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• W2749361010 abstract "In this paper we are concerned with solvers for the systems arising from the plane wave discretizations of three dimensional Helmholtz equations with large wave numbers. For simplicity, we consider only the plane wave weighted least squares (PWLS) method for Helmholtz equations. The main goal of this paper is to construct efficient multilevel preconditioners for solving the resulting Helmholtz systems. To this end, we first build a multilevel space decomposition for the plane wave discretization space based on overlapping domain decompositions. Then, corresponding to the space decomposition, we construct two additive multilevel preconditioners with smoothers for the underlying Helmholtz systems. In these preconditioners, each subproblem to be solved has a very small number of degrees of freedom, which just equals the number of the plane wave basis functions on one element. Moreover, the preconditioners possess the optimal computational complexity per iteration. We apply the proposed multilevel preconditioners with a constant coarse mesh size to solve the systems generated by the PWLS discretization for three dimensional Helmholtz equations, and we find that the new preconditioners possess nearly stable convergence, i.e., the iteration counts of the preconditioned CG methods with the preconditioners increase very slowly when the wave number increases (and the fine mesh size decreases)." @default.
• W2749361010 created "2017-08-31" @default.
• W2749361010 creator A5027937292 @default.
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• W2749361010 date "2017-01-01" @default.
• W2749361010 modified "2023-09-22" @default.
• W2749361010 title "Efficient Multilevel Preconditioners for Three-Dimensional Plane Wave Helmholtz Systems with Large Wave Numbers" @default.
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• W2749361010 doi "https://doi.org/10.1137/16m1084791" @default.
• W2749361010 hasPublicationYear "2017" @default.
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