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A Numerical Study on the Weak Galerkin Method for the Helmholtz Equation

Published online by Cambridge University Press:  03 June 2015

Lin Mu ,
Junping Wang ,
Xiu Ye  and
Shan Zhao
Lin Mu*
Affiliation:
Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA
Junping Wang*
Affiliation:
Division of Mathematical Sciences, National Science Foundation, Arlington, VA 22230, USA
Xiu Ye*
Affiliation:
Department of Mathematics and Statistics, University of Arkansas at Little Rock, Little Rock, AR 72204, USA
Shan Zhao*
Affiliation:
Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487, USA
*
Email:jwang@nsf.gov
Email:jwang@nsf.gov
Email:xxye@ualr.edu
Corresponding author.Email:szhao@as.ua.edu
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Abstract

A weak Galerkin (WG) method is introduced and numerically tested for the Helmholtz equation. This method is flexible by using discontinuous piecewise polynomials and retains the mass conservation property. At the same time, the WG finite element formulation is symmetric and parameter free. Several test scenarios are designed for a numerical investigation on the accuracy, convergence, and robustness of the WG method in both inhomogeneous and homogeneous media over convex and non-convex domains. Challenging problems with high wave numbers are also examined. Our numerical experiments indicate that the weak Galerkin is a finite element technique that is easy to implement, and provides very accurate and robust numerical solutions for the Helmholtz problem with high wave numbers.

Keywords

65N1565N3076D0735B4535J50Galerkin finite element methodsdiscrete gradientHelmholtz equationlarge wave numbersweak Galerkin
Type
Research Article
Information
Communications in Computational Physics , Volume 15 , Issue 5 , May 2014 , pp. 1461 - 1479
Copyright
Copyright © Global Science Press Limited 2014

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