Theory and Modern Applications
Table 3 Performance of FCG, CG, and Gauss while \(s=0\)
From: Fast collocation method for a two-dimensional variable-coefficient linear nonlocal diffusion model
| Â | \(N_{x} = N_{y}\) | \(\| \mathbf{u}_{h} - \mathbf{u} \|_{L^{2}}\) | # of iter. | CPUs |
|---|---|---|---|---|
Gauss | 24 | 1.0974 × 10−2 |  | 0.59 s |
25 | 4.4807 × 10−3 |  | 14.6 s | |
26 | 1.4500 × 10−3 |  | 19 m 1 s | |
27 | Â | Â | > 10Â h | |
28 | Â | out of memory | Â | |
|  |  | \(C_{\alpha } = 0.65\), α = 1.46 |  |  |
CGS | 24 | 1.0974 × 10−2 | 22 | 0.27 s |
25 | 4.4807 × 10−3 | 34 | 4.2 s | |
26 | 1.4500 × 10−3 | 44 | 2 m 41 s | |
27 | 3.7331 × 10−4 | 53 | 5 h 28 m 14 s | |
28 | Â | out of memory | Â | |
|  |  | \(C_{\alpha } = 1.12\), α = 1.63 |  |  |
FCGS | 24 | 1.0974 × 10−2 | 22 | 0.19 s |
25 | 4.4807 × 10−3 | 34 | 0.44 s | |
26 | 1.4500 × 10−3 | 44 | 5.33 s | |
27 | 3.7331 × 10−4 | 53 | 18.9 s | |
28 | 2.2977 × 10−5 | 62 | 1 m 40 s | |
|  |  | \(C_{\alpha } = 6.6\), α = 2.14 |  |  |