A Twisted Block Tangential Filtering Decomposition Preconditioner

Table 2

Results for Case 2: Nonhomogenous problems with large jumps in the coefficients in two dimensions. Top results are using 𝐭=(𝟏,𝟏,…,𝟏)^𝐓 as filtering vector, bottom results are using Ritz vector corresponding to the smallest eigenvalue of 𝐀.

	𝑀𝐼𝐿𝑈		𝑀𝑇𝐹𝐹𝐷		𝑀𝑇𝐵𝑇𝐷		𝑀𝐼𝑇𝐹		𝑀𝐼𝑇𝐵
1/ℎ	iters	error	iters	error	iters	error	iters	error	iters	error
50	61	6.62𝑒−11	43	5.67𝑒−12	44	1.07𝑒−11	18	2.27𝑒−11	16	9.90𝑒−11
100	108	4.71𝑒−10	62	6.91𝑒−12	64	2.23𝑒−11	26	1.43𝑒−10	23	1.01𝑒−10
200	187	1.54𝑒−9	89	9.23𝑒−12	92	2.14𝑒−11	37	3.10𝑒−10	33	1.92𝑒−10
300	×	×	109	1.81𝑒−11	112	3.33𝑒−11	45	6.06𝑒−10	40	7.31𝑒−10
50	61	6.62𝑒−11	43	5.44𝑒−12	45	8.40𝑒−12	18	3.14𝑒−11	16	3.29𝑒−11
100	108	4.71𝑒−10	62	9.16𝑒−12	64	1.85𝑒−11	26	1.07𝑒−10	23	1.08𝑒−10
200	187	1.54𝑒−9	89	1.03𝑒−11	92	1.75𝑒−11	37	2.73𝑒−10	33	1.76𝑒−10
300	×	×	109	1.41𝑒−11	112	3.28𝑒−11	45	5.94𝑒−10	40	4.80𝑒−10