GMRES-based multigrid for the complex scaled preconditoner for the indefinite Helmholtz equation
Numerical Analysis
2015-03-17 v2
Abstract
Multigrid preconditioners and solvers for the indefinite Helmholtz equation suffer from non-stability of the stationary smoothers due to the indefinite spectrum of the operator. In this paper we explore GMRES as a replacement for the stationary smoothers of the standard multigrid method. This results in a robust and efficient solver for a complex shifted or stretched Helmholtz problem that can be used as a preconditioner. Very few GMRES iterations are required on each level to build a good multigrid method. The convergence behavior is compared to a theoretically derived stable polynomial smoother. We test this method on some benchmark problems and report on the observed convergence behavior.
Cite
@article{arxiv.1012.5379,
title = {GMRES-based multigrid for the complex scaled preconditoner for the indefinite Helmholtz equation},
author = {Bram Reps and Wim Vanroose and Hisham bin Zubair},
journal= {arXiv preprint arXiv:1012.5379},
year = {2015}
}