Analysis of the Shifted Helmholtz Expansion Preconditioner for the Helmholtz Equation
We study in this paper the so-called expansion preconditioner which is a generalization of the shifted Helmholtz preconditioner. We show that this preconditioner can reduce the number of GMRES iterations if the meshsize is small enough and the shift is at most of the size of the wavenumber. For larger shifts however, for which the preconditioner would become easier to invert than the underlying Helmholtz operator, the performance degrades, like for the Shifted Helmholtz preconditioner.
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