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arXiv · 1012.5379

GMRES-based multigrid for the complex scaled preconditoner for the indefinite Helmholtz equation

Bram Reps·Wim Vanroose·Hisham bin Zubair
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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.

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Bram Reps, Wim Vanroose, Hisham bin Zubair. 2010-12-24. GMRES-based multigrid for the complex scaled preconditoner for the indefinite Helmholtz equation. https://arxiv.org/abs/1012.5379

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