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Table 8 Memory consumption in MB, timings in sec. for assembly and matrix–vector multiplication of \(\varvec{\mathsf {S}}\!^{+}\) and corresponding \(H^2\)-matrix approximation \(\overline{\varvec{\mathsf {S}}\!^{+}}\) for \(g=0.5\)

From: On Robustly Convergent and Efficient Iterative Methods for Anisotropic Radiative Transfer

\(n_S^+\)

Mem \(\varvec{\mathsf {S}}\!^{+}\)

Setup \(\varvec{\mathsf {S}}\!^{+}\)

Apply \(\varvec{\mathsf {S}}\!^{+}\)

64

0.0312

0.171

\(6.9\cdot 10^{-5}\)

256

0.5 (16.0)

0.203 (1.2)

\(6.5\cdot 10^{-5}\) (0.9)

1024

8 (16.0)

0.438 (2.2)

0.000313 (4.8)

4096

128 (16.0)

4.2 (9.6)

0.00517 (16.5)

16,384

\(2.05\cdot 10^3\) (16.0)

189 (45.0)

0.0805 (15.6)

65,536

\(3.28\cdot 10^4\) (16.0)

\(1.09\cdot 10^4\) (57.5)

2.67 (33.1)

262,144

1,048,576

\(n_S^+\)

mem \(\overline{\varvec{\mathsf {S}}\!^{+}}\)

Setup \(\overline{\varvec{\mathsf {S}}\!^{+}}\)

Apply \(\overline{\varvec{\mathsf {S}}\!^{+}}\)

64

0.0313

0.00109

0.00025

256

0.502 (16.0)

0.0116 (10.7)

0.000547 (2.2)

1024

11.3 (22.5)

0.139 (11.9)

0.0086 (15.7)

4096

89.2 (7.9)

0.902 (6.5)

0.0841 (9.8)

16,384

484 (5.4)

4.75 (5.3)

0.328 (3.9)

65,536

\(2.27\cdot 10^3\) (4.7)

24.6 (5.2)

1.46 (4.4)

262,144

\(9.53\cdot 10^3\) (4.2)

182 (7.4)

6.92 (4.7)

1,048,576

\(3.82\cdot 10^4\) (4.0)

\(1.46\cdot 10^3\) (8.0)

28.5 (4.1)

  1. Numbers in brackets indicate the ratio to the previous refinement level