Abstract
In this paper, Fourier analysis is used for finding efficient multigrid components. The individual multigrid components for several discrete partial differential operators are chosen automatically by a genetic optimization method. From a set of multigrid components, such as different smoothers, coarse grid correction components, cycle types, number of smoothing iterations, and relaxation parameters, an optimal three-grid Fourier convergence factor corrected for computational complexity is obtained by the genetic search. The resulting methods can be tuned for optimal efficiency or toward robustness. The analysis results are verified by numerical experiments.
| Original language | English |
|---|---|
| Pages (from-to) | 924-944 |
| Number of pages | 21 |
| Journal | SIAM Journal on Scientific Computing |
| Volume | 24 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 2003 |
| Externally published | Yes |
Keywords
- Fourier three-grid analysis
- Genetic optimization algorithm
- Optimal multigrid components
- Standard coarsening