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Advances in Iterative Methods and Preconditioners for the Helmholtz Equation

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Abstract

In this paper we survey the development of fast iterative solvers aimed at solving 2D/3D Helmholtz problems. In the first half of the paper, a survey on some recently developed methods is given. The second half of the paper focuses on the development of the shifted Laplacian preconditioner used to accelerate the convergence of Krylov subspace methods applied to the Helmholtz equation. Numerical examples are given for some difficult problems, which had not been solved iteratively before.

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  1. TU Berlin, Institut für Mathematik, MA 3-3, Strasse des 17. Juni 136, 10623, Berlin, Germany

    Yogi A. Erlangga

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Erlangga, Y.A. Advances in Iterative Methods and Preconditioners for the Helmholtz Equation. Arch Computat Methods Eng 15, 37–66 (2008). https://doi.org/10.1007/s11831-007-9013-7

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