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) |