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Multigrid preconditioners and solvers for the indefinite Helmholtz equationsuffer from non-stability of the stationary smoothers due to the indefinitespectrum of the operator. In this paper we explore GMRES as a replacement forthe stationary smoothers of the standard multigrid method. This results in arobust and efficient solver for a complex shifted or stretched Helmholtzproblem that can be used as a preconditioner. Very few GMRES iterations arerequired on each level to build a good multigrid method. The convergencebehavior is compared to a theoretically derived stable polynomial smoother. Wetest this method on some benchmark problems and report on the observedconvergence behavior.

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