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

Table 2

Statistic results of refactorization of Example 2.

Changed elements	Changed DOFs		Affected DOFs				Number of operations (MFLOP)				Factorization time (sec)
Full refactorization	442331		442331				141251				48.87
Partial refactorization	Average		Min	Max	Average		Min	Max	Average		Min	Max	Average
1	9	0.002%	1662	5472	4410	1.00%	7330	21280	16521	11.70%	3.54	8.76	6.34	12.96%
2	15	0.003%	1674	6018	4901	1.11%	7330	21515	17389	12.31%	3.17	8.75	6.82	13.96%
5	30	0.01%	1701	8760	5344	1.21%	7330	22401	17705	12.53%	3.01	8.78	6.71	13.72%
10	54	0.01%	1761	12972	5906	1.34%	7330	38960	18622	13.18%	3.05	14.95	7.08	14.48%
20	98	0.02%	1803	13734	6558	1.48%	7330	39431	19774	14.00%	3.09	12.89	7.32	14.98%
50	198	0.04%	1893	18411	7185	1.62%	7330	39616	20212	14.31%	3.42	14.3	7.61	15.57%
100	345	0.08%	2016	19326	7553	1.71%	7330	39810	20259	14.34%	3.55	13.84	7.56	15.48%
200	597	0.14%	2103	23763	8185	1.85%	7330	40123	20360	14.41%	3.07	13.57	7.65	15.65%
400	2472	0.56%	6525	25506	10995	2.49%	16097	40123	21653	15.33%	5.88	14.92	8.07	16.51%
1000	3288	0.74%	20766	42306	26598	6.01%	29494	42004	35659	25.25%	10.06	15.76	12.81	26.20%