Theory and Modern Applications
Table 4 Performance of FCG, CG, and Gauss while \(s=-1/2\)
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 | 6.3004 × 10−3 |  | 0.69 s |
25 | 1.8866 × 10−3 |  | 13.5 s | |
26 | 4.3221 × 10−4 |  | 19 m 28 s | |
27 | Â | Â | > 10Â h | |
28 | Â | out of memory | Â | |
|  |  | \(C_{\alpha } = 1.4\), α = 1.93 |  |  |
CGS | 24 | 6.3004 × 10−3 | 15 | 0.48 s |
25 | 1.8866 × 10−3 | 20 | 4.75 s | |
26 | 4.3221 × 10−4 | 24 | 2 m 53 s | |
27 | 2.8420 × 10−5 |  | 7 h 18 m 40 s | |
28 | Â | out of memory | Â | |
|  |  | \(C_{\alpha } = 10.3\), α = 2.55 |  |  |
FCGS | 24 | 6.3004 × 10−3 | 15 | 0.09 s |
25 | 1.8866 × 10−3 | 20 | 0.25 s | |
26 | 4.3221 × 10−4 | 24 | 2.33 s | |
27 | 2.8420 × 10−5 | 27 | 10.6 s | |
28 | 8.2241 × 10−6 | 35 | 54.5 s | |
|  |  | \(C_{\alpha } = 9.3\), α = 2.52 |  |  |