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

ESAIM: Mathematical Modelling and Numerical Analysis (2012)

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

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topClaeys, 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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