Parallel Rayleigh Quotient Optimization with FSAI-Based Preconditioning

Table 6

Number of iterations, timings, and scalability of LOBPCG-hypre preconditioned by Parasails.

	𝑝	iter	𝑇prec	𝑇iter	𝑇tot	𝑆^𝑝(4)	𝐸^𝑝(4)
FAULT-639; pcgitr =5	4	155	2.5	331.2	333.7
	8	156	1.3	167.6	168.9	7.9	0.99
	16	156	0.8	79.5	80.3	16.6	1.04
	32	150	0.5	38.8	39.3	34.0	1.06
	64	145	0.3	22.2	22.5	59.4	0.93
	128	157	0.1	14.8	14.9	89.7	0.70
PO-878; pcgitr = 30	4	45	3.3	438.4	441.7
	8	50	1.3	232.3	234.0	7.6	0.94
	16	45	1.0	117.0	118.0	15.0	0.94
	32	45	0.7	63.2	63.9	27.6	0.86
	64	47	0.4	34.4	34.8	50.8	0.79
	128	41	0.3	19.44	19.74	89.5	0.70
GEO-1438; pcgitr = 30	4	26	7.7	478.0	485.7
	8	22	4.0	256.8	260.8	7.5	0.93
	16	23	2.1	123.7	125.8	15.4	0.96
	32	28	1.2	73.1	74.3	26.2	0.82
	64	23	0.8	35.5	36.3	53.5	0.84
	128	25	0.5	20.3	20.8	93.2	0.73
	256	26	0.3	12.9	13.2	147.2	0.57
	𝑝	iter	𝑇prec	𝑇iter	𝑇tot	𝑆^𝑝(16)	𝐸^𝑝(16)
CUBE-6091	16	38	9.2	1536.7	1545.9
	32	36	4.7	807.5	812.2	30.5	0.95
	64	38	3.2	408.2	411.4	60.1	0.94
	128	41	1.6	251.4	253.0	97.8	0.76
	256	35	0.9	105.9	106.8	231.6	0.90
	512	39	0.6	65.3	65.9	375.3	0.73
	1024	37	0.3	37.7	38.0	650.9	0.64