A Twisted Block Tangential Filtering Decomposition Preconditioner

Table 1

Results for Case 1: the advection-diffusion problem with a rotating velocity in two dimensions. Top resuls are using 𝐭=(𝟏,𝟏,…,𝟏)^𝐓, bottom resuls 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	60	1.31𝑒−10	43	6.50𝑒−12	44	1.10𝑒−11	18	4.18𝑒−11	16	2.94𝑒−11
100	108	5.40𝑒−10	63	8.00𝑒−12	64	1.69𝑒−11	26	1.57𝑒−10	23	7.52𝑒−11
200	186	1.15𝑒−9	90	1.10𝑒−11	91	2.81𝑒−11	37	5.67𝑒−10	32	3.44𝑒−10
300	×	×	110	1.50𝑒−11	111	2.72𝑒−11	45	6.88𝑒−10	39	8.56𝑒−10
50	60	1.31𝑒−10	43	5.50𝑒−12	44	1.26𝑒−11	18	5.22𝑒−11	16	3.43𝑒−11
100	108	5.40𝑒−10	62	9.30𝑒−12	64	1.49𝑒−11	26	1.82𝑒−10	23	6.79𝑒−11
200	186	1.15𝑒−9	90	1.02𝑒−11	91	3.05𝑒−11	37	5.72𝑒−10	33	1.57𝑒−10
300	×	×	110	1.83𝑒−11	111	3.00𝑒−11	45	6.70𝑒−10	39	7.10𝑒−10