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arXiv · 0912.0180

On the indefinite Helmholtz equation: complex stretched absorbing boundary layers, iterative analysis, and preconditioning

Bram Reps·Wim Vanroose·Hisham bin Zubair
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Abstract

This paper studies and analyzes a preconditioned Krylov solver for Helmholtz problems that are formulated with absorbing boundary layers based on complex coordinate stretching. The preconditioner problem is a Helmholtz problem where not only the coordinates in the absorbing layer have an imaginary part, but also the coordinates in the interior region. This results into a preconditioner problem that is invertible with a multigrid cycle. We give a numerical analysis based on the eigenvalues and evaluate the performance with several numerical experiments. The method is an alternative to the complex shifted Laplacian and it gives a comparable performance for the studied model problems.

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Bram Reps, Wim Vanroose, Hisham bin Zubair. 2009-12-01. On the indefinite Helmholtz equation: complex stretched absorbing boundary layers, iterative analysis, and preconditioning. https://doi.org/10.1016/j.jcp.2010.07.022

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