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Approximation by generalized impedance boundary conditions of a transmission problem in acoustic scattering

Xavier AntoineHélène Barucq — 2005

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

This paper addresses some results on the development of an approximate method for computing the acoustic field scattered by a three-dimensional penetrable object immersed into an incompressible fluid. The basic idea of the method consists in using on-surface differential operators that locally reproduce the interior propagation phenomenon. This approach leads to integral equation formulations with a reduced computational cost compared to standard integral formulations coupling both the transmitted...

Approximation by generalized impedance boundary conditions of a transmission problem in acoustic scattering

Xavier AntoineHélène Barucq — 2010

ESAIM: Mathematical Modelling and Numerical Analysis

This paper addresses some results on the development of an approximate method for computing the acoustic field scattered by a three-dimensional penetrable object immersed into an incompressible fluid. The basic idea of the method consists in using on-surface differential operators that locally reproduce the interior propagation phenomenon. This approach leads to integral equation formulations with a reduced computational cost compared to standard integral formulations coupling both the transmitted...

Generalized combined field integral equations for the iterative solution of the three-dimensional Helmholtz equation

Xavier AntoineMarion Darbas — 2007

ESAIM: Mathematical Modelling and Numerical Analysis

This paper addresses the derivation of new second-kind Fredholm combined field integral equations for the Krylov iterative solution of tridimensional acoustic scattering problems by a smooth closed surface. These integral equations need the introduction of suitable tangential square-root operators to regularize the formulations. Existence and uniqueness occur for these formulations. They can be interpreted as generalizations of the well-known Brakhage-Werner [A. Brakhage and P. Werner, ...

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