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

Xavier Claeys; Ralf Hiptmair

ESAIM: Mathematical Modelling and Numerical Analysis (2012)

  • Volume: 46, Issue: 6, page 1421-1445
  • ISSN: 0764-583X

Abstract

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

How to cite

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Claeys, Xavier, and Hiptmair, Ralf. "Electromagnetic scattering at composite objects : a novel multi-trace boundary integral formulation." ESAIM: Mathematical Modelling and Numerical Analysis 46.6 (2012): 1421-1445. <http://eudml.org/doc/276374>.

@article{Claeys2012,
abstract = {Since matrix compression has paved the way for discretizing the boundary integral equation formulations of electromagnetics scattering on very fine meshes, preconditioners for the resulting linear systems have become key to efficient simulations. Operator preconditioning based on Calderón identities has proved to be a powerful device for devising preconditioners. However, this is not possible for the usual first-kind boundary formulations for electromagnetic scattering at general penetrable composite obstacles. We propose a new first-kind boundary integral equation formulation following the reasoning employed in [X. Clayes and R. Hiptmair, Report 2011-45, SAM, ETH Zürich (2011)] for acoustic scattering. We call it multi-trace formulation, because its unknowns are two pairs of traces on interfaces in the interior of the scatterer. We give a comprehensive analysis culminating in a proof of coercivity, and uniqueness and existence of solution. We establish a Calderón identity for the multi-trace formulation, which forms the foundation for operator preconditioning in the case of conforming Galerkin boundary element discretization.},
author = {Claeys, Xavier, Hiptmair, Ralf},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Integral equations; boundary element method; domain decomposition; Maxwell’s equations; integral equations; Maxwell's equations},
language = {eng},
month = {5},
number = {6},
pages = {1421-1445},
publisher = {EDP Sciences},
title = {Electromagnetic scattering at composite objects : a novel multi-trace boundary integral formulation},
url = {http://eudml.org/doc/276374},
volume = {46},
year = {2012},
}

TY - JOUR
AU - Claeys, Xavier
AU - Hiptmair, Ralf
TI - Electromagnetic scattering at composite objects : a novel multi-trace boundary integral formulation
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2012/5//
PB - EDP Sciences
VL - 46
IS - 6
SP - 1421
EP - 1445
AB - Since matrix compression has paved the way for discretizing the boundary integral equation formulations of electromagnetics scattering on very fine meshes, preconditioners for the resulting linear systems have become key to efficient simulations. Operator preconditioning based on Calderón identities has proved to be a powerful device for devising preconditioners. However, this is not possible for the usual first-kind boundary formulations for electromagnetic scattering at general penetrable composite obstacles. We propose a new first-kind boundary integral equation formulation following the reasoning employed in [X. Clayes and R. Hiptmair, Report 2011-45, SAM, ETH Zürich (2011)] for acoustic scattering. We call it multi-trace formulation, because its unknowns are two pairs of traces on interfaces in the interior of the scatterer. We give a comprehensive analysis culminating in a proof of coercivity, and uniqueness and existence of solution. We establish a Calderón identity for the multi-trace formulation, which forms the foundation for operator preconditioning in the case of conforming Galerkin boundary element discretization.
LA - eng
KW - Integral equations; boundary element method; domain decomposition; Maxwell’s equations; integral equations; Maxwell's equations
UR - http://eudml.org/doc/276374
ER -

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