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Numerical methods for solving Helmholtz problems

Magdalena Grigoroscuta-Strugaru 1, 2 
1 Magique 3D - Advanced 3D Numerical Modeling in Geophysics
LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau], Inria Bordeaux - Sud-Ouest
Abstract : In this work we focus on the design and the analysis of numerical methods for solving efficiently 2D Helmholtz problems in the mid- and high-frequency regime. We propose a new discontinuous Galerkin (DG) method for solving high frequency Helmholtz problems. At the element level, the solution is approximated by a superposition of plane waves. The continuity of the solution at the interior interfaces is enforced weakly with Lagrange multipliers. The proposed formulation can be viewed as a two-step procedure in which we solve well-posed local problems, and then a global system arising from the continuity condition. The main features of the proposed solution methodology are: (a) the resulting local problems are associated with positive definite Hermitian matrices, and (b) the global system to be solved in the second step corresponds to a positive semi-definite Hermitian matrix. The obtained numerical results clearly indicate that the proposed solution methodology outperforms standard finite element methods, as well as existing DG methodologies, such as the method proposed by Farhat et al (2003).
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Submitted on : Thursday, October 7, 2010 - 11:32:45 AM
Last modification on : Friday, January 21, 2022 - 4:11:23 AM
Long-term archiving on: : Monday, January 10, 2011 - 11:23:08 AM


  • HAL Id : tel-00473486, version 3



Magdalena Grigoroscuta-Strugaru. Numerical methods for solving Helmholtz problems. Mathematics [math]. Université de Pau et des Pays de l'Adour, 2009. English. ⟨tel-00473486v3⟩



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