Theory and Modern Applications
Table 1 The number of multigrid V-cycles with two schemes and different values of \(\pmb{k=10,50, 100,500,1\text{,}000}\) and \(\pmb{\lambda=-0.9}\) for Example 1 , where \(\pmb{e^{-5}=10^{-5}}\)
|  | k | N  = 16 | N  = 32 | N  = 64 | N  = 128 |
|---|---|---|---|---|---|
CDS | 10 | \(3.4623e^{-5}\) | \(2.4504e^{-5}\) | \(2.1089e^{-5}\) | \(3.2161e^{-5}\) |
50 | \(2.7134e^{-5}\) | \(2.3692e^{-5}\) | \(1.9880e^{-5}\) | \(1.7322e^{-5}\) | |
100 | \(1.7091e^{-5}\) | \(1.6700e^{-5}\) | \(1.4650e^{-5}\) | \(1.3705e^{-5}\) | |
500 | \(1.1898e^{-5}\) | \(1.1662e^{-5}\) | \(1.1497e^{-5}\) | \(1.1403e^{-5}\) | |
1,000 | \(1.1697e^{-5}\) | \(1.3534e^{-5}\) | \(1.9545e^{-5}\) | \(1.6564e^{-5}\) | |
HOC | 10 | \(7.2104e^{-5}\) | \(1.1268e^{-5}\) | \(9.9271e^{-6}\) | \(9.3180e^{-7}\) |
50 | \(5.2183e^{-5}\) | \(1.6971e^{-5}\) | \(9.9128e^{-6}\) | \(9.3345e^{-7}\) | |
100 | \(3.6107e^{-5}\) | \(1.6881e^{-5}\) | \(7.5263e^{-6}\) | \(9.2791e^{-7}\) | |
500 | \(2.1945e^{-5}\) | \(1.5213e^{-5}\) | \(7.6298e^{-6}\) | \(8.4423e^{-7}\) | |
1,000 | \(4.3177e^{-5}\) | \(2.2813e^{-5}\) | \(2.1970e^{-5}\) | \(9.9281e^{-7}\) |