Volume 15, Issue 5
A Numerical Study on the Weak Galerkin Method for the Helmholtz Equation

Lin Mu, Junping Wang, Xiu Ye & Shan Zhao

Commun. Comput. Phys., 15 (2014), pp. 1461-1479.

Published online: 2014-05

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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.

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@Article{CiCP-15-1461, author = {}, title = {A Numerical Study on the Weak Galerkin Method for the Helmholtz Equation}, journal = {Communications in Computational Physics}, year = {2014}, volume = {15}, number = {5}, pages = {1461--1479}, 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.251112.211013a}, url = {http://global-sci.org/intro/article_detail/cicp/7145.html} }
TY - JOUR T1 - A Numerical Study on the Weak Galerkin Method for the Helmholtz Equation JO - Communications in Computational Physics VL - 5 SP - 1461 EP - 1479 PY - 2014 DA - 2014/05 SN - 15 DO - http://dor.org/10.4208/cicp.251112.211013a UR - https://global-sci.org/intro/article_detail/cicp/7145.html KW - AB -

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.

Lin Mu, Junping Wang, Xiu Ye & Shan Zhao. (2020). A Numerical Study on the Weak Galerkin Method for the Helmholtz Equation. Communications in Computational Physics. 15 (5). 1461-1479. doi:10.4208/cicp.251112.211013a
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