. Author manuscript; available in PMC: 2020 Sep 15.

Published in final edited form as: Comput Mech. 2019 Feb 6;64:717–739. doi: 10.1007/s00466-019-01678-3

Table 2:

The number of iterations and the portion of compute time consumed by the linear solver for the pipe benchmark problem with rigid walls. The number of linear solver iterations is counted for 10 time step calculations. t_T is the total compute time, t_LS is the compute time consumed by solving the linear system.

BIPN-RPC /ϵ = 10⁻³
N_bipn	t_Ls/t_T	N_gmres	t_gmres/t_LS	N_cg	t_cg/t_LS
129	89.5%	1475	5.3%	38582	77.6%
BIPN-RPC /ϵ = 10⁻⁶
N_bipn	t_LS/t_T	N_gmres	t_gmres /t_LS	N_cg	t_cg/t_LS
847	95.1%	22699	17.25%	91470	55.7%
BIPN-RPC /ϵ = 10⁻⁹
N_bipn	t_LS/t_T	N_gmres	t_gmres/t_LS	N_cg	t_cg/t_LS
1923	95.0%	247142	43.2%	791817	49.4%

ϵ = 10⁻³	GMRES		BICG
PC	N_gmres	t_LS/t_T	N_bicgs	t_LS/t_T
Diag	155544	98.8%	N/A	N/A
Block-D	147768	98.7%	30027	94.4%
ILU	2768	85.3%	3104	89.6%
ILUT	1493	88.0%	2360	92.1%
IC	3636	40.5%	3290	41.3%
ML	1080	51.9%	1054	66.7%
ϵ = 10⁻⁶	GMRES		BICGS
PC	N_gmres	t_LS/t_T	N_bicgs	t_LS/t_T
Diag	492752	99.9%	N/A	N/A
Block-D	491185	99.9%	110237	96.3%
ILU	6632	89.6%	6770	91.7%
ILUT	3382	89.8%	4045	92.9%
IC	8191	54.3%	7710	51.3%
ML	2526	64.6%	2376	76.6%
ϵ = 10⁻⁹	GMRES		BICGS
PC	N_gmres	t_LS/t_T	N_bicgs	t_LS/t_T
Diag	1252448	100%	N/A	N/A
Block-D	1251025	100%	N/A	N/A
ILU	10066	91.0%	9766	92.2%
ILUT	5132	90.6%	5468	93.0%
IC	13728	59.8%	11022	53.4%
ML	3992	69.6%	3711	80.4%