A new family of second-order absorbing boundary conditions for the acoustic wave equation - Part II : Mathematical and numerical studies of a simplified formulation

Hélène Barucq 1, 2 Julien Diaz 1, 2 Véronique Duprat 1, 2
2 Magique 3D - Advanced 3D Numerical Modeling in Geophysics
LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau], Inria Bordeaux - Sud-Ouest
Abstract : We interest ourselves on the mathematical and the numerical properties of a simplified formulation of a new family of absorbing boundary conditions (ABCs) for the acoustic wave equation introduced in the first part of this work. Considering a sound-soft scatterer, we prove the well-posedness of the corresponding boundary value problem and the exponential decay of the solution. We perform a numerical analysis. We propose to use a Discontinuous Galerkin method for the space discretization and by defining a discrete energy we prove the stability of the numerical scheme. Numerical results confirm the theoretical properties we have obtained and illustrate the performances of the new ABCs.
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Hélène Barucq, Julien Diaz, Véronique Duprat. A new family of second-order absorbing boundary conditions for the acoustic wave equation - Part II : Mathematical and numerical studies of a simplified formulation. [Research Report] RR-7575, INRIA. 2011. ⟨inria-00578152⟩

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