Theory and Modern Applications
Table 2 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 2 , where \(\pmb{e^{-5}=10^{-5}}\)
|  | k | N  = 16 | N  = 32 | N  = 64 | N  = 128 |
|---|---|---|---|---|---|
CDS | 10 | \(8.4161e^{-3}\) | \(4.2104e^{-3}\) | \(9.2610e^{-5}\) | \(2.6041e^{-5}\) |
50 | \(8.3413e^{-3}\) | \(4.2390e^{-3}\) | \(9.8707e^{-5}\) | \(2.1374e^{-5}\) | |
100 | \(7.7917e^{-3}\) | \(4.7540e^{-3}\) | \(8.6342e^{-5}\) | \(1.9792e^{-5}\) | |
500 | \(7.6893e^{-3}\) | \(3.6964e^{-3}\) | \(7.4763e^{-5}\) | \(1.4136e^{-5}\) | |
1,000 | \(7.6712e^{-3}\) | \(3.8533e^{-3}\) | \(9.1249e^{-5}\) | \(2.2693e^{-5}\) | |
HOC | 10 | \(3.8844e^{-5}\) | \(2.8600e^{-6}\) | \(8.7210e^{-7}\) | \(5.3421e^{-7}\) |
50 | \(3.2736e^{-5}\) | \(2.9751e^{-6}\) | \(8.1872e^{-6}\) | \(5.3453e^{-7}\) | |
100 | \(3.1673e^{-5}\) | \(2.2360e^{-6}\) | \(8.2453e^{-6}\) | \(5.2198e^{-7}\) | |
500 | \(2.9764e^{-5}\) | \(1.7590e^{-6}\) | \(7.9678e^{-6}\) | \(5.4340e^{-7}\) | |
1,000 | \(4.7337e^{-5}\) | \(3.2187e^{-6}\) | \(7.9711e^{-6}\) | \(5.2891e^{-7}\) |