Feature-driven Parallel Algebraic Multigrid Methods for Multi-group Radiation Diffusion Problems

doi:10.19596/j.cnki.1001-246x.8768

Abstract

Abstract:

Firstly, a review is given by classifying the existing fast algorithms for solving large-scale discrete linear systems arising from the Multi-Group Radiation Diffusion (MGRD) equations. Secondly, based on our recent work on parallel algebraic multigrid (AMG), two preconditioning algorithms and related theoretical frameworks are developed on a higher level. One is the approximate Schur complement type based on physical quantities and the other is the combined type based on physical and algebraic features, and the relevant components of these works are portrayed within these frameworks. Based on the above framework, a approximate Schur complement preconditioner with fundamental approximation property and low computational complexity is designed, and the corresponding spectral equivalence theory is established. Numerical experiments show that the new preconditioner has better robustness and computational efficiency. Finally, several issues that need to be further addressed are presented.

Key words: multi-group radiation diffusion equations, feature-driven, parallel algebraic multigrid method, preconditioner, approximate Schur complement

CLC Number:

Shi SHU, Xiaoqiang YUE, Jianmeng HE, Xiaowen XU, Zeyao MO. Feature-driven Parallel Algebraic Multigrid Methods for Multi-group Radiation Diffusion Problems[J]. Chinese Journal of Computational Physics, 2024, 41(1): 87-97.

Figures/Tables 4

References 41

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n	P	NT	NNL	NL	NL-Max	NL-Ave
1 575	B_U	1 644	6 349	16 414	5	2.58
1 575	B_P	1 657	6 412	19 737	200	3.07
6 093	B_U	1 598	8 666	22 475	5	2.55
6 093	B_P	1 616	8 784	28 390	200	3.23
23 961	B_U	1 637	18 768	46 200	5	2.46
23 961	B_P	1 678	19 695	60 923	200	3.09

n	P	NT	NNL	NL	NL-Max	NL-Ave
1 575	B_U	1 644	6 349	16 414	5	2.58
1 575	B_P	1 657	6 412	19 737	200	3.07
6 093	B_U	1 598	8 666	22 475	5	2.55
6 093	B_P	1 616	8 784	28 390	200	3.23
23 961	B_U	1 637	18 768	46 200	5	2.46
23 961	B_P	1 678	19 695	60 923	200	3.09

Mesh	np	BoomerAMG				B₃
Mesh	np	48	144	432	1 296	48	144	432	1 296
$\mathcal{M}$₂	T₃	26	28	28	31	3	3	3	4
$\mathcal{M}$₂	T₄	70	71	71	74	4	4	4	4
$\mathcal{M}$₃	T₅	42	45	46	44	4	4	5	5
$\mathcal{M}$₃	T₆	88	91	93	96	5	5	5	6

np	BoomerAMG					B₃
np	48	144		432	1 296	48	144	432	1 296
$\mathcal{M}$₂	100.0%	66.9%		52.1%	38.2%	100.0%	63.8%	49.3%	36.0%
$\mathcal{M}$₃	100.0%	70.1%		58.4%	47.0%	100.0%	69.1%	56.4%	44.5%

Mesh	np	BoomerAMG				B₃
Mesh	np	48	144	432	1 296	48	144	432	1 296
$\mathcal{M}$₂	T₃	26	28	28	31	3	3	3	4
$\mathcal{M}$₂	T₄	70	71	71	74	4	4	4	4
$\mathcal{M}$₃	T₅	42	45	46	44	4	4	5	5
$\mathcal{M}$₃	T₆	88	91	93	96	5	5	5	6

np	BoomerAMG					B₃
np	48	144		432	1 296	48	144	432	1 296
$\mathcal{M}$₂	100.0%	66.9%		52.1%	38.2%	100.0%	63.8%	49.3%	36.0%
$\mathcal{M}$₃	100.0%	70.1%		58.4%	47.0%	100.0%	69.1%	56.4%	44.5%

np	BoomerAMG				Euclid(1)				B₂
np	352	704	1 408	2 816	352	704	1 408	2 816	352	704	1 408	2 816
M₁	47	49	49	51	3	3	3	3	3	4	3	3
M₂	31	33	34	33	21	21	21	21	4	4	4	4
M₃	29	31	31	30	2	2	3	2	4	4	4	4
M₄	58	59	57	43	4	4	4	4	5	5	5	5
M₅	41	42	41	43	>200	>200	>200	>200	4	4	5	4
M₆	44	43	46	46	>200	>200	>200	>200	5	5	5	5

np	BoomerAMG				Euclid(1)				B₂
np	352	704	1 408	2 816	352	704	1 408	2 816	352	704	1 408	2 816
M₁	18.4	16.1	12.7	9.5	1.8	1.2	0.8	0.5	6.6	5.2	2.3	1.4
M₂	12.2	10.9	8.9	6.6	12.7	7.7	4.8	2.9	9.2	5.4	3.2	1.9
M₃	11.0	9.8	8.1	6.1	1.3	0.8	0.5	0.3	9.1	5.3	3.1	1.8
M₄	20.1	17.6	14.0	10.3	2.6	1.6	0.9	0.6	11.1	6.5	3.8	2.2
M₅	14.3	12.7	10.2	7.7	-	-	-	-	9.2	5.4	4.0	1.9
M₆	16.2	14.2	11.1	8.3	-	-	-	-	11.2	6.6	3.9	2.3