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The Halfspace Matching Method : a new method to solve scattering problem in infinite media

Anne-Sophie Bonnet-Ben Dhia 1 Sonia Fliss 1 Antoine Tonnoir 1, 2
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
Abstract : We are interested in acoustic wave propagation in time harmonic regime in a two-dimensional medium which is a local perturbation of an infinite isotropic or anisotropic homogeneous medium. We investigate the question of finding artificial boundary conditions to reduce the numerical computations to a neighborhood of this perturbation. Our objective is to derive a method which can extend to the anisotropic elastic problem for which classical approaches fail. The idea consists in coupling several semi-analytical representations of the solution in halfspaces surrounding the defect with a Finite Element computation of the solution around the defect. As representations of the same function, they have to match in the infinite intersections of the halfspaces. It leads to a formulation which couples, via integral operators, the solution in a bounded domain including the defect and its traces on the edge of the halfspaces. A stability property is shown for this new formulation.
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Anne-Sophie Bonnet-Ben Dhia, Sonia Fliss, Antoine Tonnoir. The Halfspace Matching Method : a new method to solve scattering problem in infinite media. Journal of Computational and Applied Mathematics, Elsevier, 2018, 338, pp.44-68. ⟨10.1016/j.cam.2018.01.021⟩. ⟨hal-01561339v3⟩

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