Partial Refactorization in Sparse Matrix Solution: A New Possibility for Faster Nonlinear Finite Element Analysis

Table 1

Statistic results of refactorization of Example 1.

Changed elements	Changed DOFs		Affected DOFs				Number of operations (MFLOP)				Factorization time (sec)
Full refactorization	321210		321210				30630				10.71
Partial refactorization	Average		Min	Max	Average		Min	Max	Average		Min	Max	Average
1	8	0.003%	159	3219	2283	0.71%	72	4654	2894	9.45%	0.2	2.19	1.45	13.54%
2	13	0.004%	159	3936	2431	0.76%	72	4837	2930	9.57%	0.18	2.22	1.47	13.71%
5	26	0.01%	1977	4512	2834	0.88%	2524	4916	3252	10.62%	1.33	2.19	1.60	14.94%
10	51	0.02%	2193	5295	3317	1.03%	2524	4953	3416	11.15%	1.36	2.23	1.64	15.33%
20	95	0.03%	2247	5466	3526	1.10%	2524	4955	3426	11.18%	1.27	2.33	1.66	15.53%
50	227	0.07%	2487	10101	3975	1.24%	2528	6246	3507	11.45%	1.25	2.55	1.67	15.62%
100	358	0.11%	2541	10452	4124	1.28%	2528	6252	3511	11.46%	1.28	2.63	1.68	15.67%
200	533	0.17%	2622	10548	4560	1.42%	2528	7911	3677	12.00%	1.3	3.35	1.72	16.11%
500	1175	0.37%	3714	15978	7947	2.47%	3357	10655	6237	20.36%	1.6	3.88	2.62	24.44%
1000	2167	0.67%	4770	19347	13351	4.16%	3371	14167	9370	30.59%	1.56	5.43	3.69	34.43%
2000	4949	1.54%	12462	29079	17262	5.37%	5314	14005	10234	33.41%	2.12	5.34	4.06	37.94%