On the indefinite Helmholtz equation: Complex stretched absorbing boundary layers,iterative analysis,and preconditioning |
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Authors: | Bram Reps Wim Vanroose Hisham bin Zubair |
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Institution: | Department of Mathematics and Information Technology, University of Antwerp, Middelheim Campus, Middelheimlaan 1, 2020 Antwerp, Belgium |
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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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Keywords: | Complex stretched grid (CSG) preconditioner Complex shifted Laplacian (CSL) preconditioner Multigrid preconditioning (MGP) Bi-CGSTAB IDR(s) Exterior complex scaled (ECS) absorbing boundary layers |
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