Sweeping Preconditioner for the Helmholtz Equation: Moving Perfectly Matched Layers
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Publication:3098543
DOI10.1137/100804644zbMATH Open1228.65234arXiv1007.4291OpenAlexW2024381649MaRDI QIDQ3098543
Author name not available (Why is that?)
Publication date: 17 November 2011
Published in: (Search for Journal in Brave)
Abstract: This paper introduces a new sweeping preconditioner for the iterative solution of the variable coefficient Helmholtz equation in two and three dimensions. The algorithms follow the general structure of constructing an approximate factorization by eliminating the unknowns layer by layer starting from an absorbing layer or boundary condition. The central idea of this paper is to approximate the Schur complement matrices of the factorization using moving perfectly matched layers (PMLs) introduced in the interior of the domain. Applying each Schur complement matrix is equivalent to solving a quasi-1D problem with a banded LU factorization in the 2D case and to solving a quasi-2D problem with a multifrontal method in the 3D case. The resulting preconditioner has linear application cost and the preconditioned iterative solver converges in a number of iterations that is essentially indefinite of the number of unknowns or the frequency. Numerical results are presented in both two and three dimensions to demonstrate the efficiency of this new preconditioner.
Full work available at URL: https://arxiv.org/abs/1007.4291
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