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Mathematical Modelling and Numerical Analysis Will be set by the publisher Modelisation Mathematique et Analyse Numerique
 

Summary: Mathematical Modelling and Numerical Analysis Will be set by the publisher
Mod´elisation Math´ematique et Analyse Num´erique
APPROXIMATION BY GENERALIZED IMPEDANCE BOUNDARY
CONDITIONS OF A TRANSMISSION PROBLEM IN ACOUSTIC SCATTERING
Xavier ANTOINE1
and H´el`ene BARUCQ2
Abstract. This paper adresses some results on the development of an approximate method for com-
puting the acoustic field scattered by a three-dimensional penetrable object immersed into an incom-
pressible fluid. The basic idea of the method consists in using on-surface differential operators that
microlocally 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 and scattered waves. Theoretical aspects of the problem and numerical experi-
ments are reported to analyze the efficiency of the method and precise its validity domain.
R´esum´e. On s'int´eresse dans ce travail au d´eveloppement d'un mod`ele approch´e pour le calcul du
champ acoustique diffract´e par un obstacle p´en´etrable tridimensionnel immerg´e dans un fluide incom-
pressible. L'id´ee de base de la m´ethode consiste `a utiliser des op´erateurs de surface diff´erentiels qui
reproduisent microlocalement les ph´enom`enes de p´en´etration du champ. L'approche conduit `a une for-
mulation int´egrale qui poss`ede un co^ut r´eduit de calculs si on la compare `a une formulation standard
couplant les champs int´erieur et ext´erieur. On aborde ici des aspects `a la fois th´eoriques du probl`eme
et num´eriques pour analyser l'efficacit´e de l'approche et son domaine d'applicabilit´e.

  

Source: Antoine, Xavier - Institut de Mathématiques Élie Cartan, Université Henri Poincaré - Nancy 1

 

Collections: Mathematics