A robust multilevel method for hybridizable discontinuous Galerkin method for the Helmholtz equation

Authors:
Huangxin Chen;Peipei Lu;Xuejun Xu
Affiliations:
School of Mathematical Sciences, Xiamen University, Xiamen, China;School of Mathematics Sciences, Soochow University, Suzhou, 215006, China and LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and System S ...;LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, P.O. Box 2719, Beijing, 100190, China
Venue:
Journal of Computational Physics
Year:
2014

Citing 6
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Discontinuous Galerkin Methods for the Helmholtz Equation with Large Wave Number

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Abstract

A robust multilevel preconditioner based on the hybridizable discontinuous Galerkin method for the Helmholtz equation with high wave number is presented in this paper. There are two keys in our algorithm, one is how to choose a suitable intergrid transfer operator, and the other is using GMRES smoothing on the coarse grids. The multilevel method is performed as a preconditioner in the outer GMRES iteration. To give a quantitative insight of our algorithm, we use local Fourier analysis to analyze the convergence property of the proposed multilevel method. Numerical results show that for fixed wave number, the convergence of the algorithm is mesh independent. Moreover, the performance of the algorithm depends relatively mildly on wave number.