id	sid	tid	token	lemma	pos
ng451g08z42	1	1	this	this	DET
ng451g08z42	1	2	dissertation	dissertation	NOUN
ng451g08z42	1	3	seeks	seek	VERB
ng451g08z42	1	4	to	to	PART
ng451g08z42	1	5	reduce	reduce	VERB
ng451g08z42	1	6	the	the	DET
ng451g08z42	1	7	computational	computational	ADJ
ng451g08z42	1	8	cost	cost	NOUN
ng451g08z42	1	9	in	in	ADP
ng451g08z42	1	10	radiation	radiation	NOUN
ng451g08z42	1	11	transport	transport	NOUN
ng451g08z42	1	12	calculations	calculation	NOUN
ng451g08z42	1	13	using	use	VERB
ng451g08z42	1	14	dynamical	dynamical	ADJ
ng451g08z42	1	15	low	low	ADJ
ng451g08z42	1	16	-	-	PUNCT
ng451g08z42	1	17	rank	rank	NOUN
ng451g08z42	1	18	approximation	approximation	NOUN
ng451g08z42	1	19	(	(	PUNCT
ng451g08z42	1	20	dlr	dlr	NOUN
ng451g08z42	1	21	)	)	PUNCT
ng451g08z42	1	22	methods	method	NOUN
ng451g08z42	1	23	,	,	PUNCT
ng451g08z42	1	24	a	a	DET
ng451g08z42	1	25	complexity	complexity	NOUN
ng451g08z42	1	26	reduction	reduction	NOUN
ng451g08z42	1	27	technique	technique	NOUN
ng451g08z42	1	28	to	to	PART
ng451g08z42	1	29	approximate	approximate	VERB
ng451g08z42	1	30	a	a	DET
ng451g08z42	1	31	tensor	tensor	NOUN
ng451g08z42	1	32	or	or	CCONJ
ng451g08z42	1	33	a	a	DET
ng451g08z42	1	34	matrix	matrix	NOUN
ng451g08z42	1	35	with	with	ADP
ng451g08z42	1	36	a	a	DET
ng451g08z42	1	37	reduced	reduce	VERB
ng451g08z42	1	38	rank	rank	NOUN
ng451g08z42	1	39	.	.	PUNCT
ng451g08z42	2	1	a	a	DET
ng451g08z42	2	2	dlr	dlr	NOUN
ng451g08z42	2	3	approximation	approximation	NOUN
ng451g08z42	2	4	method	method	NOUN
ng451g08z42	2	5	is	be	AUX
ng451g08z42	2	6	developed	develop	VERB
ng451g08z42	2	7	for	for	ADP
ng451g08z42	2	8	the	the	DET
ng451g08z42	2	9	time	time	NOUN
ng451g08z42	2	10	-	-	PUNCT
ng451g08z42	2	11	dependent	dependent	ADJ
ng451g08z42	2	12	radiation	radiation	NOUN
ng451g08z42	2	13	transport	transport	NOUN
ng451g08z42	2	14	equation	equation	NOUN
ng451g08z42	2	15	in	in	ADP
ng451g08z42	2	16	1	1	NUM
ng451g08z42	2	17	-	-	PUNCT
ng451g08z42	2	18	d	d	NOUN
ng451g08z42	2	19	and	and	CCONJ
ng451g08z42	2	20	2	2	NUM
ng451g08z42	2	21	-	-	PUNCT
ng451g08z42	2	22	d	d	NOUN
ng451g08z42	2	23	cartesian	cartesian	NOUN
ng451g08z42	2	24	geometries	geometry	NOUN
ng451g08z42	2	25	.	.	PUNCT
ng451g08z42	3	1	a	a	DET
ng451g08z42	3	2	low	low	ADJ
ng451g08z42	3	3	-	-	PUNCT
ng451g08z42	3	4	rank	rank	NOUN
ng451g08z42	3	5	system	system	NOUN
ng451g08z42	3	6	that	that	PRON
ng451g08z42	3	7	evolves	evolve	VERB
ng451g08z42	3	8	on	on	ADP
ng451g08z42	3	9	a	a	DET
ng451g08z42	3	10	low	low	ADJ
ng451g08z42	3	11	-	-	PUNCT
ng451g08z42	3	12	rank	rank	NOUN
ng451g08z42	3	13	manifold	manifold	NOUN
ng451g08z42	3	14	via	via	ADP
ng451g08z42	3	15	an	an	DET
ng451g08z42	3	16	operator	operator	NOUN
ng451g08z42	3	17	-	-	PUNCT
ng451g08z42	3	18	splitting	split	VERB
ng451g08z42	3	19	approach	approach	NOUN
ng451g08z42	3	20	is	be	AUX
ng451g08z42	3	21	constructed	construct	VERB
ng451g08z42	3	22	using	use	VERB
ng451g08z42	3	23	a	a	DET
ng451g08z42	3	24	finite	finite	NOUN
ng451g08z42	3	25	volume	volume	NOUN
ng451g08z42	3	26	(	(	PUNCT
ng451g08z42	3	27	fv	fv	PROPN
ng451g08z42	3	28	)	)	PUNCT
ng451g08z42	3	29	method	method	NOUN
ng451g08z42	3	30	in	in	ADP
ng451g08z42	3	31	space	space	NOUN
ng451g08z42	3	32	and	and	CCONJ
ng451g08z42	3	33	a	a	DET
ng451g08z42	3	34	spherical	spherical	ADJ
ng451g08z42	3	35	harmonics	harmonic	NOUN
ng451g08z42	3	36	(	(	PUNCT
ng451g08z42	3	37	pn	pn	NOUN
ng451g08z42	3	38	)	)	PUNCT
ng451g08z42	3	39	basis	basis	NOUN
ng451g08z42	3	40	in	in	ADP
ng451g08z42	3	41	angle	angle	NOUN
ng451g08z42	3	42	.	.	PUNCT
ng451g08z42	4	1	numerical	numerical	ADJ
ng451g08z42	4	2	results	result	NOUN
ng451g08z42	4	3	demonstrate	demonstrate	VERB
ng451g08z42	4	4	that	that	SCONJ
ng451g08z42	4	5	the	the	DET
ng451g08z42	4	6	low	low	ADJ
ng451g08z42	4	7	-	-	PUNCT
ng451g08z42	4	8	rank	rank	NOUN
ng451g08z42	4	9	solution	solution	NOUN
ng451g08z42	4	10	requires	require	VERB
ng451g08z42	4	11	less	less	ADJ
ng451g08z42	4	12	memory	memory	NOUN
ng451g08z42	4	13	than	than	ADP
ng451g08z42	4	14	solving	solve	VERB
ng451g08z42	4	15	the	the	DET
ng451g08z42	4	16	full	full	ADJ
ng451g08z42	4	17	-	-	PUNCT
ng451g08z42	4	18	rank	rank	NOUN
ng451g08z42	4	19	equations	equation	NOUN
ng451g08z42	4	20	with	with	ADP
ng451g08z42	4	21	the	the	DET
ng451g08z42	4	22	same	same	ADJ
ng451g08z42	4	23	accuracy	accuracy	NOUN
ng451g08z42	4	24	.	.	PUNCT
ng451g08z42	5	1	furthermore	furthermore	ADV
ng451g08z42	5	2	,	,	PUNCT
ng451g08z42	5	3	the	the	DET
ng451g08z42	5	4	low	low	ADJ
ng451g08z42	5	5	-	-	PUNCT
ng451g08z42	5	6	rank	rank	NOUN
ng451g08z42	5	7	algorithm	algorithm	NOUN
ng451g08z42	5	8	can	can	AUX
ng451g08z42	5	9	obtain	obtain	VERB
ng451g08z42	5	10	much	much	ADV
ng451g08z42	5	11	better	well	ADJ
ng451g08z42	5	12	results	result	NOUN
ng451g08z42	5	13	at	at	ADP
ng451g08z42	5	14	a	a	DET
ng451g08z42	5	15	moderate	moderate	ADJ
ng451g08z42	5	16	extra	extra	ADJ
ng451g08z42	5	17	cost	cost	NOUN
ng451g08z42	5	18	by	by	ADP
ng451g08z42	5	19	refining	refine	VERB
ng451g08z42	5	20	the	the	DET
ng451g08z42	5	21	discretization	discretization	NOUN
ng451g08z42	5	22	while	while	SCONJ
ng451g08z42	5	23	keeping	keep	VERB
ng451g08z42	5	24	the	the	DET
ng451g08z42	5	25	rank	rank	NOUN
ng451g08z42	5	26	fixed	fix	VERB
ng451g08z42	5	27	.	.	PUNCT
ng451g08z42	6	1	the	the	DET
ng451g08z42	6	2	dlr	dlr	NOUN
ng451g08z42	6	3	method	method	NOUN
ng451g08z42	6	4	does	do	AUX
ng451g08z42	6	5	not	not	PART
ng451g08z42	6	6	preserve	preserve	VERB
ng451g08z42	6	7	the	the	DET
ng451g08z42	6	8	number	number	NOUN
ng451g08z42	6	9	of	of	ADP
ng451g08z42	6	10	particles	particle	NOUN
ng451g08z42	6	11	,	,	PUNCT
ng451g08z42	6	12	which	which	PRON
ng451g08z42	6	13	limits	limit	VERB
ng451g08z42	6	14	its	its	PRON
ng451g08z42	6	15	practicability	practicability	NOUN
ng451g08z42	6	16	.	.	PUNCT
ng451g08z42	7	1	this	this	DET
ng451g08z42	7	2	conservation	conservation	NOUN
ng451g08z42	7	3	issue	issue	NOUN
ng451g08z42	7	4	is	be	AUX
ng451g08z42	7	5	addressed	address	VERB
ng451g08z42	7	6	by	by	ADP
ng451g08z42	7	7	solving	solve	VERB
ng451g08z42	7	8	a	a	DET
ng451g08z42	7	9	low	low	ADJ
ng451g08z42	7	10	-	-	PUNCT
ng451g08z42	7	11	order	order	NOUN
ng451g08z42	7	12	equation	equation	NOUN
ng451g08z42	7	13	with	with	ADP
ng451g08z42	7	14	closure	closure	NOUN
ng451g08z42	7	15	terms	term	NOUN
ng451g08z42	7	16	coupled	couple	VERB
ng451g08z42	7	17	to	to	ADP
ng451g08z42	7	18	a	a	DET
ng451g08z42	7	19	low	low	ADJ
ng451g08z42	7	20	-	-	PUNCT
ng451g08z42	7	21	rank	rank	NOUN
ng451g08z42	7	22	approximation	approximation	NOUN
ng451g08z42	7	23	with	with	ADP
ng451g08z42	7	24	the	the	DET
ng451g08z42	7	25	high	high	ADJ
ng451g08z42	7	26	-	-	PUNCT
ng451g08z42	7	27	order	order	NOUN
ng451g08z42	7	28	solution	solution	NOUN
ng451g08z42	7	29	.	.	PUNCT
ng451g08z42	8	1	the	the	DET
ng451g08z42	8	2	high	high	ADJ
ng451g08z42	8	3	-	-	PUNCT
ng451g08z42	8	4	order	order	NOUN
ng451g08z42	8	5	solution	solution	NOUN
ng451g08z42	8	6	approximates	approximate	VERB
ng451g08z42	8	7	the	the	DET
ng451g08z42	8	8	closure	closure	NOUN
ng451g08z42	8	9	term	term	NOUN
ng451g08z42	8	10	well	well	ADV
ng451g08z42	8	11	,	,	PUNCT
ng451g08z42	8	12	and	and	CCONJ
ng451g08z42	8	13	the	the	DET
ng451g08z42	8	14	low	low	ADJ
ng451g08z42	8	15	-	-	PUNCT
ng451g08z42	8	16	order	order	NOUN
ng451g08z42	8	17	solution	solution	NOUN
ng451g08z42	8	18	corrects	correct	VERB
ng451g08z42	8	19	the	the	DET
ng451g08z42	8	20	low	low	ADJ
ng451g08z42	8	21	-	-	PUNCT
ng451g08z42	8	22	rank	rank	NOUN
ng451g08z42	8	23	evolution	evolution	NOUN
ng451g08z42	8	24	's	's	PART
ng451g08z42	8	25	conservation	conservation	NOUN
ng451g08z42	8	26	bias	bias	NOUN
ng451g08z42	8	27	.	.	PUNCT
ng451g08z42	9	1	the	the	DET
ng451g08z42	9	2	so	so	ADV
ng451g08z42	9	3	-	-	PUNCT
ng451g08z42	9	4	called	call	VERB
ng451g08z42	9	5	high	high	ADJ
ng451g08z42	9	6	-	-	PUNCT
ng451g08z42	9	7	order	order	NOUN
ng451g08z42	9	8	/	/	SYM
ng451g08z42	9	9	low	low	ADJ
ng451g08z42	9	10	-	-	PUNCT
ng451g08z42	9	11	order	order	NOUN
ng451g08z42	9	12	(	(	PUNCT
ng451g08z42	9	13	holo	holo	PROPN
ng451g08z42	9	14	)	)	PUNCT
ng451g08z42	9	15	algorithm	algorithm	PROPN
ng451g08z42	9	16	is	be	AUX
ng451g08z42	9	17	demonstrated	demonstrate	VERB
ng451g08z42	9	18	that	that	SCONJ
ng451g08z42	9	19	overcomes	overcome	VERB
ng451g08z42	9	20	the	the	DET
ng451g08z42	9	21	conservation	conservation	NOUN
ng451g08z42	9	22	difficulty	difficulty	NOUN
ng451g08z42	9	23	while	while	SCONJ
ng451g08z42	9	24	the	the	DET
ng451g08z42	9	25	computational	computational	ADJ
ng451g08z42	9	26	efficiency	efficiency	NOUN
ng451g08z42	9	27	and	and	CCONJ
ng451g08z42	9	28	accuracy	accuracy	NOUN
ng451g08z42	9	29	are	be	AUX
ng451g08z42	9	30	preserved	preserve	VERB
ng451g08z42	9	31	.	.	PUNCT
ng451g08z42	10	1	the	the	DET
ng451g08z42	10	2	low	low	ADJ
ng451g08z42	10	3	-	-	PUNCT
ng451g08z42	10	4	rank	rank	NOUN
ng451g08z42	10	5	scheme	scheme	NOUN
ng451g08z42	10	6	is	be	AUX
ng451g08z42	10	7	extended	extend	VERB
ng451g08z42	10	8	for	for	ADP
ng451g08z42	10	9	the	the	DET
ng451g08z42	10	10	time	time	NOUN
ng451g08z42	10	11	-	-	PUNCT
ng451g08z42	10	12	dependent	dependent	ADJ
ng451g08z42	10	13	radiation	radiation	NOUN
ng451g08z42	10	14	transport	transport	NOUN
ng451g08z42	10	15	equation	equation	NOUN
ng451g08z42	10	16	in	in	ADP
ng451g08z42	10	17	2	2	NUM
ng451g08z42	10	18	-	-	PUNCT
ng451g08z42	10	19	d	d	NOUN
ng451g08z42	10	20	and	and	CCONJ
ng451g08z42	10	21	3	3	NUM
ng451g08z42	10	22	-	-	PUNCT
ng451g08z42	10	23	d	d	NOUN
ng451g08z42	10	24	cartesian	cartesian	NOUN
ng451g08z42	10	25	geometries	geometry	NOUN
ng451g08z42	10	26	with	with	ADP
ng451g08z42	10	27	discrete	discrete	ADJ
ng451g08z42	10	28	ordinates	ordinate	NOUN
ng451g08z42	10	29	(	(	PUNCT
ng451g08z42	10	30	sn	sn	PROPN
ng451g08z42	10	31	)	)	PUNCT
ng451g08z42	10	32	discretization	discretization	NOUN
ng451g08z42	10	33	in	in	ADP
ng451g08z42	10	34	angle	angle	NOUN
ng451g08z42	10	35	.	.	PUNCT
ng451g08z42	11	1	the	the	DET
ng451g08z42	11	2	reduced	reduced	ADJ
ng451g08z42	11	3	system	system	NOUN
ng451g08z42	11	4	that	that	PRON
ng451g08z42	11	5	evolves	evolve	VERB
ng451g08z42	11	6	on	on	ADP
ng451g08z42	11	7	a	a	DET
ng451g08z42	11	8	low	low	ADJ
ng451g08z42	11	9	-	-	PUNCT
ng451g08z42	11	10	rank	rank	NOUN
ng451g08z42	11	11	manifold	manifold	NOUN
ng451g08z42	11	12	is	be	AUX
ng451g08z42	11	13	constructed	construct	VERB
ng451g08z42	11	14	via	via	ADP
ng451g08z42	11	15	an	an	DET
ng451g08z42	11	16	"	"	PUNCT
ng451g08z42	11	17	unconventional	unconventional	ADJ
ng451g08z42	11	18	"	"	PUNCT
ng451g08z42	11	19	basis	basis	NOUN
ng451g08z42	11	20	update	update	NOUN
ng451g08z42	11	21	&	&	CCONJ
ng451g08z42	11	22	amp	amp	PROPN
ng451g08z42	11	23	;	;	PUNCT
ng451g08z42	11	24	galerkin	galerkin	PROPN
ng451g08z42	11	25	integrator	integrator	PROPN
ng451g08z42	11	26	to	to	PART
ng451g08z42	11	27	avoid	avoid	VERB
ng451g08z42	11	28	a	a	DET
ng451g08z42	11	29	substep	substep	NOUN
ng451g08z42	11	30	that	that	PRON
ng451g08z42	11	31	is	be	AUX
ng451g08z42	11	32	backward	backward	ADJ
ng451g08z42	11	33	in	in	ADP
ng451g08z42	11	34	time	time	NOUN
ng451g08z42	11	35	,	,	PUNCT
ng451g08z42	11	36	which	which	PRON
ng451g08z42	11	37	could	could	AUX
ng451g08z42	11	38	be	be	AUX
ng451g08z42	11	39	unstable	unstable	ADJ
ng451g08z42	11	40	for	for	ADP
ng451g08z42	11	41	dissipative	dissipative	ADJ
ng451g08z42	11	42	problems	problem	NOUN
ng451g08z42	11	43	.	.	PUNCT
ng451g08z42	12	1	the	the	DET
ng451g08z42	12	2	resulting	result	VERB
ng451g08z42	12	3	system	system	NOUN
ng451g08z42	12	4	preserves	preserve	VERB
ng451g08z42	12	5	the	the	DET
ng451g08z42	12	6	information	information	NOUN
ng451g08z42	12	7	on	on	ADP
ng451g08z42	12	8	angular	angular	ADJ
ng451g08z42	12	9	direction	direction	NOUN
ng451g08z42	12	10	by	by	ADP
ng451g08z42	12	11	applying	apply	VERB
ng451g08z42	12	12	separate	separate	ADJ
ng451g08z42	12	13	low	low	ADJ
ng451g08z42	12	14	-	-	PUNCT
ng451g08z42	12	15	rank	rank	NOUN
ng451g08z42	12	16	decompositions	decomposition	NOUN
ng451g08z42	12	17	in	in	ADP
ng451g08z42	12	18	each	each	DET
ng451g08z42	12	19	octant	octant	NOUN
ng451g08z42	12	20	where	where	SCONJ
ng451g08z42	12	21	angular	angular	ADJ
ng451g08z42	12	22	intensity	intensity	NOUN
ng451g08z42	12	23	has	have	VERB
ng451g08z42	12	24	the	the	DET
ng451g08z42	12	25	same	same	ADJ
ng451g08z42	12	26	sign	sign	NOUN
ng451g08z42	12	27	as	as	ADP
ng451g08z42	12	28	the	the	DET
ng451g08z42	12	29	direction	direction	NOUN
ng451g08z42	12	30	cosines	cosine	NOUN
ng451g08z42	12	31	.	.	PUNCT
ng451g08z42	13	1	then	then	ADV
ng451g08z42	13	2	,	,	PUNCT
ng451g08z42	13	3	transport	transport	NOUN
ng451g08z42	13	4	sweeps	sweep	NOUN
ng451g08z42	13	5	and	and	CCONJ
ng451g08z42	13	6	source	source	NOUN
ng451g08z42	13	7	iteration	iteration	NOUN
ng451g08z42	13	8	can	can	AUX
ng451g08z42	13	9	efficiently	efficiently	ADV
ng451g08z42	13	10	solve	solve	VERB
ng451g08z42	13	11	this	this	DET
ng451g08z42	13	12	low	low	ADJ
ng451g08z42	13	13	-	-	PUNCT
ng451g08z42	13	14	rank	rank	NOUN
ng451g08z42	13	15	-	-	PUNCT
ng451g08z42	13	16	sn	sn	NOUN
ng451g08z42	13	17	system	system	NOUN
ng451g08z42	13	18	.	.	PUNCT
ng451g08z42	14	1	the	the	DET
ng451g08z42	14	2	numerical	numerical	ADJ
ng451g08z42	14	3	results	result	NOUN
ng451g08z42	14	4	in	in	ADP
ng451g08z42	14	5	2	2	NUM
ng451g08z42	14	6	-	-	PUNCT
ng451g08z42	14	7	d	d	NOUN
ng451g08z42	14	8	and	and	CCONJ
ng451g08z42	14	9	3	3	NUM
ng451g08z42	14	10	-	-	PUNCT
ng451g08z42	14	11	d	d	NOUN
ng451g08z42	14	12	cartesian	cartesian	NOUN
ng451g08z42	14	13	geometries	geometry	NOUN
ng451g08z42	14	14	demonstrate	demonstrate	VERB
ng451g08z42	14	15	that	that	SCONJ
ng451g08z42	14	16	the	the	DET
ng451g08z42	14	17	low	low	ADJ
ng451g08z42	14	18	-	-	PUNCT
ng451g08z42	14	19	rank	rank	NOUN
ng451g08z42	14	20	solution	solution	NOUN
ng451g08z42	14	21	requires	require	VERB
ng451g08z42	14	22	less	less	ADJ
ng451g08z42	14	23	memory	memory	NOUN
ng451g08z42	14	24	and	and	CCONJ
ng451g08z42	14	25	computational	computational	ADJ
ng451g08z42	14	26	time	time	NOUN
ng451g08z42	14	27	than	than	ADP
ng451g08z42	14	28	solving	solve	VERB
ng451g08z42	14	29	the	the	DET
ng451g08z42	14	30	full	full	ADJ
ng451g08z42	14	31	-	-	PUNCT
ng451g08z42	14	32	rank	rank	NOUN
ng451g08z42	14	33	equations	equation	NOUN
ng451g08z42	14	34	using	use	VERB
ng451g08z42	14	35	transport	transport	NOUN
ng451g08z42	14	36	sweeps	sweep	NOUN
ng451g08z42	14	37	without	without	ADP
ng451g08z42	14	38	losing	lose	VERB
ng451g08z42	14	39	accuracy	accuracy	NOUN
ng451g08z42	14	40	.	.	PUNCT