Theory and Modern Applications
Table 2 Performance of CGS, FCGS, and BCCB-FCGS in Example 2
From: A preconditioned fast collocation method for a linear bond-based peridynamic model
h | \(\| \mathbf{u}_{h} - \mathbf{u}\|_{L^{2}}\) | # of iter. | CPUs | |
|---|---|---|---|---|
CGS | 1/24 | 1.6387 × 10−2 | 35 | 0.04 s |
1/25 | 6.8624 × 10−3 | 48 | 0.93 s | |
1/26 | 2.3722 × 10−3 | 59 | 18.05 s | |
1/27 | 9.4000 × 10−4 | 78 | >10 h | |
1/28 | out of memory | |||
1/29 | out of memory | |||
\(C_{\alpha } = 0.81\), α = 1.39 | ||||
FCGS | 1/24 | 1.6387 × 10−2 | 35 | 0.8 s |
1/25 | 6.8624 × 10−3 | 49 | 3.4 s | |
1/26 | 2.3722 × 10−3 | 59 | 15.9 s | |
1/27 | 9.4000 × 10−4 | 78 | 1 m 10 s | |
1/28 | 7.2921 × 10−4 | 99 | 4 m 11 s | |
1/29 | 2.2423 × 10−4 | 113 | 38 m 58 s | |
\(C_{\alpha } = 0.41\), α = 1.20 | ||||
BCCB-FCGS | 1/24 | 1.6374 × 10−2 | 19 | 1 s |
1/25 | 6.8154 × 10−3 | 23 | 2.4 s | |
1/26 | 2.3057 × 10−3 | 26 | 8.8 s | |
1/27 | 8.6494 × 10−4 | 29 | 22.9 s | |
1/28 | 6.9507 × 10−4 | 34 | 1 m 18 s | |
1/29 | 1.8282 × 10−4 | 31 | 8 m 24 s | |
1/210 | 8.6238 × 10−4 | 36 | 1 h 2 m 57 s | |
\(C_{\alpha } = 0.13\), α = 0.89 |