A Modified Discontinuous Galerkin Method for Solving Efficiently Helmholtz Problems
Magdalena Grigoroscuta-Strugaru 1, Mohamed Amara 2, Henri Calandra 3, Rabia Djellouli 4*1 INRIA Bordeaux Sud-Ouest Research Center, Team Project Magique-3D and LMA/CNRS UMR 5142, Universite de Pau et des Pays de l'Adour, France; BCAM, Basque Center for Applied Mathematics, Bilbao, Spain.
2 INRIA Bordeaux Sud-Ouest Research Center, Team Project Magique-3D and LMA/CNRS UMR 5142, Universite de Pau et des Pays de l'Adour, France.
3 TOTAL, Avenue Larribau, Pau, France.
4 Department of Mathematics, California State University Northridge and Interdisciplinary Research Institute for the Sciences, IRIS, USA.
Received 8 December 2009; Accepted (in revised version) 7 July 2010
Available online 24 October 2011
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.AMS subject classifications: 35J05, 65N30, 49M27, 35L05, 93E24
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Key words: Helmholtz equation, discontinuous Galerkin, plane waves, Lagrange multipliers, inf-sup condition, waveguide problems.
Email: firstname.lastname@example.org (M. Grigoroscuta-Strugaru), email@example.com (M. Amara), firstname.lastname@example.org (H. Calandra), email@example.com (R. Djellouli)