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Micro-Differential Boundary Conditions Modelling the Absorption of Acoustic Waves by 2D Arbitrarily-Shaped Convex Surfaces

Published online by Cambridge University Press:  20 August 2015

Hélène Barucq ,
Julien Diaz  and
Véronique Duprat
Hélène Barucq*
Affiliation:
INRIA Bordeaux-Sud Ouest, Team-project MAGIQUE-3D LMA, CNRS UMR 5142, University of Pau, France
Julien Diaz*
Affiliation:
INRIA Bordeaux-Sud Ouest, Team-project MAGIQUE-3D LMA, CNRS UMR 5142, University of Pau, France
Véronique Duprat*
Affiliation:
INRIA Bordeaux-Sud Ouest, Team-project MAGIQUE-3D LMA, CNRS UMR 5142, University of Pau, France
*
Email address:helene.barucq@inria.fr
Email address:julien.diaz@inria.fr
Corresponding author.Email:veronique.duprat@univ-pau.fr
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Abstract

We propose a new Absorbing Boundary Condition (ABC) for the acoustic wave equation which is derived from a micro-local diagonalization process formerly defined by M.E. Taylor and which does not depend on the geometry of the surface bearing the ABC. By considering the principal symbol of the wave equation both in the hyperbolic and the elliptic regions, we show that a second-order ABC can be constructed as the combination of an existing first-order ABC and a Fourier-Robin condition. We compare the new ABC with other ABCs and we show that it performs well in simple configurations and that it improves the accuracy of the numerical solution without increasing the computational burden.

Keywords

35L05Wave equationmicro-local diagonalizationabsorbing boundary conditionfinite element formulation
Type
Research Article
Information
Communications in Computational Physics , Volume 11 , Issue 2 , February 2012 , pp. 674 - 690
Copyright
Copyright © Global Science Press Limited 2012

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