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Electromagnetic scattering at composite objects : a novelmulti-trace boundary integral formulation

Published online by Cambridge University Press:  31 May 2012

Xavier Claeys  and
Ralf Hiptmair
Xavier Claeys
Affiliation:
Universitéde Toulouse, ISAE, 10 Avenue Edouard-Belin, 31055 Toulouse, France. [email protected]
Ralf Hiptmair
Affiliation:
Seminar of Applied Mathematics, ETHZ, 8092 Zürich, Switzerland; [email protected]
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Abstract

Since matrix compression has paved the way for discretizing the boundary integralequation formulations of electromagnetics scattering on very fine meshes, preconditionersfor the resulting linear systems have become key to efficient simulations. Operatorpreconditioning based on Calderón identities has proved to be a powerful device fordevising preconditioners. However, this is not possible for the usual first-kind boundaryformulations for electromagnetic scattering at general penetrable composite obstacles. Wepropose a new first-kind boundary integral equation formulation following the reasoningemployed in [X. Clayes and R. Hiptmair, Report 2011-45, SAM, ETH Zürich (2011)] foracoustic scattering. We call it multi-trace formulation, because itsunknowns are two pairs of traces on interfaces in the interior of the scatterer. We give acomprehensive analysis culminating in a proof of coercivity, and uniqueness and existenceof solution. We establish a Calderón identity for the multi-trace formulation, which formsthe foundation for operator preconditioning in the case of conforming Galerkin boundaryelement discretization.

Keywords

Integral equationsboundary element methoddomain decompositionMaxwell’s equations
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 46 , Issue 6 , November 2012 , pp. 1421 - 1445
Copyright
© EDP Sciences, SMAI, 2012

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