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Operator Factorization for Multiple-Scattering Problems and an Application to Periodic Media

Published online by Cambridge University Press:  20 August 2015

J. Coatléven  and
P. Joly
J. Coatléven*
Affiliation:
POems Project Team, UMR ENSTA/CNRS/INRIA, Inria Rocquencourt, 78153 Le Chesnay Cedex, France
P. Joly*
Affiliation:
POems Project Team, UMR ENSTA/CNRS/INRIA, Inria Rocquencourt, 78153 Le Chesnay Cedex, France
*
Corresponding author.Email:julien.coatleven@inria.fr
Email address:patrick.joly@inria.fr
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Abstract

This work concerns multiple-scattering problems for time-harmonic equations in a reference generic media. We consider scatterers that can be sources, obstacles or compact perturbations of the reference media. Our aim is to restrict the computational domain to small compact domains containing the scatterers. We use Robin-to-Robin (RtR) operators (in the most general case) to express boundary conditions for the interior problem. We show that one can always factorize the RtR map using only operators defined using single-scatterer problems. This factorization is based on a decomposition of the diffracted field, on the whole domain where it is defined. Assuming that there exists a good method for solving single-scatterer problems, it then gives a convenient way to compute RtR maps for a random number of scatterers.

Keywords

35C1535J0535Q6074J20Multiple-scatteringharmonic wave equationexact boundary conditionsperiodic media
Type
Research Article
Information
Communications in Computational Physics , Volume 11 , Issue 2 , February 2012 , pp. 303 - 318
Copyright
Copyright © Global Science Press Limited 2012

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