A Modified Discontinuous Galerkin Method for Solving Efficiently Helmholtz Problems

被引：6

作者：

Grigoroscuta-Strugaru, Magdalena ^{[2
,3
,4
]}

Amara, Mohamed ^{[2
,3
]}

Calandra, Henri ^{[5
]}

Djellouli, Rabia ^{[1
]}

机构：

[1] Calif State Univ Northridge, Dept Math, Northridge, CA 91330 USA

[2] Univ Pau & Pays Adour, INRIA Bordeaux Sud Ouest Res Ctr, Team Project Magique 3D, Pau, France

[3] Univ Pau & Pays Adour, LMA CNRS, UMR 5142, Pau, France

[4] Basque Ctr Appl Math, BCAM, Bilbao, Spain

[5] TOTAL, Pau, France

来源：

COMMUNICATIONS IN COMPUTATIONAL PHYSICS | 2012年 / 11卷 / 02期

关键词：

Helmholtz equation; discontinuous Galerkin; plane waves; Lagrange multipliers; inf-sup condition; waveguide problems; LAGRANGE MULTIPLIERS; PLANE-WAVES; EQUATION; SYSTEMS;

D O I：

10.4208/cicp.081209.070710s

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

A new solution methodology is proposed for solving efficiently Helmholtz problems. The proposed method falls in the category of the discontinuous Galerkin methods. However, unlike the existing solution methodologies, this method requires solving (a) well-posed local problems to determine the primal variable, and (b) a global positive semi-definite Hermitian system to evaluate the Lagrange multiplier needed to restore the continuity across the element edges. Illustrative numerical results obtained for two-dimensional interior Helmholtz problems are presented to assess the accuracy and the stability of the proposed solution methodology.

引用

页码：335 / 350

页数：16

共 27 条

[1]

Amara M., 2008, THEORETICAL COMPUTAT, P139

[2]

Amara M, 2009, 7050 INRIA

[3] CONVERGENCE ANALYSIS OF A DISCONTINUOUS GALERKIN METHOD WITH PLANE WAVES AND LAGRANGE MULTIPLIERS FOR THE SOLUTION OF HELMHOLTZ PROBLEMS [J].