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Evaluation of 3-D Singular and Nearly Singular Integrals in Galerkin BEM for Thin Layers

Marc Lenoir 1 Nicolas Salles 1
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
CNRS - Centre National de la Recherche Scientifique : UMR7231, UMA - Unité de Mathématiques Appliquées, Inria Saclay - Ile de France
Abstract : An explicit method for the evaluation of singular and near-singular integrals arising in three-dimensional Galerkin BEM is presented. It is based on a recursive reduction of the dimension of the integration domain leading to a linear combination of one-dimensional regular integrals, which can be exactly evaluated. This method has appealing properties in terms of reliability, precision, and flexibility. The results we present here are devoted to the case of thin layers for the Helmholtz equation, a situation where the panels are close and parallel, known to be difficult in terms of accuracy. Nevertheless, the method applies as well to two-dimensional BEM, secant planes, or even volume integral equations. A MATLAB implementation of the formulas presented here is available online.
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Submitted on : Wednesday, April 2, 2014 - 10:57:12 AM
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Marc Lenoir, Nicolas Salles. Evaluation of 3-D Singular and Nearly Singular Integrals in Galerkin BEM for Thin Layers. SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics, 2012, 36, pp.3057–-3078. ⟨10.1137/120866567⟩. ⟨hal-00969175⟩



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