s	s	VERB
ma-241	214	36	=	=	X
ma-241	214	37	q	q	X
ma-241	215	1	(	(	PUNCT
ma-241	215	2	1	1	NUM
ma-241	215	3	+	+	CCONJ
ma-241	215	4	ξ2	ξ2	NOUN
ma-241	215	5	)	)	PUNCT
ma-241	215	6	.	.	PUNCT
ma-241	216	1	theorem	theorem	ADJ
ma-241	216	2	4	4	NUM
ma-241	216	3	.	.	PUNCT
ma-241	217	1	the	the	DET
ma-241	217	2	contraction	contraction	NOUN
ma-241	217	3	factor	factor	NOUN
ma-241	217	4	of	of	ADP
ma-241	217	5	the	the	DET
ma-241	217	6	non	non	ADJ
ma-241	217	7	-	-	ADJ
ma-241	217	8	overlapping	overlapping	ADJ
ma-241	217	9	schwarz	schwarz	PROPN
ma-241	217	10	algorithm	algorithm	NOUN
ma-241	217	11	(	(	PUNCT
ma-241	217	12	second	second	ADJ
ma-241	217	13	order	order	NOUN
ma-241	217	14	ic	ic	NUM
ma-241	217	15	)	)	PUNCT
ma-241	217	16	is	be	AUX
ma-241	217	17	given	give	VERB
ma-241	217	18	by	by	ADP
ma-241	217	19	the	the	DET
ma-241	217	20	mathematical	mathematical	ADJ
ma-241	217	21	expression	expression	NOUN
ma-241	217	22	r2	r2	PROPN
ma-241	217	23	osm	osm	PROPN
ma-241	217	24	,	,	PUNCT
ma-241	217	25	soic(ν	soic(ν	PROPN
ma-241	217	26	,	,	PUNCT
ma-241	217	27	q	q	NOUN
ma-241	217	28	,	,	PUNCT
ma-241	217	29	ξ	ξ	NOUN
ma-241	217	30	)	)	PUNCT
ma-241	217	31	=	=	SYM
ma-241	217	32	|3ν2|ξ|2	|3ν2|ξ|2	NUM
ma-241	217	33	−	−	ADP
ma-241	217	34	4ν|ξ|q	4ν|ξ|q	NUM
ma-241	217	35	(	(	PUNCT
ma-241	217	36	1	1	NUM
ma-241	217	37	+	+	CCONJ
ma-241	217	38	ξ2	ξ2	NOUN
ma-241	217	39	)	)	PUNCT
ma-241	218	1	+	+	NUM
ma-241	218	2	q2	q2	NOUN
ma-241	218	3	(	(	PUNCT
ma-241	218	4	1	1	NUM
ma-241	218	5	+	+	CCONJ
ma-241	218	6	ξ2	ξ2	NOUN
ma-241	218	7	)	)	PUNCT
ma-241	218	8	2	2	NUM
ma-241	218	9	|2	|2	NUM
ma-241	218	10	|3ν2|ξ|2	|3ν2|ξ|2	NOUN
ma-241	218	11	+	+	CCONJ
ma-241	218	12	4ν|ξ|q	4ν|ξ|q	NUM
ma-241	218	13	(	(	PUNCT
ma-241	218	14	1	1	NUM
ma-241	218	15	+	+	CCONJ
ma-241	218	16	ξ2	ξ2	ADJ
ma-241	218	17	)	)	PUNCT
ma-241	219	1	+	+	NUM
ma-241	219	2	q2	q2	NOUN
ma-241	219	3	(	(	PUNCT
ma-241	219	4	1	1	NUM
ma-241	219	5	+	+	CCONJ
ma-241	219	6	ξ2)2	ξ2)2	PRON
ma-241	219	7	|2	|2	NUM
ma-241	219	8	(	(	PUNCT
ma-241	219	9	46	46	NUM
ma-241	219	10	)	)	PUNCT
ma-241	219	11	where	where	SCONJ
ma-241	219	12	q	q	X
ma-241	219	13	>	>	X
ma-241	219	14	0	0	X
ma-241	219	15	.	.	PUNCT
ma-241	220	1	proof	proof	NOUN
ma-241	220	2	.	.	PUNCT
ma-241	221	1	the	the	DET
ma-241	221	2	calculations	calculation	NOUN
ma-241	221	3	follow	follow	VERB
ma-241	221	4	through	through	ADP
ma-241	221	5	in	in	ADP
ma-241	221	6	the	the	DET
ma-241	221	7	same	same	ADJ
ma-241	221	8	spirit	spirit	NOUN
ma-241	221	9	as	as	ADP
ma-241	221	10	the	the	DET
ma-241	221	11	optimized	optimize	VERB
ma-241	221	12	schwarz	schwarz	PROPN
ma-241	221	13	methods	method	NOUN
ma-241	221	14	withthe	withthe	PROPN
ma-241	221	15	robin	robin	PROPN
ma-241	221	16	transmission	transmission	NOUN
ma-241	221	17	conditions	condition	NOUN
ma-241	221	18	.	.	PUNCT
ma-241	222	1	instead	instead	ADV
ma-241	222	2	of	of	ADP
ma-241	222	3	γ	γ	PROPN
ma-241	222	4	,	,	PUNCT
ma-241	222	5	the	the	DET
ma-241	222	6	symbol	symbol	NOUN
ma-241	222	7	s	s	NOUN
ma-241	222	8	is	be	AUX
ma-241	222	9	used	use	VERB
ma-241	222	10	and	and	CCONJ
ma-241	222	11	the	the	DET
ma-241	222	12	convergence	convergence	NOUN
ma-241	222	13	factoris	factoris	NOUN
ma-241	222	14	obtained	obtain	VERB
ma-241	222	15	naturally	naturally	ADV
ma-241	222	16	.	.	PUNCT
ma-241	223	1	�	�	PROPN
ma-241	223	2	corollary	corollary	NOUN
ma-241	223	3	1	1	NUM
ma-241	223	4	.	.	PUNCT
ma-241	224	1	the	the	DET
ma-241	224	2	reduction	reduction	NOUN
ma-241	224	3	factor	factor	NOUN
ma-241	224	4	of	of	ADP
ma-241	224	5	the	the	DET
ma-241	224	6	parallel	parallel	ADJ
ma-241	224	7	schwarz	schwarz	PROPN
ma-241	224	8	method	method	NOUN
ma-241	224	9	(	(	PUNCT
ma-241	224	10	dirichlet	dirichlet	PROPN
ma-241	224	11	ic	ic	PROPN
ma-241	224	12	)	)	PUNCT
ma-241	224	13	given	give	VERB
ma-241	224	14	by	by	ADP
ma-241	224	15	(	(	PUNCT
ma-241	224	16	5	5	NUM
ma-241	224	17	)	)	PUNCT
ma-241	224	18	satisfies	satisfy	VERB
ma-241	224	19	the	the	DET
ma-241	224	20	following	following	NOUN
ma-241	224	21	rpsm	rpsm	PROPN
ma-241	224	22	,	,	PUNCT
ma-241	224	23	d(ξ	d(ξ	PROPN
ma-241	224	24	,	,	PUNCT
ma-241	224	25	h	h	NOUN
ma-241	224	26	)	)	PUNCT
ma-241	224	27	=	=	SYM
ma-241	224	28			NUM
ma-241	224	29	1	1	NUM
ma-241	224	30	,	,	PUNCT
ma-241	224	31	h	h	NOUN
ma-241	224	32	=	=	SYM
ma-241	224	33	0	0	NUM
ma-241	224	34	0	0	NUM
ma-241	224	35	,	,	PUNCT
ma-241	224	36	|ξ|	|ξ|	PROPN
ma-241	224	37	→	→	SYM
ma-241	224	38	+	+	PROPN
ma-241	224	39	∞	∞	PROPN
ma-241	224	40	0	0	NUM
ma-241	224	41	,	,	PUNCT
ma-241	224	42	h	h	NOUN
ma-241	225	1	→	→	SYM
ma-241	225	2	+	+	NUM
ma-241	225	3	∞	∞	PROPN
ma-241	225	4	<	<	X
ma-241	225	5	1	1	NUM
ma-241	225	6	,	,	PUNCT
ma-241	225	7	ξ	ξ	PROPN
ma-241	225	8	>	>	X
ma-241	225	9	0	0	NUM
ma-241	225	10	.	.	PUNCT
ma-241	226	1	(	(	PUNCT
ma-241	226	2	47	47	NUM
ma-241	226	3	)	)	PUNCT
ma-241	226	4	proof	proof	NOUN
ma-241	226	5	.	.	PUNCT
ma-241	227	1	the	the	DET
ma-241	227	2	result	result	NOUN
ma-241	227	3	(	(	PUNCT
ma-241	227	4	47)1	47)1	NUM
ma-241	227	5	occurs	occur	VERB
ma-241	227	6	by	by	ADP
ma-241	227	7	replacing	replace	VERB
ma-241	227	8	h	h	NOUN
ma-241	227	9	=	=	NOUN
ma-241	227	10	0	0	NUM
ma-241	227	11	back	back	ADV
ma-241	227	12	to	to	ADP
ma-241	227	13	the	the	DET
ma-241	227	14	formula	formula	NOUN
ma-241	227	15	(	(	PUNCT
ma-241	227	16	5	5	NUM
ma-241	227	17	)	)	PUNCT
ma-241	227	18	.	.	PUNCT
ma-241	228	1	as	as	ADP
ma-241	228	2	a	a	DET
ma-241	228	3	consequence	consequence	NOUN
ma-241	228	4	,	,	PUNCT
ma-241	228	5	itmeans	itmean	VERB
ma-241	228	6	that	that	SCONJ
ma-241	228	7	the	the	DET
ma-241	228	8	schwarz	schwarz	PROPN
ma-241	228	9	method	method	NOUN
ma-241	228	10	stagnates	stagnate	VERB
ma-241	228	11	without	without	ADP
ma-241	228	12	overlap	overlap	NOUN
ma-241	228	13	,	,	PUNCT
ma-241	228	14	something	something	PRON
ma-241	228	15	which	which	PRON
ma-241	228	16	is	be	AUX
ma-241	228	17	very	very	ADV
ma-241	228	18	usual	usual	ADJ
ma-241	228	19	in	in	ADP
ma-241	228	20	theliterature	theliterature	NOUN
ma-241	228	21	.	.	PUNCT
ma-241	229	1	the	the	PRON
ma-241	229	2	(	(	PUNCT
ma-241	229	3	47)2	47)2	NUM
ma-241	229	4	is	be	AUX
ma-241	229	5	obtained	obtain	VERB
ma-241	229	6	by	by	ADP
ma-241	229	7	taking	take	VERB
ma-241	229	8	the	the	DET
ma-241	229	9	limit	limit	NOUN
ma-241	229	10	of	of	ADP
ma-241	229	11	(	(	PUNCT
ma-241	229	12	5	5	NUM
ma-241	229	13	)	)	PUNCT
ma-241	229	14	as	as	SCONJ
ma-241	229	15	the	the	DET
ma-241	229	16	fourier	fourier	NOUN
ma-241	229	17	frequency	frequency	NOUN
ma-241	229	18	tends	tend	VERB
ma-241	229	19	to	to	ADP
ma-241	229	20	+	+	VERB
ma-241	229	21	∞.the	∞.the	INTJ
ma-241	229	22	(	(	PUNCT
ma-241	229	23	47)3	47)3	PRON
ma-241	229	24	is	be	AUX
ma-241	229	25	coming	come	VERB
ma-241	229	26	from	from	ADP
ma-241	229	27	the	the	DET
ma-241	229	28	fact	fact	NOUN
ma-241	229	29	that	that	SCONJ
ma-241	229	30	when	when	SCONJ
ma-241	229	31	the	the	DET
ma-241	229	32	overlap	overlap	NOUN
ma-241	229	33	is	be	AUX
ma-241	229	34	sufficiently	sufficiently	ADV
ma-241	229	35	large	large	ADJ
ma-241	229	36	,	,	PUNCT
ma-241	229	37	the	the	DET
ma-241	229	38	convergence	convergence	NOUN
ma-241	229	39	factorturns	factorturn	VERB
ma-241	229	40	to	to	PART
ma-241	229	41	be	be	AUX
ma-241	229	42	zero	zero	NUM
ma-241	229	43	.	.	PUNCT
ma-241	230	1	the	the	DET
ma-241	230	2	ultimate	ultimate	ADJ
ma-241	230	3	result	result	NOUN
ma-241	230	4	(	(	PUNCT
ma-241	230	5	47)4	47)4	NUM
ma-241	230	6	comes	come	VERB
ma-241	230	7	from	from	ADP
ma-241	230	8	the	the	DET
ma-241	230	9	fact	fact	NOUN
ma-241	230	10	that	that	SCONJ
ma-241	230	11	for	for	ADP
ma-241	230	12	non	non	ADJ
ma-241	230	13	zero	zero	NUM
ma-241	230	14	fourier	fourier	NOUN
ma-241	230	15	frequency	frequency	NOUN
ma-241	230	16	,	,	PUNCT
ma-241	230	17	the	the	DET
ma-241	230	18	convergence	convergence	NOUN
ma-241	230	19	factor	factor	NOUN
ma-241	230	20	is	be	AUX
ma-241	230	21	strictly	strictly	ADV
ma-241	230	22	less	less	ADJ
ma-241	230	23	than	than	ADP
ma-241	230	24	1	1	NUM
ma-241	230	25	.	.	PUNCT
ma-241	230	26	�	�	PROPN
ma-241	230	27	corollary	corollary	NOUN
ma-241	230	28	2	2	NUM
ma-241	230	29	.	.	PUNCT
ma-241	230	30	the	the	DET
ma-241	230	31	reduction	reduction	NOUN
ma-241	230	32	factor	factor	NOUN
ma-241	230	33	of	of	ADP
ma-241	230	34	the	the	DET
ma-241	230	35	alternating	alternate	VERB
ma-241	230	36	schwarz	schwarz	PROPN
ma-241	230	37	method	method	NOUN
ma-241	230	38	(	(	PUNCT
ma-241	230	39	neumann	neumann	PROPN
ma-241	230	40	ic	ic	NUM
ma-241	230	41	)	)	PUNCT
ma-241	230	42	given	give	VERB
ma-241	230	43	by	by	ADP
ma-241	230	44	(	(	PUNCT
ma-241	230	45	22	22	NUM
ma-241	230	46	)	)	PUNCT
ma-241	230	47	,	,	PUNCT
ma-241	230	48	satisfies	satisfy	VERB
ma-241	230	49	the	the	DET
ma-241	230	50	relations	relation	NOUN
ma-241	230	51	rasm	rasm	VERB
ma-241	230	52	,	,	PUNCT
ma-241	230	53	n(ξ	n(ξ	PROPN
ma-241	230	54	,	,	PUNCT
ma-241	230	55	h	h	NOUN
ma-241	230	56	)	)	PUNCT
ma-241	230	57	=	=	SYM
ma-241	230	58			NUM
ma-241	230	59	1	1	NUM
ma-241	230	60	,	,	PUNCT
ma-241	230	61	h	h	NOUN
ma-241	230	62	=	=	SYM
ma-241	230	63	0	0	NUM
ma-241	230	64	0	0	NUM
ma-241	230	65	,	,	PUNCT
ma-241	230	66	|ξ|	|ξ|	PROPN
ma-241	230	67	→	→	SYM
ma-241	230	68	+	+	PROPN
ma-241	230	69	∞	∞	PROPN
ma-241	230	70	0	0	NUM
ma-241	230	71	,	,	PUNCT
ma-241	230	72	h	h	NOUN
ma-241	230	73	→	→	SYM
ma-241	231	1	+	+	NUM
ma-241	231	2	∞	∞	PROPN
ma-241	231	3	<	<	X
ma-241	231	4	1	1	NUM
ma-241	231	5	,	,	PUNCT
ma-241	231	6	ξ	ξ	PROPN
ma-241	231	7	>	>	X
ma-241	231	8	0	0	NUM
ma-241	231	9	.	.	PUNCT
ma-241	231	10	(	(	PUNCT
ma-241	231	11	48	48	NUM
ma-241	231	12	)	)	PUNCT
ma-241	231	13	https://doi.org/10.28924/ada/ma.5.6	https://doi.org/10.28924/ada/ma.5.6	PROPN
ma-241	231	14	eur	eur	PROPN
ma-241	231	15	.	.	PUNCT
ma-241	232	1	j.	j.	PROPN
ma-241	232	2	math	math	PROPN
ma-241	232	3	.	.	PUNCT
ma-241	233	1	anal	anal	PROPN
ma-241	233	2	.	.	PUNCT
ma-241	234	1	10.28924	10.28924	NUM
ma-241	234	2	/	/	SYM
ma-241	234	3	ada	ada	PROPN
ma-241	234	4	/	/	SYM
ma-241	234	5	ma.5.6	ma.5.6	ADJ
ma-241	234	6	12	12	NUM
ma-241	234	7	proof	proof	NOUN
ma-241	234	8	.	.	PUNCT
ma-241	235	1	the	the	DET
ma-241	235	2	reduction	reduction	NOUN
ma-241	235	3	factor	factor	NOUN
ma-241	235	4	is	be	AUX
ma-241	235	5	a	a	DET
ma-241	235	6	function	function	NOUN
ma-241	235	7	that	that	PRON
ma-241	235	8	depends	depend	VERB
ma-241	235	9	on	on	ADP
ma-241	235	10	the	the	DET
ma-241	235	11	size	size	NOUN
ma-241	235	12	of	of	ADP
ma-241	235	13	the	the	DET
ma-241	235	14	overlap	overlap	NOUN
ma-241	235	15	and	and	CCONJ
ma-241	235	16	the	the	DET
ma-241	235	17	fourierfrequency	fourierfrequency	NOUN
ma-241	235	18	.	.	PUNCT
ma-241	236	1	consequently	consequently	ADV
ma-241	236	2	,	,	PUNCT
ma-241	236	3	for	for	ADP
ma-241	236	4	zero	zero	NUM
ma-241	236	5	overlap	overlap	NOUN
ma-241	236	6	,	,	PUNCT
ma-241	236	7	the	the	DET
ma-241	236	8	function	function	NOUN
ma-241	236	9	becomes	become	VERB
ma-241	236	10	one	one	NUM
ma-241	236	11	and	and	CCONJ
ma-241	236	12	this	this	PRON
ma-241	236	13	leads	lead	VERB
ma-241	236	14	to	to	ADP
ma-241	236	15	stagnation	stagnation	NOUN
ma-241	236	16	ofthe	ofthe	ADJ
ma-241	236	17	algorithm	algorithm	NOUN
ma-241	236	18	(	(	PUNCT
ma-241	236	19	(	(	PUNCT
ma-241	236	20	48)1	48)1	NUM
ma-241	236	21	)	)	PUNCT
ma-241	236	22	.	.	PUNCT
ma-241	237	1	when	when	SCONJ
ma-241	237	2	the	the	DET
ma-241	237	3	fourier	fourier	ADJ
ma-241	237	4	number	number	NOUN
ma-241	237	5	grows	grow	VERB
ma-241	237	6	large	large	ADJ
ma-241	237	7	,	,	PUNCT
ma-241	237	8	the	the	DET
ma-241	237	9	function	function	NOUN
ma-241	237	10	goes	go	VERB
ma-241	237	11	to	to	ADP
ma-241	237	12	zero	zero	NUM
ma-241	237	13	as	as	ADP
ma-241	237	14	prescribedby	prescribedby	NOUN
ma-241	237	15	(	(	PUNCT
ma-241	237	16	48)2	48)2	NUM
ma-241	237	17	.	.	PUNCT
ma-241	238	1	moving	move	VERB
ma-241	238	2	to	to	ADP
ma-241	238	3	(	(	PUNCT
ma-241	238	4	48)3	48)3	NUM
ma-241	238	5	,	,	PUNCT
ma-241	238	6	a	a	DET
ma-241	238	7	big	big	ADJ
ma-241	238	8	overlap	overlap	NOUN
ma-241	238	9	leads	lead	VERB
ma-241	238	10	to	to	ADP
ma-241	238	11	better	well	ADJ
ma-241	238	12	convergence	convergence	NOUN
ma-241	238	13	because	because	SCONJ
ma-241	238	14	the	the	DET
ma-241	238	15	contraction	contraction	NOUN
ma-241	238	16	factorrapidly	factorrapidly	ADV
ma-241	238	17	tends	tend	VERB
ma-241	238	18	to	to	ADP
ma-241	238	19	zero	zero	NUM
ma-241	238	20	.	.	PUNCT
ma-241	239	1	last	last	ADJ
ma-241	239	2	but	but	CCONJ
ma-241	239	3	not	not	PART
ma-241	239	4	least	least	ADJ
ma-241	239	5	,	,	PUNCT
ma-241	239	6	for	for	ADP
ma-241	239	7	finite	finite	ADJ
ma-241	239	8	fourier	fourier	NOUN
ma-241	239	9	number	number	NOUN
ma-241	239	10	,	,	PUNCT
ma-241	239	11	the	the	DET
ma-241	239	12	convergence	convergence	NOUN
ma-241	239	13	factor	factor	NOUN
ma-241	239	14	is	be	AUX
ma-241	239	15	strictlyless	strictlyless	NOUN
ma-241	239	16	than	than	ADP
ma-241	239	17	one	one	NUM
ma-241	239	18	(	(	PUNCT
ma-241	239	19	(	(	PUNCT
ma-241	239	20	48)4	48)4	NUM
ma-241	239	21	)	)	PUNCT
ma-241	239	22	.	.	PUNCT
ma-241	240	1	�	�	PROPN
ma-241	240	2	corollary	corollary	NOUN
ma-241	240	3	3	3	NUM
ma-241	240	4	.	.	PUNCT
ma-241	241	1	the	the	DET
ma-241	241	2	contraction	contraction	NOUN
ma-241	241	3	factor	factor	NOUN
ma-241	241	4	of	of	ADP
ma-241	241	5	the	the	DET
ma-241	241	6	non	non	ADJ
ma-241	241	7	-	-	ADJ
ma-241	241	8	overlapping	overlapping	ADJ
ma-241	241	9	optimized	optimize	VERB
ma-241	241	10	schwarz	schwarz	PROPN
ma-241	241	11	method	method	NOUN
ma-241	241	12	(	(	PUNCT
ma-241	241	13	robin	robin	PROPN
ma-241	241	14	ic	ic	PROPN
ma-241	241	15	)	)	PUNCT
ma-241	241	16	given	give	VERB
ma-241	241	17	by	by	ADP
ma-241	241	18	(	(	PUNCT
ma-241	241	19	33	33	NUM
ma-241	241	20	)	)	PUNCT
ma-241	241	21	satisfies	satisfy	VERB
ma-241	241	22	the	the	DET
ma-241	241	23	properties	property	NOUN
ma-241	241	24	r2	r2	PROPN
ma-241	241	25	osm(ξ	osm(ξ	PROPN
ma-241	241	26	,	,	PUNCT
ma-241	241	27	ν	ν	PROPN
ma-241	241	28	,	,	PUNCT
ma-241	241	29	γ	γ	NOUN
ma-241	241	30	)	)	PUNCT
ma-241	241	31	=	=	SYM
ma-241	241	32			NUM
ma-241	241	33	1	1	NUM
ma-241	241	34	,	,	PUNCT
ma-241	241	35	γ	γ	NOUN
ma-241	241	36	=	=	SYM
ma-241	241	37	0	0	NUM
ma-241	241	38	1	1	NUM
ma-241	241	39	,	,	PUNCT
ma-241	241	40	γ	γ	X
ma-241	241	41	→	→	SYM
ma-241	241	42	+	+	PROPN
ma-241	241	43	∞	∞	PROPN
ma-241	241	44	1	1	NUM
ma-241	241	45	,	,	PUNCT
ma-241	241	46	|ξ|	|ξ|	PROPN
ma-241	241	47	→	→	SYM
ma-241	241	48	+	+	PROPN
ma-241	241	49	∞	∞	PROPN
ma-241	241	50	<	<	X
ma-241	241	51	1	1	NUM
ma-241	241	52	,	,	PUNCT
ma-241	241	53	ξ	ξ	PROPN
ma-241	241	54	∈	∈	PROPN
ma-241	241	55	(	(	PUNCT
ma-241	241	56	0,+∞	0,+∞	NUM
ma-241	241	57	)	)	PUNCT
ma-241	241	58	0	0	NUM
ma-241	241	59	,	,	PUNCT
ma-241	241	60	γ	γ	X
ma-241	241	61	=	=	X
ma-241	241	62	γ+	γ+	PUNCT
ma-241	241	63	=	=	SYM
ma-241	241	64	3ν|ξ|	3ν|ξ|	NUM
ma-241	241	65	,	,	PUNCT
ma-241	241	66	γ	γ	X
ma-241	241	67	=	=	SYM
ma-241	241	68	γ−	γ−	PROPN
ma-241	241	69	=	=	PUNCT
ma-241	241	70	ν|ξ|	ν|ξ|	NOUN
ma-241	241	71	.	.	PUNCT
ma-241	242	1	(	(	PUNCT
ma-241	242	2	49	49	NUM
ma-241	242	3	)	)	PUNCT
ma-241	242	4	proof	proof	NOUN
ma-241	242	5	.	.	PUNCT
ma-241	243	1	the	the	DET
ma-241	243	2	contraction	contraction	NOUN
ma-241	243	3	factor	factor	NOUN
ma-241	243	4	depends	depend	VERB
ma-241	243	5	on	on	ADP
ma-241	243	6	the	the	DET
ma-241	243	7	kinematic	kinematic	ADJ
ma-241	243	8	viscosity	viscosity	NOUN
ma-241	243	9	,	,	PUNCT
ma-241	243	10	the	the	DET
ma-241	243	11	fourier	fourier	NOUN
ma-241	243	12	frequency	frequency	NOUN
ma-241	243	13	and	and	CCONJ
ma-241	243	14	theparameter	theparameter	ADJ
ma-241	243	15	γ	γ	PROPN
ma-241	243	16	.	.	PUNCT
ma-241	244	1	the	the	DET
ma-241	244	2	first	first	ADJ
ma-241	244	3	three	three	NUM
ma-241	244	4	properties	property	NOUN
ma-241	244	5	in	in	ADP
ma-241	244	6	(	(	PUNCT
ma-241	244	7	49	49	NUM
ma-241	244	8	)	)	PUNCT
ma-241	244	9	are	be	AUX
ma-241	244	10	straighforward	straighforward	ADJ
ma-241	244	11	to	to	PART
ma-241	244	12	obtain	obtain	VERB
ma-241	244	13	.	.	PUNCT
ma-241	245	1	taking	take	VERB
ma-241	245	2	the	the	DET
ma-241	245	3	robinparameter	robinparameter	NOUN
ma-241	245	4	to	to	PART
ma-241	245	5	be	be	AUX
ma-241	245	6	zero	zero	NUM
ma-241	245	7	or	or	CCONJ
ma-241	245	8	tend	tend	VERB
ma-241	245	9	to	to	PART
ma-241	245	10	infinity	infinity	NOUN
ma-241	245	11	gives	give	VERB
ma-241	245	12	a	a	DET
ma-241	245	13	stagnant	stagnant	ADJ
ma-241	245	14	schwarz	schwarz	NOUN
ma-241	245	15	algorithm	algorithm	NOUN
ma-241	245	16	.	.	PUNCT
ma-241	246	1	in	in	ADP
ma-241	246	2	addition	addition	NOUN
ma-241	246	3	,	,	PUNCT
ma-241	246	4	when	when	SCONJ
ma-241	246	5	thefourier	thefouri	ADJ
ma-241	246	6	frequency	frequency	NOUN
ma-241	246	7	tends	tend	VERB
ma-241	246	8	to	to	PART
ma-241	246	9	infinity	infinity	VERB
ma-241	246	10	,	,	PUNCT
ma-241	246	11	the	the	DET
ma-241	246	12	contraction	contraction	NOUN
ma-241	246	13	factor	factor	NOUN
ma-241	246	14	becomes	become	VERB
ma-241	246	15	1	1	NUM
ma-241	246	16	.	.	PUNCT
ma-241	247	1	for	for	ADP
ma-241	247	2	finite	finite	ADJ
ma-241	247	3	fourier	fourier	NOUN
ma-241	247	4	frequency(not	frequency(not	NOUN
ma-241	247	5	growing	grow	VERB
ma-241	247	6	to	to	ADP
ma-241	247	7	infinity	infinity	NOUN
ma-241	247	8	)	)	PUNCT
ma-241	247	9	the	the	DET
ma-241	247	10	reduction	reduction	NOUN
ma-241	247	11	factor	factor	NOUN
ma-241	247	12	is	be	AUX
ma-241	247	13	less	less	ADJ
ma-241	247	14	than	than	ADP
ma-241	247	15	1	1	NUM
ma-241	247	16	.	.	PUNCT
ma-241	248	1	lastly	lastly	ADV
ma-241	248	2	,	,	PUNCT
ma-241	248	3	the	the	DET
ma-241	248	4	values	value	NOUN
ma-241	248	5	of	of	ADP
ma-241	248	6	the	the	DET
ma-241	248	7	robin	robin	PROPN
ma-241	248	8	parameterthat	parameterthat	NOUN
ma-241	248	9	make	make	VERB
ma-241	248	10	the	the	DET
ma-241	248	11	contraction	contraction	NOUN
ma-241	248	12	factor	factor	NOUN
ma-241	248	13	zero	zero	NUM
ma-241	248	14	are	be	AUX
ma-241	248	15	γ+	γ+	PUNCT
ma-241	248	16	=	=	NOUN
ma-241	248	17	3ν|ξ|	3ν|ξ|	NUM
ma-241	248	18	and	and	CCONJ
ma-241	248	19	γ−	γ−	PROPN
ma-241	248	20	=	=	SYM
ma-241	248	21	ν|ξ|	ν|ξ|	NOUN
ma-241	248	22	and	and	CCONJ
ma-241	248	23	can	can	AUX
ma-241	248	24	obtained	obtain	VERB
ma-241	248	25	by	by	ADP
ma-241	248	26	solving	solve	VERB
ma-241	248	27	atrinomial	atrinomial	ADJ
ma-241	248	28	equation	equation	NOUN
ma-241	248	29	appearing	appear	VERB
ma-241	248	30	in	in	ADP
ma-241	248	31	the	the	DET
ma-241	248	32	numerator	numerator	NOUN
ma-241	248	33	of	of	ADP
ma-241	248	34	the	the	DET
ma-241	248	35	contraction	contraction	NOUN
ma-241	248	36	factor	factor	NOUN
ma-241	248	37	.	.	PUNCT
ma-241	249	1	�	�	PROPN
ma-241	249	2	corollary	corollary	ADJ
ma-241	249	3	4	4	NUM
ma-241	249	4	.	.	PUNCT
ma-241	250	1	if	if	SCONJ
ma-241	250	2	γ	γ	NOUN
ma-241	250	3	=	=	SYM
ma-241	250	4	mν|ξ|	mν|ξ|	NOUN
ma-241	250	5	,	,	PUNCT
ma-241	250	6	m	m	NOUN
ma-241	250	7	∈	∈	NOUN
ma-241	250	8	z+	z+	NUM
ma-241	250	9	−	−	PROPN
ma-241	250	10	{	{	PUNCT
ma-241	250	11	1	1	NUM
ma-241	250	12	,	,	PUNCT
ma-241	250	13	3	3	NUM
ma-241	250	14	}	}	PUNCT
ma-241	250	15	,	,	PUNCT
ma-241	250	16	then	then	ADV
ma-241	250	17	the	the	DET
ma-241	250	18	convergence	convergence	NOUN
ma-241	250	19	factor	factor	NOUN
ma-241	250	20	(	(	PUNCT
ma-241	250	21	33	33	NUM
ma-241	250	22	)	)	PUNCT
ma-241	250	23	does	do	AUX
ma-241	250	24	not	not	PART
ma-241	250	25	depend	depend	VERB
ma-241	250	26	on	on	ADP
ma-241	250	27	viscosity	viscosity	NOUN
ma-241	250	28	and	and	CCONJ
ma-241	250	29	fourier	fourier	NOUN
ma-241	250	30	frequency	frequency	NOUN
ma-241	250	31	.	.	PUNCT
ma-241	251	1	proof	proof	NOUN
ma-241	251	2	.	.	PUNCT
ma-241	252	1	by	by	ADP
ma-241	252	2	substitution	substitution	NOUN
ma-241	252	3	,	,	PUNCT
ma-241	252	4	we	we	PRON
ma-241	252	5	obtain	obtain	VERB
ma-241	252	6	r2	r2	NOUN
ma-241	252	7	osm(ξ	osm(ξ	NOUN
ma-241	252	8	,	,	PUNCT
ma-241	252	9	ν	ν	PROPN
ma-241	252	10	,	,	PUNCT
ma-241	252	11	γ	γ	NOUN
ma-241	252	12	)	)	PUNCT
ma-241	252	13	=	=	SYM
ma-241	252	14	|3ν2|ξ|2	|3ν2|ξ|2	NUM
ma-241	252	15	−	−	NUM
ma-241	252	16	4ν|ξ|γ	4ν|ξ|γ	NUM
ma-241	253	1	+	+	CCONJ
ma-241	253	2	γ2|2	γ2|2	PROPN
ma-241	253	3	|3ν2|ξ|2	|3ν2|ξ|2	AUX
ma-241	253	4	+	+	CCONJ
ma-241	253	5	4ν|ξ|γ	4ν|ξ|γ	NUM
ma-241	253	6	+	+	CCONJ
ma-241	253	7	γ2|2	γ2|2	PROPN
ma-241	253	8	=	=	PUNCT
ma-241	253	9	|3ν2|ξ|2	|3ν2|ξ|2	PROPN
ma-241	253	10	−	−	PROPN
ma-241	253	11	4ν|ξ|mν|ξ|+m2|ξ|2ν2|2	4ν|ξ|mν|ξ|+m2|ξ|2ν2|2	PROPN
ma-241	253	12	|3ν2|ξ|2	|3ν2|ξ|2	X
ma-241	253	13	+	+	CCONJ
ma-241	253	14	4ν|ξ|mν|ξ|+m2|ξ|2ν2|2	4ν|ξ|mν|ξ|+m2|ξ|2ν2|2	NUM
ma-241	253	15	=	=	SYM
ma-241	253	16	|ν2|ξ|2	|ν2|ξ|2	PROPN
ma-241	253	17	(	(	PUNCT
ma-241	253	18	m2	m2	PROPN
ma-241	253	19	−	−	PROPN
ma-241	253	20	4	4	NUM
ma-241	253	21	m	m	NOUN
ma-241	253	22	+	+	NUM
ma-241	253	23	3	3	NUM
ma-241	253	24	)	)	PUNCT
ma-241	253	25	|2	|2	NUM
ma-241	253	26	|ν2|ξ|2	|ν2|ξ|2	NOUN
ma-241	253	27	(	(	PUNCT
ma-241	253	28	m2	m2	PROPN
ma-241	253	29	+	+	PROPN
ma-241	253	30	4	4	NUM
ma-241	253	31	m	m	NOUN
ma-241	253	32	+	+	NOUN
ma-241	253	33	3	3	NUM
ma-241	253	34	)	)	PUNCT
ma-241	253	35	|2	|2	NUM
ma-241	253	36	=	=	SYM
ma-241	253	37	|m2	|m2	PROPN
ma-241	253	38	−	−	NOUN
ma-241	253	39	4	4	NUM
ma-241	253	40	m	m	NOUN
ma-241	253	41	+	+	ADJ
ma-241	253	42	3|2	3|2	NUM
ma-241	253	43	|m2	|m2	NOUN
ma-241	253	44	+	+	CCONJ
ma-241	253	45	4	4	NUM
ma-241	253	46	m	m	NOUN
ma-241	253	47	+	+	ADJ
ma-241	253	48	3|2	3|2	NUM
ma-241	253	49	.	.	PUNCT
ma-241	254	1	�	�	PROPN
ma-241	254	2	corollary	corollary	NOUN
ma-241	254	3	5	5	NUM
ma-241	254	4	.	.	PUNCT
ma-241	255	1	the	the	DET
ma-241	255	2	contraction	contraction	NOUN
ma-241	255	3	factor	factor	NOUN
ma-241	255	4	of	of	ADP
ma-241	255	5	non	non	ADJ
ma-241	255	6	-	-	ADJ
ma-241	255	7	overlapping	overlapping	ADJ
ma-241	255	8	optimised	optimise	VERB
ma-241	255	9	schwarz	schwarz	PROPN
ma-241	255	10	method	method	NOUN
ma-241	255	11	(	(	PUNCT
ma-241	255	12	second	second	ADJ
ma-241	255	13	order	order	NOUN
ma-241	255	14	ic	ic	NUM
ma-241	255	15	)	)	PUNCT
ma-241	255	16	given	give	VERB
ma-241	255	17	by	by	ADP
ma-241	255	18	(	(	PUNCT
ma-241	255	19	46	46	NUM
ma-241	255	20	)	)	PUNCT
ma-241	255	21	satisfies	satisfy	VERB
ma-241	255	22	the	the	DET
ma-241	255	23	properties	property	NOUN
ma-241	255	24	https://doi.org/10.28924/ada/ma.5.6	https://doi.org/10.28924/ada/ma.5.6	PROPN
ma-241	255	25	eur	eur	NOUN
ma-241	255	26	.	.	PUNCT
ma-241	256	1	j.	j.	PROPN
ma-241	256	2	math	math	PROPN
ma-241	256	3	.	.	PUNCT
ma-241	257	1	anal	anal	PROPN
ma-241	257	2	.	.	PUNCT
ma-241	258	1	10.28924	10.28924	NUM
ma-241	258	2	/	/	SYM
ma-241	258	3	ada	ada	PROPN
ma-241	258	4	/	/	SYM
ma-241	258	5	ma.5.6	ma.5.6	PROPN
ma-241	258	6	13	13	NUM
ma-241	258	7	r2	r2	PROPN
ma-241	258	8	osm	osm	PROPN
ma-241	258	9	,	,	PUNCT
ma-241	258	10	soic(ν	soic(ν	PROPN
ma-241	258	11	,	,	PUNCT
ma-241	258	12	q	q	NOUN
ma-241	258	13	,	,	PUNCT
ma-241	258	14	ξ	ξ	X
ma-241	258	15	)	)	PUNCT
ma-241	258	16	=	=	SYM
ma-241	258	17			NUM
ma-241	258	18	1	1	NUM
ma-241	258	19	,	,	PUNCT
ma-241	258	20	q	q	NOUN
ma-241	258	21	=	=	SYM
ma-241	258	22	0	0	NUM
ma-241	258	23	1	1	NUM
ma-241	258	24	,	,	PUNCT
ma-241	258	25	q	q	X
ma-241	258	26	→	→	PUNCT
ma-241	258	27	+	+	ADJ
ma-241	258	28	∞	∞	PROPN
ma-241	258	29	1	1	NUM
ma-241	258	30	,	,	PUNCT
ma-241	258	31	|ξ|	|ξ|	PROPN
ma-241	258	32	→	→	SYM
ma-241	258	33	+	+	PROPN
ma-241	258	34	∞	∞	PROPN
ma-241	258	35	<	<	X
ma-241	258	36	1	1	NUM
ma-241	258	37	,	,	PUNCT
ma-241	258	38	ξ	ξ	PROPN
ma-241	258	39	∈	∈	PROPN
ma-241	258	40	(	(	PUNCT
ma-241	258	41	0,+∞	0,+∞	NUM
ma-241	258	42	)	)	PUNCT
ma-241	258	43	0	0	NUM
ma-241	258	44	,	,	PUNCT
ma-241	258	45	q	q	NOUN
ma-241	258	46	=	=	PUNCT
ma-241	258	47	q+	q+	NOUN
ma-241	258	48	=	=	NOUN
ma-241	258	49	3ν|ξ|	3ν|ξ|	NUM
ma-241	258	50	1+ξ2	1+ξ2	NUM
ma-241	258	51	,	,	PUNCT
ma-241	258	52	q	q	NOUN
ma-241	258	53	=	=	PUNCT
ma-241	258	54	q−	q−	PROPN
ma-241	258	55	=	=	PUNCT
ma-241	258	56	ν|ξ|	ν|ξ|	NOUN
ma-241	258	57	1+ξ2	1+ξ2	NUM
ma-241	258	58	.	.	PUNCT
ma-241	259	1	(	(	PUNCT
ma-241	259	2	50	50	NUM
ma-241	259	3	)	)	PUNCT
ma-241	259	4	proof	proof	NOUN
ma-241	259	5	.	.	PUNCT
ma-241	260	1	the	the	DET
ma-241	260	2	first	first	ADJ
ma-241	260	3	three	three	NUM
ma-241	260	4	relations	relation	NOUN
ma-241	260	5	in	in	ADP
ma-241	260	6	(	(	PUNCT
ma-241	260	7	50	50	NUM
ma-241	260	8	)	)	PUNCT
ma-241	260	9	can	can	AUX
ma-241	260	10	directly	directly	ADV
ma-241	260	11	be	be	AUX
ma-241	260	12	derived	derive	VERB
ma-241	260	13	by	by	ADP
ma-241	260	14	taking	take	VERB
ma-241	260	15	the	the	DET
ma-241	260	16	appropriate	appropriate	ADJ
ma-241	260	17	limits	limit	NOUN
ma-241	260	18	forthe	forthe	DET
ma-241	260	19	parameter	parameter	NOUN
ma-241	260	20	q	q	PROPN
ma-241	261	1	and	and	CCONJ
ma-241	261	2	the	the	DET
ma-241	261	3	fourier	fourier	NOUN
ma-241	261	4	frequency	frequency	NOUN
ma-241	261	5	ξ	ξ	PROPN
ma-241	261	6	.	.	PROPN
ma-241	262	1	for	for	ADP
ma-241	262	2	finite	finite	ADJ
ma-241	262	3	fourier	fourier	NOUN
ma-241	262	4	frequency	frequency	NOUN
ma-241	262	5	,	,	PUNCT
ma-241	262	6	the	the	DET
ma-241	262	7	reduction	reduction	NOUN
ma-241	262	8	factor	factor	NOUN
ma-241	262	9	isless	isless	NOUN
ma-241	262	10	than	than	ADP
ma-241	262	11	one	one	NUM
ma-241	262	12	.	.	PUNCT
ma-241	263	1	ultimately	ultimately	ADV
ma-241	263	2	,	,	PUNCT
ma-241	263	3	for	for	ADP
ma-241	263	4	the	the	DET
ma-241	263	5	indicated	indicate	VERB
ma-241	263	6	parameters	parameter	NOUN
ma-241	263	7	q−	q−	PROPN
ma-241	263	8	and	and	CCONJ
ma-241	263	9	q+	q+	PUNCT
ma-241	263	10	the	the	DET
ma-241	263	11	contraction	contraction	NOUN
ma-241	263	12	factor	factor	NOUN
ma-241	263	13	becomeszero	becomeszero	NOUN
ma-241	263	14	.	.	PUNCT
ma-241	264	1	�	�	PROPN
ma-241	264	2	corollary	corollary	NOUN
ma-241	264	3	6	6	NUM
ma-241	264	4	.	.	PUNCT
ma-241	265	1	if	if	SCONJ
ma-241	265	2	q	q	PRON
ma-241	265	3	=	=	VERB
ma-241	265	4	mν|ξ|(1	mν|ξ|(1	NOUN
ma-241	265	5	+	+	NUM
ma-241	265	6	ξ2)−1	ξ2)−1	NOUN
ma-241	265	7	,	,	PUNCT
ma-241	265	8	m	m	VERB
ma-241	265	9	∈	∈	NOUN
ma-241	265	10	z+	z+	NUM
ma-241	265	11	−	−	PROPN
ma-241	265	12	{	{	PUNCT
ma-241	265	13	1	1	NUM
ma-241	265	14	,	,	PUNCT
ma-241	265	15	3	3	NUM
ma-241	265	16	}	}	PUNCT
ma-241	265	17	,	,	PUNCT
ma-241	265	18	then	then	ADV
ma-241	265	19	the	the	DET
ma-241	265	20	convergence	convergence	NOUN
ma-241	265	21	factor	factor	NOUN
ma-241	265	22	(	(	PUNCT
ma-241	265	23	46	46	NUM
ma-241	265	24	)	)	PUNCT
ma-241	265	25	does	do	AUX
ma-241	265	26	not	not	PART
ma-241	265	27	depend	depend	VERB
ma-241	265	28	on	on	ADP
ma-241	265	29	viscosity	viscosity	NOUN
ma-241	265	30	and	and	CCONJ
ma-241	265	31	fourier	fourier	NOUN
ma-241	265	32	frequency	frequency	NOUN
ma-241	265	33	.	.	PUNCT
ma-241	266	1	proof	proof	NOUN
ma-241	266	2	.	.	PUNCT
ma-241	267	1	the	the	DET
ma-241	267	2	proof	proof	NOUN
ma-241	267	3	follows	follow	VERB
ma-241	267	4	by	by	ADP
ma-241	267	5	substitution	substitution	NOUN
ma-241	267	6	of	of	ADP
ma-241	267	7	the	the	DET
ma-241	267	8	q	q	PROPN
ma-241	267	9	parameter	parameter	NOUN
ma-241	267	10	back	back	ADV
ma-241	267	11	to	to	ADP
ma-241	267	12	(	(	PUNCT
ma-241	267	13	46	46	NUM
ma-241	267	14	)	)	PUNCT
ma-241	267	15	.	.	PUNCT
ma-241	268	1	the	the	DET
ma-241	268	2	expression	expression	NOUN
ma-241	268	3	obtainedis	obtainedi	NOUN
ma-241	268	4	identical	identical	ADJ
ma-241	268	5	to	to	ADP
ma-241	268	6	the	the	DET
ma-241	268	7	one	one	NOUN
ma-241	268	8	appearing	appear	VERB
ma-241	268	9	in	in	ADP
ma-241	268	10	the	the	DET
ma-241	268	11	corollary	corollary	ADJ
ma-241	268	12	4	4	NUM
ma-241	268	13	.	.	PUNCT
ma-241	268	14	�	�	PROPN
ma-241	268	15	6	6	NUM
ma-241	268	16	.	.	PUNCT
ma-241	269	1	numerical	numerical	ADJ
ma-241	269	2	evidence	evidence	NOUN
ma-241	269	3	-	-	PUNCT
ma-241	269	4	convergence	convergence	NOUN
ma-241	269	5	curves	curve	NOUN
ma-241	269	6	in	in	ADP
ma-241	269	7	this	this	DET
ma-241	269	8	section	section	NOUN
ma-241	269	9	,	,	PUNCT
ma-241	269	10	the	the	DET
ma-241	269	11	convergence	convergence	NOUN
ma-241	269	12	curves	curve	NOUN
ma-241	269	13	are	be	AUX
ma-241	269	14	presented	present	VERB
ma-241	269	15	for	for	ADP
ma-241	269	16	each	each	DET
ma-241	269	17	one	one	NUM
ma-241	269	18	of	of	ADP
ma-241	269	19	the	the	DET
ma-241	269	20	schwarz	schwarz	PROPN
ma-241	269	21	algorithms	algorithms	PROPN
ma-241	269	22	.	.	PUNCT
ma-241	270	1	inthe	inthe	DET
ma-241	270	2	cases	case	NOUN
ma-241	270	3	of	of	ADP
ma-241	270	4	oprimised	oprimise	VERB
ma-241	270	5	schwarz	schwarz	PROPN
ma-241	270	6	methods	method	NOUN
ma-241	270	7	with	with	ADP
ma-241	270	8	robin	robin	PROPN
ma-241	270	9	and	and	CCONJ
ma-241	270	10	second	second	ADJ
ma-241	270	11	order	order	NOUN
ma-241	270	12	transmission	transmission	NOUN
ma-241	270	13	conditions	condition	NOUN
ma-241	270	14	,	,	PUNCT
ma-241	270	15	weconsider	weconsider	NOUN
ma-241	270	16	γ	γ	NOUN
ma-241	270	17	=	=	PUNCT
ma-241	270	18	ν	ν	NOUN
ma-241	270	19	and	and	CCONJ
ma-241	270	20	q	q	NOUN
ma-241	270	21	=	=	SYM
ma-241	270	22	ν	ν	NOUN
ma-241	270	23	.	.	PUNCT
ma-241	271	1	the	the	DET
ma-241	271	2	convergence	convergence	NOUN
ma-241	271	3	curves	curve	NOUN
ma-241	271	4	are	be	AUX
ma-241	271	5	presented	present	VERB
ma-241	271	6	below	below	ADV
ma-241	271	7	.	.	PUNCT
ma-241	272	1	figure	figure	NOUN
ma-241	272	2	2	2	NUM
ma-241	272	3	.	.	PUNCT
ma-241	272	4	convergence	convergence	NOUN
ma-241	272	5	rate	rate	NOUN
ma-241	272	6	of	of	ADP
ma-241	272	7	schwarz	schwarz	PROPN
ma-241	272	8	method	method	NOUN
ma-241	272	9	using	use	VERB
ma-241	272	10	dirichlet	dirichlet	PROPN
ma-241	272	11	ic	ic	PROPN
ma-241	272	12	for	for	ADP
ma-241	272	13	varying	vary	VERB
ma-241	272	14	overlap	overlap	NOUN
ma-241	272	15	.	.	PUNCT
ma-241	273	1	https://doi.org/10.28924/ada/ma.5.6	https://doi.org/10.28924/ada/ma.5.6	PROPN
ma-241	273	2	eur	eur	PROPN
ma-241	273	3	.	.	PUNCT
ma-241	274	1	j.	j.	PROPN
ma-241	274	2	math	math	PROPN
ma-241	274	3	.	.	PUNCT
ma-241	275	1	anal	anal	PROPN
ma-241	275	2	.	.	PUNCT
ma-241	276	1	10.28924	10.28924	NUM
ma-241	276	2	/	/	SYM
ma-241	276	3	ada	ada	PROPN
ma-241	276	4	/	/	SYM
ma-241	276	5	ma.5.6	ma.5.6	PROPN
ma-241	276	6	14	14	NUM
ma-241	276	7	figure	figure	NOUN
ma-241	276	8	3	3	NUM
ma-241	276	9	.	.	PUNCT
ma-241	276	10	convergence	convergence	NOUN
ma-241	276	11	rate	rate	NOUN
ma-241	276	12	of	of	ADP
ma-241	276	13	schwarz	schwarz	PROPN
ma-241	276	14	method	method	NOUN
ma-241	276	15	using	use	VERB
ma-241	276	16	neumann	neumann	PROPN
ma-241	276	17	ic	ic	PROPN
ma-241	276	18	for	for	ADP
ma-241	276	19	varying	vary	VERB
ma-241	276	20	overlap	overlap	NOUN
ma-241	276	21	.	.	PUNCT
ma-241	277	1	figure	figure	NOUN
ma-241	277	2	4	4	NUM
ma-241	277	3	.	.	PUNCT
ma-241	277	4	convergence	convergence	NOUN
ma-241	277	5	rate	rate	NOUN
ma-241	277	6	of	of	ADP
ma-241	277	7	schwarz	schwarz	PROPN
ma-241	277	8	method	method	NOUN
ma-241	277	9	using	use	VERB
ma-241	277	10	robin	robin	PROPN
ma-241	277	11	ic	ic	PROPN
ma-241	277	12	for	for	ADP
ma-241	277	13	varying	vary	VERB
ma-241	277	14	viscosity	viscosity	NOUN
ma-241	277	15	.	.	PUNCT
ma-241	278	1	https://doi.org/10.28924/ada/ma.5.6	https://doi.org/10.28924/ada/ma.5.6	PROPN
ma-241	278	2	eur	eur	PROPN
ma-241	278	3	.	.	PUNCT
ma-241	279	1	j.	j.	PROPN
ma-241	279	2	math	math	PROPN
ma-241	279	3	.	.	PUNCT
ma-241	280	1	anal	anal	PROPN
ma-241	280	2	.	.	PUNCT
ma-241	281	1	10.28924	10.28924	NUM
ma-241	281	2	/	/	SYM
ma-241	281	3	ada	ada	PROPN
ma-241	281	4	/	/	SYM
ma-241	281	5	ma.5.6	ma.5.6	PROPN
ma-241	281	6	15	15	NUM
ma-241	281	7	figure	figure	NOUN
ma-241	281	8	5	5	NUM
ma-241	281	9	.	.	PUNCT
ma-241	281	10	convergence	convergence	NOUN
ma-241	281	11	rate	rate	NOUN
ma-241	281	12	of	of	ADP
ma-241	281	13	schwarz	schwarz	PROPN
ma-241	281	14	method	method	NOUN
ma-241	281	15	using	use	VERB
ma-241	281	16	second	second	ADJ
ma-241	281	17	order	order	NOUN
ma-241	281	18	ic	ic	INTJ
ma-241	281	19	for	for	ADP
ma-241	281	20	varying	vary	VERB
ma-241	281	21	viscosity	viscosity	NOUN
ma-241	281	22	.	.	PUNCT
ma-241	282	1	figure	figure	VERB
ma-241	282	2	6	6	NUM
ma-241	282	3	.	.	PUNCT
ma-241	282	4	comparison	comparison	NOUN
ma-241	282	5	of	of	ADP
ma-241	282	6	convergence	convergence	NOUN
ma-241	282	7	rates	rate	NOUN
ma-241	282	8	for	for	ADP
ma-241	282	9	all	all	DET
ma-241	282	10	schwarz	schwarz	PROPN
ma-241	282	11	methods	method	NOUN
ma-241	282	12	.	.	PUNCT
ma-241	283	1	employing	employ	VERB
ma-241	283	2	the	the	DET
ma-241	283	3	graphs	graph	NOUN
ma-241	283	4	of	of	ADP
ma-241	283	5	the	the	DET
ma-241	283	6	convergence	convergence	NOUN
ma-241	283	7	rates	rate	NOUN
ma-241	283	8	in	in	ADP
ma-241	283	9	figure	figure	NOUN
ma-241	283	10	2	2	NUM
ma-241	283	11	and	and	CCONJ
ma-241	283	12	figure	figure	VERB
ma-241	283	13	3	3	NUM
ma-241	283	14	,	,	PUNCT
ma-241	283	15	we	we	PRON
ma-241	283	16	can	can	AUX
ma-241	283	17	comparethe	comparethe	DET
ma-241	283	18	schwarz	schwarz	PROPN
ma-241	283	19	methods	method	NOUN
ma-241	283	20	using	use	VERB
ma-241	283	21	dirichlet	dirichlet	PROPN
ma-241	283	22	and	and	CCONJ
ma-241	283	23	neumann	neumann	PROPN
ma-241	283	24	interface	interface	NOUN
ma-241	283	25	conditions	condition	NOUN
ma-241	283	26	.	.	PUNCT
ma-241	284	1	we	we	PRON
ma-241	284	2	notice	notice	VERB
ma-241	284	3	that	that	SCONJ
ma-241	284	4	when	when	SCONJ
ma-241	284	5	https://doi.org/10.28924/ada/ma.5.6	https://doi.org/10.28924/ada/ma.5.6	PROPN
ma-241	284	6	eur	eur	PROPN
ma-241	284	7	.	.	PUNCT
ma-241	285	1	j.	j.	PROPN
ma-241	285	2	math	math	PROPN
ma-241	285	3	.	.	PUNCT
ma-241	286	1	anal	anal	PROPN
ma-241	286	2	.	.	PUNCT
ma-241	287	1	10.28924	10.28924	NUM
ma-241	287	2	/	/	SYM
ma-241	287	3	ada	ada	PROPN
ma-241	287	4	/	/	SYM
ma-241	287	5	ma.5.6	ma.5.6	ADJ
ma-241	287	6	16neumann	16neumann	NOUN
ma-241	287	7	transmission	transmission	NOUN
ma-241	287	8	conditions	condition	NOUN
ma-241	287	9	are	be	AUX
ma-241	287	10	imposed	impose	VERB
ma-241	287	11	,	,	PUNCT
ma-241	287	12	the	the	DET
ma-241	287	13	convergence	convergence	NOUN
ma-241	287	14	rate	rate	NOUN
ma-241	287	15	decays	decay	VERB
ma-241	287	16	rapidly	rapidly	ADV
ma-241	287	17	for	for	ADP
ma-241	287	18	increasingfourier	increasingfouri	ADJ
ma-241	287	19	modes	mode	NOUN
ma-241	287	20	,	,	PUNCT
ma-241	287	21	whereas	whereas	SCONJ
ma-241	287	22	using	use	VERB
ma-241	287	23	dirichlet	dirichlet	NOUN
ma-241	287	24	conditions	condition	NOUN
ma-241	287	25	makes	make	VERB
ma-241	287	26	the	the	DET
ma-241	287	27	convergence	convergence	NOUN
ma-241	287	28	slower	slow	ADJ
ma-241	287	29	.	.	PUNCT
ma-241	288	1	in	in	ADP
ma-241	288	2	addition	addition	NOUN
ma-241	288	3	,	,	PUNCT
ma-241	288	4	itis	itis	NOUN
ma-241	288	5	evident	evident	ADJ
ma-241	288	6	that	that	SCONJ
ma-241	288	7	when	when	SCONJ
ma-241	288	8	the	the	DET
ma-241	288	9	overlap	overlap	NOUN
ma-241	288	10	between	between	ADP
ma-241	288	11	the	the	DET
ma-241	288	12	subdomains	subdomain	NOUN
ma-241	288	13	is	be	AUX
ma-241	288	14	larger	large	ADJ
ma-241	288	15	then	then	ADV
ma-241	288	16	this	this	PRON
ma-241	288	17	enhances	enhance	VERB
ma-241	288	18	the	the	DET
ma-241	288	19	overallconvergence	overallconvergence	NOUN
ma-241	288	20	which	which	PRON
ma-241	288	21	is	be	AUX
ma-241	288	22	the	the	DET
ma-241	288	23	expected	expect	VERB
ma-241	288	24	result	result	NOUN
ma-241	288	25	when	when	SCONJ
ma-241	288	26	using	use	VERB
ma-241	288	27	the	the	DET
ma-241	288	28	classical	classical	ADJ
ma-241	288	29	schwarz	schwarz	NOUN
ma-241	288	30	methods	method	NOUN
ma-241	288	31	.	.	PUNCT
ma-241	289	1	in	in	ADP
ma-241	289	2	figures	figure	NOUN
ma-241	289	3	4and	4and	NOUN
ma-241	289	4	5	5	NUM
ma-241	289	5	we	we	PRON
ma-241	289	6	have	have	VERB
ma-241	289	7	the	the	DET
ma-241	289	8	convergence	convergence	NOUN
ma-241	289	9	curves	curve	NOUN
ma-241	289	10	of	of	ADP
ma-241	289	11	non	non	ADJ
ma-241	289	12	-	-	ADJ
ma-241	289	13	overlapping	overlapping	ADJ
ma-241	289	14	optimized	optimize	VERB
ma-241	289	15	schwarz	schwarz	NOUN
ma-241	289	16	methods	method	NOUN
ma-241	289	17	(	(	PUNCT
ma-241	289	18	figure4	figure4	PROPN
ma-241	289	19	-	-	PUNCT
ma-241	289	20	robin	robin	PROPN
ma-241	289	21	ic	ic	PROPN
ma-241	289	22	,	,	PUNCT
ma-241	289	23	figure	figure	VERB
ma-241	289	24	5	5	NUM
ma-241	289	25	-	-	PUNCT
ma-241	289	26	second	second	ADJ
ma-241	289	27	order	order	NOUN
ma-241	289	28	ic	ic	NUM
ma-241	289	29	)	)	PUNCT
ma-241	289	30	for	for	ADP
ma-241	289	31	varying	vary	VERB
ma-241	289	32	values	value	NOUN
ma-241	289	33	of	of	ADP
ma-241	289	34	the	the	DET
ma-241	289	35	viscosity	viscosity	NOUN
ma-241	289	36	.	.	PUNCT
ma-241	290	1	we	we	PRON
ma-241	290	2	notice	notice	VERB
ma-241	290	3	that	that	SCONJ
ma-241	290	4	thesealgorithms	thesealgorithm	NOUN
ma-241	290	5	have	have	VERB
ma-241	290	6	better	well	ADJ
ma-241	290	7	convergence	convergence	NOUN
ma-241	290	8	for	for	ADP
ma-241	290	9	small	small	ADJ
ma-241	290	10	fourier	fourier	NOUN
ma-241	290	11	frequencies	frequency	NOUN
ma-241	290	12	but	but	CCONJ
ma-241	290	13	as	as	SCONJ
ma-241	290	14	the	the	DET
ma-241	290	15	fourier	fourier	NOUN
ma-241	290	16	frequencygrows	frequencygrow	VERB
ma-241	290	17	to	to	ADP
ma-241	290	18	infinity	infinity	NOUN
ma-241	290	19	,	,	PUNCT
ma-241	290	20	the	the	DET
ma-241	290	21	reduction	reduction	NOUN
ma-241	290	22	factor	factor	NOUN
ma-241	290	23	tends	tend	VERB
ma-241	290	24	to	to	ADP
ma-241	290	25	1	1	NUM
ma-241	290	26	.	.	PUNCT
ma-241	291	1	we	we	PRON
ma-241	291	2	also	also	ADV
ma-241	291	3	notice	notice	VERB
ma-241	291	4	that	that	SCONJ
ma-241	291	5	when	when	SCONJ
ma-241	291	6	we	we	PRON
ma-241	291	7	tune	tune	VERB
ma-241	291	8	the	the	DET
ma-241	291	9	parametersof	parametersof	NOUN
ma-241	291	10	these	these	DET
ma-241	291	11	optimised	optimise	VERB
ma-241	291	12	methods	method	NOUN
ma-241	291	13	,	,	PUNCT
ma-241	291	14	we	we	PRON
ma-241	291	15	can	can	AUX
ma-241	291	16	choose	choose	VERB
ma-241	291	17	values	value	NOUN
ma-241	291	18	to	to	PART
ma-241	291	19	make	make	VERB
ma-241	291	20	the	the	DET
ma-241	291	21	convergence	convergence	NOUN
ma-241	291	22	rate	rate	NOUN
ma-241	291	23	equal	equal	ADJ
ma-241	291	24	to	to	ADP
ma-241	291	25	zero.last	zero.last	NUM
ma-241	291	26	but	but	CCONJ
ma-241	291	27	not	not	PART
ma-241	291	28	least	least	ADJ
ma-241	291	29	,	,	PUNCT
ma-241	291	30	we	we	PRON
ma-241	291	31	compare	compare	VERB
ma-241	291	32	all	all	DET
ma-241	291	33	the	the	DET
ma-241	291	34	convergence	convergence	NOUN
ma-241	291	35	curves	curve	NOUN
ma-241	291	36	and	and	CCONJ
ma-241	291	37	obtain	obtain	VERB
ma-241	291	38	figure	figure	NOUN
ma-241	291	39	6	6	NUM
ma-241	291	40	,	,	PUNCT
ma-241	291	41	which	which	PRON
ma-241	291	42	indicatesthat	indicatesthat	VERB
ma-241	291	43	the	the	DET
ma-241	291	44	schwarz	schwarz	PROPN
ma-241	291	45	methods	method	NOUN
ma-241	291	46	with	with	ADP
ma-241	291	47	neummann	neummann	NOUN
ma-241	291	48	and	and	CCONJ
ma-241	291	49	dirichlet	dirichlet	PROPN
ma-241	291	50	transmission	transmission	NOUN
ma-241	291	51	conditions	condition	NOUN
ma-241	291	52	are	be	AUX
ma-241	291	53	slower	slow	ADJ
ma-241	291	54	forlow	forlow	NOUN
ma-241	291	55	frequencies	frequency	NOUN
ma-241	291	56	,	,	PUNCT
ma-241	291	57	and	and	CCONJ
ma-241	291	58	the	the	DET
ma-241	291	59	optimised	optimise	VERB
ma-241	291	60	methods	method	NOUN
ma-241	291	61	perform	perform	VERB
ma-241	291	62	better	well	ADV
ma-241	291	63	in	in	ADP
ma-241	291	64	this	this	DET
ma-241	291	65	regime	regime	NOUN
ma-241	291	66	.	.	PUNCT
ma-241	292	1	however	however	ADV
ma-241	292	2	,	,	PUNCT
ma-241	292	3	the	the	DET
ma-241	292	4	problemsoccur	problemsoccur	NOUN
ma-241	292	5	when	when	SCONJ
ma-241	292	6	the	the	DET
ma-241	292	7	frequencies	frequency	NOUN
ma-241	292	8	are	be	AUX
ma-241	292	9	large	large	ADJ
ma-241	292	10	which	which	PRON
ma-241	292	11	means	mean	VERB
ma-241	292	12	that	that	SCONJ
ma-241	292	13	the	the	DET
ma-241	292	14	reduction	reduction	NOUN
ma-241	292	15	factor	factor	NOUN
ma-241	292	16	tends	tend	VERB
ma-241	292	17	to	to	ADP
ma-241	292	18	1	1	NUM
ma-241	292	19	,	,	PUNCT
ma-241	292	20	which	which	PRON
ma-241	292	21	isnot	isnot	ADV
ma-241	292	22	desirable	desirable	ADJ
ma-241	292	23	when	when	SCONJ
ma-241	292	24	dealing	deal	VERB
ma-241	292	25	with	with	ADP
ma-241	292	26	schwarz	schwarz	PROPN
ma-241	292	27	algorithms	algorithm	NOUN
ma-241	292	28	.	.	PUNCT
ma-241	293	1	7	7	X
ma-241	293	2	.	.	X
ma-241	293	3	conclusions	conclusion	NOUN
ma-241	293	4	in	in	ADP
ma-241	293	5	this	this	DET
ma-241	293	6	work	work	NOUN
ma-241	293	7	we	we	PRON
ma-241	293	8	focused	focus	VERB
ma-241	293	9	on	on	ADP
ma-241	293	10	the	the	DET
ma-241	293	11	convergence	convergence	NOUN
ma-241	293	12	analysis	analysis	NOUN
ma-241	293	13	of	of	ADP
ma-241	293	14	the	the	DET
ma-241	293	15	schwarz	schwarz	PROPN
ma-241	293	16	algorithms	algorithm	NOUN
ma-241	293	17	for	for	ADP
ma-241	293	18	stokes	stoke	NOUN
ma-241	293	19	-	-	PUNCT
ma-241	293	20	stokesconfiguration	stokesconfiguration	NOUN
ma-241	293	21	for	for	ADP
ma-241	293	22	varying	vary	VERB
ma-241	293	23	interface	interface	NOUN
ma-241	293	24	conditions	condition	NOUN
ma-241	293	25	.	.	PUNCT
ma-241	294	1	we	we	PRON
ma-241	294	2	carried	carry	VERB
ma-241	294	3	out	out	ADP
ma-241	294	4	the	the	DET
ma-241	294	5	analysis	analysis	NOUN
ma-241	294	6	using	use	VERB
ma-241	294	7	partial	partial	ADJ
ma-241	294	8	fouriertransform	fouriertransform	NOUN
ma-241	294	9	and	and	CCONJ
ma-241	294	10	we	we	PRON
ma-241	294	11	obtained	obtain	VERB
ma-241	294	12	the	the	DET
ma-241	294	13	contraction	contraction	NOUN
ma-241	294	14	factors	factor	NOUN
ma-241	294	15	for	for	ADP
ma-241	294	16	each	each	DET
ma-241	294	17	one	one	NUM
ma-241	294	18	of	of	ADP
ma-241	294	19	the	the	DET
ma-241	294	20	methods	method	NOUN
ma-241	294	21	introduced	introduce	VERB
ma-241	294	22	.	.	PUNCT
ma-241	295	1	afterconducting	afterconducte	VERB
ma-241	295	2	the	the	DET
ma-241	295	3	convergence	convergence	NOUN
ma-241	295	4	analysis	analysis	NOUN
ma-241	295	5	,	,	PUNCT
ma-241	295	6	we	we	PRON
ma-241	295	7	notice	notice	VERB
ma-241	295	8	that	that	SCONJ
ma-241	295	9	the	the	DET
ma-241	295	10	neumann	neumann	PROPN
ma-241	295	11	conditions	condition	NOUN
ma-241	295	12	result	result	VERB
ma-241	295	13	in	in	ADP
ma-241	295	14	faster	fast	ADJ
ma-241	295	15	decayof	decayof	NOUN
ma-241	295	16	reduction	reduction	NOUN
ma-241	295	17	factor	factor	NOUN
ma-241	295	18	when	when	SCONJ
ma-241	295	19	ξ	ξ	PROPN
ma-241	295	20	grows	grow	VERB
ma-241	295	21	sufficiently	sufficiently	ADV
ma-241	295	22	large	large	ADJ
ma-241	295	23	compared	compare	VERB
ma-241	295	24	to	to	ADP
ma-241	295	25	the	the	DET
ma-241	295	26	dirichlet	dirichlet	PROPN
ma-241	295	27	ic	ic	PROPN
ma-241	295	28	.	.	PUNCT
ma-241	296	1	the	the	DET
ma-241	296	2	optimisedschwarz	optimisedschwarz	PROPN
ma-241	296	3	methods	method	NOUN
ma-241	296	4	have	have	VERB
ma-241	296	5	advantage	advantage	NOUN
ma-241	296	6	in	in	ADP
ma-241	296	7	the	the	DET
ma-241	296	8	low	low	ADJ
ma-241	296	9	frequency	frequency	NOUN
ma-241	296	10	regime	regime	NOUN
ma-241	296	11	,	,	PUNCT
ma-241	296	12	but	but	CCONJ
ma-241	296	13	as	as	SCONJ
ma-241	296	14	the	the	DET
ma-241	296	15	fourier	fourier	ADJ
ma-241	296	16	number	number	NOUN
ma-241	296	17	growsthe	growsthe	PROPN
ma-241	296	18	contraction	contraction	NOUN
ma-241	296	19	rate	rate	NOUN
ma-241	296	20	tends	tend	VERB
ma-241	296	21	to	to	ADP
ma-241	296	22	one	one	NUM
ma-241	296	23	which	which	PRON
ma-241	296	24	is	be	AUX
ma-241	296	25	not	not	PART
ma-241	296	26	desirable	desirable	ADJ
ma-241	296	27	behavior	behavior	NOUN
ma-241	296	28	.	.	PUNCT
ma-241	297	1	the	the	DET
ma-241	297	2	convergence	convergence	NOUN
ma-241	297	3	analysis	analysis	NOUN
ma-241	297	4	forstokes	forstoke	NOUN
ma-241	297	5	-	-	PUNCT
ma-241	297	6	stokes	stoke	NOUN
ma-241	297	7	configuration	configuration	NOUN
ma-241	297	8	is	be	AUX
ma-241	297	9	useful	useful	ADJ
ma-241	297	10	for	for	ADP
ma-241	297	11	studying	study	VERB
ma-241	297	12	the	the	DET
ma-241	297	13	behavior	behavior	NOUN
ma-241	297	14	of	of	ADP
ma-241	297	15	schwarz	schwarz	PROPN
ma-241	297	16	algorithms	algorithm	NOUN
ma-241	297	17	and	and	CCONJ
ma-241	297	18	gettinga	gettinga	ADJ
ma-241	297	19	general	general	ADJ
ma-241	297	20	insight	insight	NOUN
ma-241	297	21	.	.	PUNCT
ma-241	298	1	so	so	ADV
ma-241	298	2	far	far	ADV
ma-241	298	3	there	there	PRON
ma-241	298	4	is	be	VERB
ma-241	298	5	such	such	ADJ
ma-241	298	6	analysis	analysis	NOUN
ma-241	298	7	for	for	ADP
ma-241	298	8	stokes	stokes	PROPN
ma-241	298	9	-	-	PUNCT
ma-241	298	10	darcy	darcy	PROPN
ma-241	298	11	coupling	coupling	PROPN
ma-241	298	12	[	[	X
ma-241	298	13	18	18	NUM
ma-241	298	14	]	]	X
ma-241	298	15	,	,	PUNCT
ma-241	298	16	as	as	SCONJ
ma-241	298	17	a	a	DET
ma-241	298	18	result	result	NOUN
ma-241	298	19	thiswork	thiswork	NOUN
ma-241	298	20	could	could	AUX
ma-241	298	21	enrich	enrich	VERB
ma-241	298	22	the	the	DET
ma-241	298	23	existing	exist	VERB
ma-241	298	24	mathematical	mathematical	ADJ
ma-241	298	25	literature	literature	NOUN
ma-241	298	26	.	.	PUNCT
ma-241	299	1	references	reference	NOUN
ma-241	299	2	[	[	X
ma-241	299	3	1	1	NUM
ma-241	299	4	]	]	X
ma-241	299	5	m.j	m.j	PROPN
ma-241	299	6	.	.	PROPN
ma-241	299	7	gander	gander	NOUN
ma-241	299	8	,	,	PUNCT
ma-241	299	9	optimized	optimize	VERB
ma-241	299	10	schwarz	schwarz	PROPN
ma-241	299	11	methods	method	NOUN
ma-241	299	12	for	for	ADP
ma-241	299	13	helmholtz	helmholtz	NOUN
ma-241	299	14	problems	problem	NOUN
ma-241	299	15	,	,	PUNCT
ma-241	299	16	in	in	ADP
ma-241	299	17	:	:	PUNCT
ma-241	299	18	proceedings	proceeding	NOUN
ma-241	299	19	of	of	ADP
ma-241	299	20	the	the	DET
ma-241	299	21	13th	13th	ADJ
ma-241	299	22	international	international	ADJ
ma-241	299	23	con	con	NOUN
ma-241	299	24	-	-	PUNCT
ma-241	299	25	ference	ference	NOUN
ma-241	299	26	on	on	ADP
ma-241	299	27	domain	domain	NOUN
ma-241	299	28	decomposition	decomposition	NOUN
ma-241	299	29	,	,	PUNCT
ma-241	299	30	cimne	cimne	PROPN
ma-241	299	31	(	(	PUNCT
ma-241	299	32	2001	2001	NUM
ma-241	299	33	)	)	PUNCT
ma-241	299	34	245	245	NUM
ma-241	299	35	-	-	SYM
ma-241	299	36	252.[2	252.[2	NUM
ma-241	299	37	]	]	X
ma-241	299	38	m.j	m.j	PROPN
ma-241	299	39	.	.	PROPN
ma-241	299	40	gander	gander	PROPN
ma-241	299	41	,	,	PUNCT
ma-241	299	42	l.	l.	PROPN
ma-241	299	43	halpern	halpern	PROPN
ma-241	299	44	,	,	PUNCT
ma-241	299	45	f.	f.	PROPN
ma-241	299	46	nataf	nataf	PROPN
ma-241	299	47	,	,	PUNCT
ma-241	299	48	optimized	optimize	VERB
ma-241	299	49	schwarz	schwarz	PROPN
ma-241	299	50	methods	method	NOUN
ma-241	299	51	,	,	PUNCT
ma-241	299	52	in	in	ADP
ma-241	299	53	:	:	PUNCT
ma-241	299	54	proceedings	proceeding	NOUN
ma-241	299	55	of	of	ADP
ma-241	299	56	the	the	DET
ma-241	299	57	12th	12th	ADJ
ma-241	299	58	international	international	ADJ
ma-241	299	59	conferenceon	conferenceon	NOUN
ma-241	299	60	domain	domain	NOUN
ma-241	299	61	decomposition	decomposition	NOUN
ma-241	299	62	,	,	PUNCT
ma-241	299	63	ddm.org	ddm.org	NUM
ma-241	299	64	(	(	PUNCT
ma-241	299	65	2000	2000	NUM
ma-241	299	66	)	)	PUNCT
ma-241	299	67	15	15	NUM
ma-241	299	68	-	-	SYM
ma-241	299	69	27.[3	27.[3	NUM
ma-241	299	70	]	]	X
ma-241	299	71	p.l	p.l	PROPN
ma-241	299	72	.	.	PROPN
ma-241	299	73	lions	lion	NOUN
ma-241	299	74	,	,	PUNCT
ma-241	299	75	on	on	ADP
ma-241	299	76	the	the	DET
ma-241	299	77	schwarz	schwarz	PROPN
ma-241	299	78	alternating	alternate	VERB
ma-241	299	79	method	method	PROPN
ma-241	299	80	iii	iii	PROPN
ma-241	299	81	:	:	PUNCT
ma-241	299	82	a	a	DET
ma-241	299	83	variant	variant	NOUN
ma-241	299	84	for	for	ADP
ma-241	299	85	nonoverlapping	nonoverlapping	ADJ
ma-241	299	86	subdomains	subdomain	NOUN
ma-241	299	87	,	,	PUNCT
ma-241	299	88	in	in	ADP
ma-241	299	89	:	:	PUNCT
ma-241	299	90	t.	t.	PROPN
ma-241	299	91	chan	chan	PROPN
ma-241	299	92	,	,	PUNCT
ma-241	299	93	r.	r.	PROPN
ma-241	299	94	glowinski	glowinski	PROPN
ma-241	299	95	,	,	PUNCT
ma-241	299	96	j.	j.	PROPN
ma-241	299	97	periaux	periaux	PROPN
ma-241	299	98	,	,	PUNCT
ma-241	299	99	o.b	o.b	PROPN
ma-241	299	100	.	.	PROPN
ma-241	299	101	widlund	widlund	PROPN
ma-241	299	102	(	(	PUNCT
ma-241	299	103	eds	ed	NOUN
ma-241	299	104	.	.	PUNCT
ma-241	299	105	)	)	PUNCT
ma-241	299	106	,	,	PUNCT
ma-241	299	107	third	third	ADJ
ma-241	299	108	international	international	ADJ
ma-241	299	109	symposium	symposium	NOUN
ma-241	299	110	on	on	ADP
ma-241	299	111	domain	domain	NOUN
ma-241	299	112	decomposition	decomposition	NOUN
ma-241	299	113	methods	method	NOUN
ma-241	299	114	for	for	ADP
ma-241	299	115	partialdifferential	partialdifferential	ADJ
ma-241	299	116	equations	equation	NOUN
ma-241	299	117	,	,	PUNCT
ma-241	299	118	siam	siam	X
ma-241	299	119	(	(	PUNCT
ma-241	299	120	1990	1990	NUM
ma-241	299	121	)	)	PUNCT
ma-241	299	122	202	202	NUM
ma-241	299	123	-	-	SYM
ma-241	299	124	223.[4	223.[4	NUM
ma-241	299	125	]	]	X
ma-241	299	126	m.j	m.j	PROPN
ma-241	299	127	.	.	PROPN
ma-241	299	128	gander	gander	PROPN
ma-241	299	129	,	,	PUNCT
ma-241	299	130	g.	g.	PROPN
ma-241	299	131	wanner	wanner	NOUN
ma-241	299	132	,	,	PUNCT
ma-241	299	133	the	the	DET
ma-241	299	134	origins	origin	NOUN
ma-241	299	135	of	of	ADP
ma-241	299	136	the	the	DET
ma-241	299	137	alternating	alternate	VERB
ma-241	299	138	schwarz	schwarz	PROPN
ma-241	299	139	method	method	NOUN
ma-241	299	140	,	,	PUNCT
ma-241	299	141	in	in	ADP
ma-241	299	142	:	:	PUNCT
ma-241	299	143	domain	domain	NOUN
ma-241	299	144	decomposition	decomposition	NOUN
ma-241	299	145	methods	method	NOUN
ma-241	299	146	inscience	inscience	NOUN
ma-241	299	147	and	and	CCONJ
ma-241	299	148	engineering	engineer	VERB
ma-241	299	149	xxi	xxi	PROPN
ma-241	299	150	,	,	PUNCT
ma-241	299	151	lncse	lncse	NOUN
ma-241	299	152	,	,	PUNCT
ma-241	299	153	springer	springer	NOUN
ma-241	299	154	-	-	PUNCT
ma-241	299	155	verlag	verlag	PROPN
ma-241	299	156	(	(	PUNCT
ma-241	299	157	2014	2014	NUM
ma-241	299	158	)	)	PUNCT
ma-241	299	159	487	487	NUM
ma-241	299	160	-	-	SYM
ma-241	299	161	496.[5	496.[5	NUM
ma-241	299	162	]	]	X
ma-241	299	163	m.j	m.j	PROPN
ma-241	299	164	.	.	PROPN
ma-241	299	165	gander	gander	NOUN
ma-241	299	166	,	,	PUNCT
ma-241	299	167	schwarz	schwarz	NOUN
ma-241	299	168	methods	method	NOUN
ma-241	299	169	over	over	ADP
ma-241	299	170	the	the	DET
ma-241	299	171	course	course	NOUN
ma-241	299	172	of	of	ADP
ma-241	299	173	time	time	NOUN
ma-241	299	174	,	,	PUNCT
ma-241	299	175	elec	elec	PROPN
ma-241	299	176	.	.	PUNCT
ma-241	300	1	trans	trans	PROPN
ma-241	300	2	.	.	PUNCT
ma-241	301	1	numer	numer	PROPN
ma-241	301	2	.	.	PUNCT
ma-241	302	1	anal	anal	PROPN
ma-241	302	2	.	.	PUNCT
ma-241	303	1	31	31	NUM
ma-241	303	2	(	(	PUNCT
ma-241	303	3	2008	2008	NUM
ma-241	303	4	)	)	PUNCT
ma-241	303	5	228	228	NUM
ma-241	303	6	-	-	SYM
ma-241	303	7	255	255	NUM
ma-241	303	8	.	.	PUNCT
ma-241	304	1	https://doi.org/10.28924/ada/ma.5.6	https://doi.org/10.28924/ada/ma.5.6	PROPN
ma-241	304	2	eur	eur	PROPN
ma-241	304	3	.	.	PUNCT
ma-241	305	1	j.	j.	PROPN
ma-241	305	2	math	math	PROPN
ma-241	305	3	.	.	PUNCT
ma-241	306	1	anal	anal	PROPN
ma-241	306	2	.	.	PUNCT
ma-241	307	1	10.28924	10.28924	NUM
ma-241	307	2	/	/	SYM
ma-241	307	3	ada	ada	PROPN
ma-241	307	4	/	/	SYM
ma-241	307	5	ma.5.6	ma.5.6	PROPN
ma-241	307	6	17	17	NUM
ma-241	307	7	[	[	SYM
ma-241	307	8	6	6	NUM
ma-241	307	9	]	]	X
ma-241	307	10	h.a	h.a	PROPN
ma-241	307	11	.	.	PROPN
ma-241	307	12	schwarz	schwarz	PROPN
ma-241	307	13	,	,	PUNCT
ma-241	307	14	uber	uber	ADJ
ma-241	307	15	einen	einen	PROPN
ma-241	307	16	grenzubergang	grenzubergang	NOUN
ma-241	307	17	durch	durch	NOUN
ma-241	307	18	alternierendes	alternierende	VERB
ma-241	307	19	verfahren	verfahren	NOUN
ma-241	307	20	,	,	PUNCT
ma-241	307	21	vierteljahrsschrift	vierteljahrsschrift	NOUN
ma-241	307	22	der	der	NOUN
ma-241	307	23	naturforschendengesellschaft	naturforschendengesellschaft	NOUN
ma-241	307	24	in	in	ADP
ma-241	307	25	zurich	zurich	PROPN
ma-241	307	26	15	15	NUM
ma-241	307	27	(	(	PUNCT
ma-241	307	28	1870	1870	NUM
ma-241	307	29	)	)	PUNCT
ma-241	307	30	272	272	NUM
ma-241	307	31	-	-	SYM
ma-241	307	32	286.[7	286.[7	NUM
ma-241	307	33	]	]	PUNCT
ma-241	307	34	v.	v.	CCONJ
ma-241	307	35	dolean	dolean	PROPN
ma-241	307	36	,	,	PUNCT
ma-241	307	37	p.	p.	PROPN
ma-241	307	38	jolivet	jolivet	PROPN
ma-241	307	39	,	,	PUNCT
ma-241	307	40	f.	f.	PROPN
ma-241	307	41	nataf	nataf	PROPN
ma-241	307	42	,	,	PUNCT
ma-241	307	43	an	an	DET
ma-241	307	44	introduction	introduction	NOUN
ma-241	307	45	to	to	ADP
ma-241	307	46	domain	domain	VERB
ma-241	307	47	decomposition	decomposition	NOUN
ma-241	307	48	methods	method	NOUN
ma-241	307	49	:	:	PUNCT
ma-241	307	50	algorithms	algorithm	NOUN
ma-241	307	51	,	,	PUNCT
ma-241	307	52	theory	theory	NOUN
ma-241	307	53	,	,	PUNCT
ma-241	307	54	and	and	CCONJ
ma-241	307	55	parallelimplementation	parallelimplementation	NOUN
ma-241	307	56	,	,	PUNCT
ma-241	307	57	siam	siam	PROPN
ma-241	307	58	(	(	PUNCT
ma-241	307	59	2016).[8	2016).[8	NOUN
ma-241	307	60	]	]	X
ma-241	307	61	g.	g.	PROPN
ma-241	307	62	ciaramella	ciaramella	PROPN
ma-241	307	63	,	,	PUNCT
ma-241	307	64	m.j	m.j	PROPN
ma-241	307	65	.	.	PROPN
ma-241	307	66	gander	gander	NOUN
ma-241	307	67	,	,	PUNCT
ma-241	307	68	iterative	iterative	NOUN
ma-241	307	69	methods	method	NOUN
ma-241	307	70	and	and	CCONJ
ma-241	307	71	preconditioners	preconditioner	NOUN
ma-241	307	72	for	for	ADP
ma-241	307	73	systems	system	NOUN
ma-241	307	74	of	of	ADP
ma-241	307	75	linear	linear	PROPN
ma-241	307	76	equations	equation	NOUN
ma-241	307	77	,	,	PUNCT
ma-241	308	1	siam	siam	PROPN
ma-241	308	2	(	(	PUNCT
ma-241	308	3	2022).[9	2022).[9	NOUN
ma-241	308	4	]	]	PUNCT
ma-241	308	5	b.	b.	PROPN
ma-241	308	6	smith	smith	PROPN
ma-241	308	7	,	,	PUNCT
ma-241	308	8	p.	p.	PROPN
ma-241	308	9	bjorstad	bjorstad	PROPN
ma-241	308	10	,	,	PUNCT
ma-241	308	11	w.	w.	PROPN
ma-241	308	12	gropp	gropp	PROPN
ma-241	308	13	,	,	PUNCT
ma-241	308	14	domain	domain	NOUN
ma-241	308	15	decomposition	decomposition	NOUN
ma-241	308	16	:	:	PUNCT
ma-241	308	17	parallel	parallel	ADJ
ma-241	308	18	multilevel	multilevel	NOUN
ma-241	308	19	methods	method	NOUN
ma-241	308	20	for	for	ADP
ma-241	308	21	elliptic	elliptic	ADJ
ma-241	308	22	partial	partial	ADJ
ma-241	308	23	differentialequations	differentialequation	NOUN
ma-241	308	24	,	,	PUNCT
ma-241	308	25	cambridge	cambridge	PROPN
ma-241	308	26	university	university	PROPN
ma-241	308	27	press.[10	press.[10	NOUN
ma-241	308	28	]	]	X
ma-241	308	29	a.	a.	NOUN
ma-241	308	30	quarteroni	quarteroni	NOUN
ma-241	308	31	,	,	PUNCT
ma-241	308	32	a.	a.	PROPN
ma-241	308	33	valli	valli	PROPN
ma-241	308	34	,	,	PUNCT
ma-241	308	35	domain	domain	NOUN
ma-241	308	36	decomposition	decomposition	NOUN
ma-241	308	37	methods	method	NOUN
ma-241	308	38	for	for	ADP
ma-241	308	39	partial	partial	ADJ
ma-241	308	40	differential	differential	NOUN
ma-241	308	41	equations	equation	NOUN
ma-241	308	42	,	,	PUNCT
ma-241	308	43	oxford	oxford	PROPN
ma-241	308	44	science	science	PROPN
ma-241	308	45	publications(1999).[11	publications(1999).[11	PROPN
ma-241	308	46	]	]	PUNCT
ma-241	308	47	o.	o.	PROPN
ma-241	308	48	ernst	ernst	PROPN
ma-241	308	49	,	,	PUNCT
ma-241	308	50	m.j	m.j	PROPN
ma-241	308	51	.	.	PROPN
ma-241	308	52	gander	gander	NOUN
ma-241	308	53	,	,	PUNCT
ma-241	308	54	why	why	SCONJ
ma-241	308	55	it	it	PRON
ma-241	308	56	is	be	AUX
ma-241	308	57	difficult	difficult	ADJ
ma-241	308	58	to	to	PART
ma-241	308	59	solve	solve	VERB
ma-241	308	60	helmholtz	helmholtz	NOUN
ma-241	308	61	problems	problem	NOUN
ma-241	308	62	with	with	ADP
ma-241	308	63	classical	classical	ADJ
ma-241	308	64	iterative	iterative	NOUN
ma-241	308	65	methods	method	NOUN
ma-241	308	66	,	,	PUNCT
ma-241	308	67	in	in	ADP
ma-241	308	68	:	:	PUNCT
ma-241	308	69	i.	i.	PROPN
ma-241	308	70	graham	graham	PROPN
ma-241	308	71	,	,	PUNCT
ma-241	308	72	t.	t.	PROPN
ma-241	308	73	hou	hou	PROPN
ma-241	308	74	,	,	PUNCT
ma-241	308	75	o.	o.	PROPN
ma-241	308	76	lakkis	lakkis	PROPN
ma-241	308	77	,	,	PUNCT
ma-241	308	78	r.	r.	PROPN
ma-241	308	79	scheichl	scheichl	PROPN
ma-241	308	80	(	(	PUNCT
ma-241	308	81	eds	ed	NOUN
ma-241	308	82	.	.	PUNCT
ma-241	308	83	)	)	PUNCT
ma-241	308	84	,	,	PUNCT
ma-241	308	85	numerical	numerical	ADJ
ma-241	308	86	analysis	analysis	NOUN
ma-241	308	87	of	of	ADP
ma-241	308	88	multiscale	multiscale	ADJ
ma-241	308	89	problems	problem	NOUN
ma-241	308	90	,	,	PUNCT
ma-241	308	91	springer	springer	NOUN
ma-241	308	92	verlag	verlag	PROPN
ma-241	308	93	(	(	PUNCT
ma-241	308	94	2012	2012	NUM
ma-241	308	95	)	)	PUNCT
ma-241	308	96	325	325	NUM
ma-241	308	97	-	-	SYM
ma-241	308	98	363.[12	363.[12	NUM
ma-241	308	99	]	]	X
ma-241	308	100	m.j	m.j	PROPN
ma-241	308	101	.	.	PROPN
ma-241	308	102	gander	gander	PROPN
ma-241	308	103	,	,	PUNCT
ma-241	308	104	h.	h.	PROPN
ma-241	308	105	zhang	zhang	PROPN
ma-241	308	106	,	,	PUNCT
ma-241	308	107	decomposition	decomposition	NOUN
ma-241	308	108	de	de	X
ma-241	308	109	domaine	domaine	X
ma-241	308	110	et	et	PROPN
ma-241	308	111	probleme	probleme	PROPN
ma-241	308	112	de	de	X
ma-241	308	113	helmholtz	helmholtz	PROPN
ma-241	308	114	:	:	PUNCT
ma-241	308	115	thirty	thirty	NUM
ma-241	308	116	years	year	NOUN
ma-241	308	117	after	after	ADP
ma-241	308	118	and	and	CCONJ
ma-241	308	119	still	still	ADV
ma-241	308	120	unique	unique	ADJ
ma-241	308	121	,	,	PUNCT
ma-241	308	122	in	in	ADP
ma-241	308	123	:	:	PUNCT
ma-241	308	124	domain	domain	NOUN
ma-241	308	125	decomposition	decomposition	NOUN
ma-241	308	126	methods	method	NOUN
ma-241	308	127	in	in	ADP
ma-241	308	128	science	science	NOUN
ma-241	308	129	and	and	CCONJ
ma-241	308	130	engineering	engineering	NOUN
ma-241	308	131	xxvi	xxvi	NOUN
ma-241	308	132	,	,	PUNCT
ma-241	308	133	lncse	lncse	NOUN
ma-241	308	134	,	,	PUNCT
ma-241	308	135	springer	springer	NOUN
ma-241	308	136	-	-	PUNCT
ma-241	308	137	verlag	verlag	PROPN
ma-241	308	138	(	(	PUNCT
ma-241	308	139	2021).[13	2021).[13	NUM
ma-241	308	140	]	]	PUNCT
ma-241	309	1	p.-l	p.-l	ADV
ma-241	309	2	.	.	PUNCT
ma-241	310	1	lions	lion	NOUN
ma-241	310	2	,	,	PUNCT
ma-241	310	3	on	on	ADP
ma-241	310	4	the	the	DET
ma-241	310	5	schwarz	schwarz	PROPN
ma-241	310	6	alternating	alternate	VERB
ma-241	310	7	method	method	NOUN
ma-241	310	8	.	.	PUNCT
ma-241	311	1	i	i	PRON
ma-241	311	2	,	,	PUNCT
ma-241	311	3	in	in	ADP
ma-241	311	4	:	:	PUNCT
ma-241	311	5	r.	r.	PROPN
ma-241	311	6	glowinski	glowinski	PROPN
ma-241	311	7	,	,	PUNCT
ma-241	311	8	g.h	g.h	PROPN
ma-241	311	9	.	.	PROPN
ma-241	311	10	golub	golub	PROPN
ma-241	311	11	,	,	PUNCT
ma-241	311	12	g.a	g.a	PROPN
ma-241	311	13	.	.	PROPN
ma-241	311	14	meurant	meurant	PROPN
ma-241	311	15	,	,	PUNCT
ma-241	311	16	j.	j.	PROPN
ma-241	311	17	periaux	periaux	PROPN
ma-241	311	18	(	(	PUNCT
ma-241	311	19	eds	ed	NOUN
ma-241	311	20	.	.	PUNCT
ma-241	311	21	)	)	PUNCT
ma-241	311	22	,	,	PUNCT
ma-241	311	23	firstinternational	firstinternational	ADJ
ma-241	311	24	symposium	symposium	NOUN
ma-241	311	25	on	on	ADP
ma-241	311	26	domain	domain	NOUN
ma-241	311	27	decomposition	decomposition	NOUN
ma-241	311	28	methods	method	NOUN
ma-241	311	29	for	for	ADP
ma-241	311	30	partial	partial	ADJ
ma-241	311	31	differential	differential	NOUN
ma-241	311	32	equations	equation	NOUN
ma-241	311	33	,	,	PUNCT
ma-241	311	34	siam	siam	PROPN
ma-241	311	35	,	,	PUNCT
ma-241	311	36	philadelphia(1988	philadelphia(1988	PROPN
ma-241	311	37	)	)	PUNCT
ma-241	311	38	1	1	NUM
ma-241	311	39	-	-	SYM
ma-241	311	40	42.[14	42.[14	PROPN
ma-241	311	41	]	]	X
ma-241	311	42	v.	v.	ADP
ma-241	311	43	dolean	dolean	PROPN
ma-241	311	44	,	,	PUNCT
ma-241	311	45	m.j	m.j	PROPN
ma-241	311	46	.	.	PROPN
ma-241	311	47	gander	gander	PROPN
ma-241	311	48	,	,	PUNCT
ma-241	311	49	a.	a.	NOUN
ma-241	311	50	kyriakis	kyriakis	PROPN
ma-241	311	51	,	,	PUNCT
ma-241	311	52	optimizing	optimize	VERB
ma-241	311	53	transmission	transmission	NOUN
ma-241	311	54	conditions	condition	NOUN
ma-241	311	55	for	for	ADP
ma-241	311	56	multiple	multiple	ADJ
ma-241	311	57	subdomains	subdomain	NOUN
ma-241	311	58	in	in	ADP
ma-241	311	59	the	the	DET
ma-241	311	60	magnetotel	magnetotel	NOUN
ma-241	311	61	-	-	PUNCT
ma-241	311	62	luric	luric	ADJ
ma-241	311	63	approximation	approximation	NOUN
ma-241	311	64	of	of	ADP
ma-241	311	65	maxwell	maxwell	PROPN
ma-241	311	66	’s	’s	PART
ma-241	311	67	equations	equation	NOUN
ma-241	311	68	,	,	PUNCT
ma-241	311	69	in	in	ADP
ma-241	311	70	:	:	PUNCT
ma-241	311	71	domain	domain	NOUN
ma-241	311	72	decomposition	decomposition	NOUN
ma-241	311	73	methods	method	NOUN
ma-241	311	74	in	in	ADP
ma-241	311	75	science	science	NOUN
ma-241	311	76	and	and	CCONJ
ma-241	311	77	engineering	engineering	NOUN
ma-241	311	78	xxvi	xxvi	NOUN
ma-241	311	79	,	,	PUNCT
ma-241	311	80	lncse	lncse	NOUN
ma-241	311	81	,	,	PUNCT
ma-241	311	82	springer	springer	NOUN
ma-241	311	83	-	-	PUNCT
ma-241	311	84	verlag	verlag	PROPN
ma-241	311	85	(	(	PUNCT
ma-241	311	86	2021).[15	2021).[15	NUM
ma-241	311	87	]	]	X
ma-241	311	88	a.	a.	NOUN
ma-241	311	89	kyriakis	kyriakis	PROPN
ma-241	311	90	,	,	PUNCT
ma-241	311	91	scalable	scalable	ADJ
ma-241	311	92	domain	domain	NOUN
ma-241	311	93	decomposition	decomposition	NOUN
ma-241	311	94	methods	method	NOUN
ma-241	311	95	for	for	ADP
ma-241	311	96	time	time	NOUN
ma-241	311	97	harmonic	harmonic	ADJ
ma-241	311	98	wave	wave	NOUN
ma-241	311	99	propagation	propagation	NOUN
ma-241	311	100	problems	problem	NOUN
ma-241	311	101	,	,	PUNCT
ma-241	311	102	ph.d	ph.d	PROPN
ma-241	311	103	.	.	PUNCT
ma-241	312	1	thesis	thesis	NOUN
ma-241	312	2	,	,	PUNCT
ma-241	312	3	university	university	NOUN
ma-241	312	4	of	of	ADP
ma-241	312	5	strathclyde	strathclyde	PROPN
ma-241	312	6	(	(	PUNCT
ma-241	312	7	2021).[16	2021).[16	NUM
ma-241	312	8	]	]	X
ma-241	312	9	v.	v.	ADP
ma-241	312	10	dolean	dolean	PROPN
ma-241	312	11	,	,	PUNCT
ma-241	312	12	m.j	m.j	PROPN
ma-241	312	13	.	.	PROPN
ma-241	312	14	gander	gander	PROPN
ma-241	312	15	,	,	PUNCT
ma-241	312	16	a.	a.	NOUN
ma-241	312	17	kyriakis	kyriakis	PROPN
ma-241	312	18	,	,	PUNCT
ma-241	312	19	closed	close	VERB
ma-241	312	20	form	form	NOUN
ma-241	312	21	optimized	optimize	VERB
ma-241	312	22	transmission	transmission	NOUN
ma-241	312	23	conditions	condition	NOUN
ma-241	312	24	for	for	ADP
ma-241	312	25	complex	complex	ADJ
ma-241	312	26	diffusion	diffusion	NOUN
ma-241	312	27	with	with	ADP
ma-241	312	28	manysubdomains	manysubdomain	NOUN
ma-241	312	29	,	,	PUNCT
ma-241	312	30	siam	siam	PROPN
ma-241	312	31	j.	j.	PROPN
ma-241	312	32	sci	sci	PROPN
ma-241	312	33	.	.	PUNCT
ma-241	313	1	comput	comput	PROPN
ma-241	313	2	.	.	PUNCT
ma-241	314	1	45	45	NUM
ma-241	314	2	(	(	PUNCT
ma-241	314	3	2023	2023	NUM
ma-241	314	4	)	)	PUNCT
ma-241	314	5	a829	a829	NUM
ma-241	314	6	-	-	SYM
ma-241	314	7	a848.[17	a848.[17	PROPN
ma-241	314	8	]	]	PUNCT
ma-241	314	9	a.	a.	NOUN
ma-241	314	10	kyriakis	kyriakis	PROPN
ma-241	314	11	,	,	PUNCT
ma-241	314	12	analysis	analysis	NOUN
ma-241	314	13	of	of	ADP
ma-241	314	14	schwarz	schwarz	PROPN
ma-241	314	15	algorithms	algorithm	NOUN
ma-241	314	16	for	for	ADP
ma-241	314	17	a	a	DET
ma-241	314	18	scalar	scalar	ADJ
ma-241	314	19	elliptic	elliptic	ADJ
ma-241	314	20	problem	problem	NOUN
ma-241	314	21	,	,	PUNCT
ma-241	314	22	adv	adv	PROPN
ma-241	314	23	.	.	PUNCT
ma-241	314	24	appl	appl	PROPN
ma-241	314	25	.	.	PROPN
ma-241	314	26	math	math	PROPN
ma-241	314	27	.	.	PUNCT
ma-241	315	1	sci	sci	PROPN
ma-241	315	2	.	.	PROPN
ma-241	316	1	22	22	NUM
ma-241	316	2	(	(	PUNCT
ma-241	316	3	12	12	NUM
ma-241	316	4	)	)	PUNCT
ma-241	316	5	(	(	PUNCT
ma-241	316	6	2023)2227	2023)2227	NUM
ma-241	316	7	-	-	SYM
ma-241	316	8	2242.[18	2242.[18	NUM
ma-241	316	9	]	]	PUNCT
ma-241	316	10	m.	m.	NOUN
ma-241	316	11	discacciati	discacciati	PROPN
ma-241	316	12	,	,	PUNCT
ma-241	316	13	g.	g.	PROPN
ma-241	316	14	giorda	giorda	PROPN
ma-241	316	15	,	,	PUNCT
ma-241	316	16	optimized	optimize	VERB
ma-241	316	17	schwarz	schwarz	NOUN
ma-241	316	18	methods	method	NOUN
ma-241	316	19	for	for	ADP
ma-241	316	20	the	the	DET
ma-241	316	21	stokes	stokes	PROPN
ma-241	316	22	-	-	PUNCT
ma-241	316	23	darcy	darcy	PROPN
ma-241	316	24	coupling	coupling	PROPN
ma-241	316	25	,	,	PUNCT
ma-241	316	26	i	i	PRON
ma-241	316	27	m	m	VERB
ma-241	316	28	a	a	PROPN
ma-241	316	29	j.	j.	PROPN
ma-241	316	30	numer	numer	PROPN
ma-241	316	31	.	.	PROPN
ma-241	317	1	anal	anal	PROPN
ma-241	317	2	.	.	PUNCT
ma-241	318	1	38	38	NUM
ma-241	318	2	(	(	PUNCT
ma-241	318	3	4)(2018	4)(2018	NOUN
ma-241	318	4	)	)	PUNCT
ma-241	318	5	1959–1983	1959–1983	NUM
ma-241	318	6	.	.	PUNCT
ma-241	319	1	https://doi.org/10.28924/ada/ma.5.6	https://doi.org/10.28924/ada/ma.5.6	PROPN
ma-241	320	1	1	1	NUM
ma-241	320	2	.	.	PUNCT
ma-241	320	3	introduction	introduction	NOUN
ma-241	320	4	2	2	NUM
ma-241	320	5	.	.	PUNCT
ma-241	320	6	parallel	parallel	ADJ
ma-241	320	7	schwarz	schwarz	PROPN
ma-241	320	8	method	method	PROPN
ma-241	320	9	-	-	PUNCT
ma-241	320	10	dirichlet	dirichlet	NOUN
ma-241	320	11	ic	ic	PROPN
ma-241	320	12	3	3	NUM
ma-241	320	13	.	.	PUNCT
ma-241	320	14	alternating	alternate	VERB
ma-241	320	15	schwarz	schwarz	PROPN
ma-241	320	16	method	method	PROPN
ma-241	320	17	-	-	PUNCT
ma-241	320	18	neumann	neumann	NOUN
ma-241	320	19	ic	ic	PROPN
ma-241	320	20	4	4	NUM
ma-241	320	21	.	.	PUNCT
ma-241	320	22	non	non	ADJ
ma-241	320	23	-	-	ADJ
ma-241	320	24	overlapping	overlapping	ADJ
ma-241	320	25	optimized	optimize	VERB
ma-241	320	26	schwarz	schwarz	PROPN
ma-241	320	27	algorithm	algorithm	PROPN
ma-241	320	28	-	-	PUNCT
ma-241	320	29	robin	robin	PROPN
ma-241	320	30	ic	ic	PROPN
ma-241	320	31	5	5	NUM
ma-241	320	32	.	.	PUNCT
ma-241	320	33	non	non	ADJ
ma-241	320	34	-	-	ADJ
ma-241	320	35	overlapping	overlapping	ADJ
ma-241	320	36	optimized	optimize	VERB
ma-241	320	37	schwarz	schwarz	PROPN
ma-241	320	38	algorithm	algorithm	NOUN
ma-241	320	39	-	-	PUNCT
ma-241	320	40	second	second	NOUN
ma-241	320	41	order	order	NOUN
ma-241	320	42	ic	ic	X
ma-241	320	43	6	6	NUM
ma-241	320	44	.	.	PUNCT
ma-241	320	45	numerical	numerical	ADJ
ma-241	320	46	evidence	evidence	NOUN
ma-241	320	47	-	-	PUNCT
ma-241	320	48	convergence	convergence	NOUN
ma-241	320	49	curves	curve	NOUN
ma-241	320	50	7	7	NUM
ma-241	320	51	.	.	PUNCT
ma-241	321	1	conclusions	conclusion	NOUN
ma-241	321	2	references	reference	NOUN