Table 6:

The impact of the accuracy of the inner solver on the performance of the linear solver. The CPU time is collected for the linear solver only; $\widehat{l}$ represents the total number of nonlinear iterations; n represents the total number of FGMRES iterations; ${\overline{n}}_A$ represents the averaged number of iterations for solving with A in (4.3) and (4.5); ${\overline{n}}_S$ represents the averaged number of iterations for solving (4.4); ${\overline{n}}_I$ represents the averaged number of iterations for solving (4.6).

	${\delta }_I^r$	CPU time (sec.)	$\widehat{l}$	n	${\overline{n}}_A$	${\overline{n}}_S$	${\overline{n}}_I$
${\delta }_A^r={\delta }_S^r={10}^{-10}$	100	7.56 × 101	1	47	16.81	19.81	-
	10−2	7.19 × 101	1	9	15.78	58.56	1.95
	10−4	6.52 × 101	1	5	15.30	58.80	3.75
	10−6	6.20 × 101	1	3	14.33	58.33	7.81
	10−8	5.83 × 101	1	2	13.75	59.50	11.85
	10−10	7.55 × 101	1	2	13.75	60.00	15.19
${\delta }_A^r={\delta }_S^r={10}^{-6}$	100	4.38 × 101	1	47	7.83	12.02	-
	10−2	4.20 × 101	1	9	8.17	34.22	1.97
	10−4	3.67 × 101	1	5	7.90	34.40	3.40
	10−6	4.73 × 101	1	4	7.50	35.75	7.37
	10−8	6.87 × 101	1	4	7.00	35.75	11.50
	10−10	8.23 × 101	1	4	7.00	35.75	15.47