A Genetic Search for Optimal Multigrid Components Within a Fourier Analysis Setting

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.