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Computational Science, Engineering & Technology Series
ISSN 17593158 CSETS: 18
COMPUTATIONAL METHODS FOR ACOUSTICS PROBLEMS Edited by: F. Magoulès
Chapter 1
Boundary Integral Equations Methods in Acoustic Scattering A. Bendali^{1,2} and M. Fares^{2}
^{1}Institute of Mathematics in Toulouse, INSA, Department of Mathematics, Toulouse, France A. Bendali, M. Fares, "Boundary Integral Equations Methods in Acoustic Scattering", in F. Magoulès, (Editor), "Computational Methods for Acoustics Problems", SaxeCoburg Publications, Stirlingshire, UK, Chapter 1, pp 136, 2008. doi:10.4203/csets.18.1
Keywords: acoustic scattering, Helmholtz equation, boundary integral equations, finite
element method, coupling, domain decomposition method, crosspoints.
Abstract
The main subject of this contribution is to present some recent methods, specially designed
to be implemented on parallel platforms, to deal with acoustic scattering problems
involving a bounded zone filled by a heterogeneous medium. The main approach
is to couple a finite element method for handling this zone, with a boundary integral
equation specially adapted to treat the unbounded part of the computational domain.
After giving a short review of some alternative methods, we focus on the methods
based on this approach and give a framework which makes it possible to construct
almost all the standard boundary integral equations. As is wellknown, each instance
of this kind of scattering problem can be solved by a manifold of such equations. This
framework allows one to have a good insight into the advantages and the drawbacks of
each of them. It is seen next that the above coupling gives rise to non standard linear
systems, with a matrix being partly sparse and partly dense. Serious difficulties then
arise when the solution of such systems has to be tackled on a parallel platform. It is
shown how techniques from domain decomposition methods can be used to efficiently
overcome these difficulties.
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