On multigrid solution of the implicit equations of hydrodynamics - Experiments for the compressible Euler equations in general coordinates

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Volume 544 (August 2012)

A&A, 544 (2012) A47

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Table 2

Number of F(1, 0) multigrid cycles, computational work, and CPU times (in seconds) on a single processor of an Intel Xeon system required to reduce the defect by six orders of magnitude for the bump problem.

		MS5E			MS3I/SGS			MS3I/RBGS(4)			MS3I/RBGS(8)
M_∞	Mesh	N_cyc	Work	CPU	N_cyc	Work	CPU	N_cyc	Work	CPU	N_cyc	Work	CPU

0.3	32 × 16	383	3404	2.6	18	96	0.29	18	96	0.32	14	75	0.34
	64 × 32	588	5227	16	22	117	1.5	25	133	1.8	17	91	1.7
	128 × 64	1151	10 231	123	31	165	10	38	203	13	24	128	11
	256 × 128	2069	18 391	892	48	256	66	64	341	101	36	192	75

0.5	32 × 16	269	2391	1.8	13	69	0.21	14	75	0.26	12	64	0.27
	64 × 32	406	3609	11	14	75	0.94	18	96	1.3	13	69	1.3
	128 × 64	752	6684	79	20	107	6.4	26	139	8.7	18	96	8.0
	256 × 128	1330	11 822	575	30	160	41	42	224	66	26	139	56

0.8	32 × 16	298	2649	2.2	21	112	0.33	24	128	0.40	23	123	0.55
	64 × 32	556	4942	16	58	309	4.2	57	304	4.1	54	288	5.4
	128 × 64	720	6400	83	43	229	14	40	213	13	36	192	16
	256 × 128	DNC	–	–	81	432	112	67	357	107	107	571	217

1.4	32 × 16	319	2836	2.3	29	155	0.45	27	144	0.48	47	251	1.1
	64 × 32	445	3956	13	25	133	1.7	27	144	1.9	25	133	2.5
	128 × 64	DNC	–	–	25	133	8.2	34	181	11	30	160	15
	256 × 128	DNC	–	–	29	155	40	62	331	99	41	219	83

Notes. DNC: did not converge, MS5E: multigrid solver based on explicit five-stage smoothing scheme, MS3I/SGS, MS3I/RBGS: multigrid solver based on a three-stage implicit smoothing scheme with either symmetric or red-black Gauss-Seidel smoothing stages. Values in parentheses denote the number of Gauss-Seidel sweeps per implicit stage.

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