Theory and Modern Applications
Table 6 The number of multigrid V-cycles and CPU time with two schemes and different relaxation methods with \(\pmb{32^{2}}\) for Example 2
Scheme | λ | Line GS | Red-black GS | Natural GS | |||
|---|---|---|---|---|---|---|---|
Iterations | CPU | Iterations | CPU | Iterations | CPU | ||
CDS | 0.0 | 11 | 0.534 | 12 | 0.550 | 12 | 1.480 |
−0.2 | 11 | 0.562 | 12 | 0.630 | 13 | 1.960 | |
−0.4 | 11 | 0.584 | 12 | 0.980 | 17 | 2.488 | |
−0.6 | 12 | 1.765 | 13 | 1.382 | 19 | 3.600 | |
−0.8 | 17 | 1.936 | 19 | 1.996 | 33 | 5.853 | |
−0.9 | 27 | 3.145 | 33 | 4.162 | 43 | 6.980 | |
HOC | 0.0 | 9 | 0.310 | 9 | 0.532 | 12 | 1.330 |
−0.2 | 9 | 0.330 | 10 | 0.572 | 12 | 1.860 | |
−0.4 | 9 | 0.415 | 11 | 0.677 | 13 | 2.200 | |
−0.6 | 10 | 0.970 | 12 | 1.238 | 18 | 2.890 | |
−0.8 | 11 | 1.770 | 16 | 1.720 | 22 | 3.973 | |
−0.9 | 13 | 2.245 | 19 | 4.080 | 23 | 5.560 | |