Theory and Modern Applications
Table 4 The number of multigrid V-cycles and CPU time with two schemes and different relaxation methods with \(\pmb{32^{2}}\) for Example 1
Scheme | λ | Line GS | Red-black GS | Natural GS | |||
|---|---|---|---|---|---|---|---|
Iterations | CPU | Iterations | CPU | Iterations | CPU | ||
CDS | 0.0 | 9 | 0.334 | 10 | 0.350 | 12 | 1.840 |
−0.2 | 10 | 0.362 | 11 | 0.432 | 13 | 1.920 | |
−0.4 | 10 | 1.400 | 12 | 1.860 | 15 | 2.940 | |
−0.6 | 11 | 1.521 | 12 | 2.032 | 17 | 3.660 | |
−0.8 | 21 | 2.230 | 36 | 4.564 | 43 | 6.583 | |
−0.9 | 33 | 3.345 | 43 | 7.216 | 55 | 8.000 | |
HOC | 0.0 | 9 | 0.300 | 9 | 0.810 | 12 | 1.832 |
−0.2 | 10 | 0.340 | 11 | 0.830 | 12 | 1.980 | |
−0.4 | 11 | 0.810 | 12 | 1.767 | 14 | 2.200 | |
−0.6 | 11 | 0.900 | 12 | 2.203 | 18 | 3.80 | |
−0.8 | 12 | 1.800 | 13 | 3.720 | 22 | 4.960 | |
−0.9 | 15 | 2.200 | 21 | 6.318 | 33 | 6.550 | |