A boundary-element solution of the Leontovitch problem

Bendali, Abderrahmane; Fares, M’Barek; Gay, J.

doi:10.1109/8.805905

Cited by 44 publications

(36 citation statements)

References 20 publications

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“…These spaces are a vectorial counterparts of the spaces considered in [19], Section 2. Our choices take the cue from the work of Bendali and co-workers on classical single-trace formulation of Maxwell's equations for diffraction by composite structures [4,5].…”

Section: Trace Spaces Adapted To Multi-subdomain Geometriesmentioning

confidence: 99%

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

Claeys

Hiptmair

2012

ESAIM: M2AN

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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.Mathematics Subject Classification. 78A45, 35A35, 35Q60, 78M15.

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Section: Trace Spaces Adapted To Multi-subdomain Geometriesmentioning

confidence: 99%

“…We adhere to a variational perspective pioneered in the work of Bendali et al (see [4,5]) based on Rumsey's principle. It is the same perspective employed in the mathematical analysis of single-trace formulations in [38] (for acoustics) and [6] (for electromagnetics).…”

Section: Classical Single-trace Formulation Of the First Kindmentioning

confidence: 99%

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

Claeys

Hiptmair

2012

ESAIM: M2AN

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“…Several boundary integral equations can be constructed to determine the currents, all of them amounts to combine (2.11) and (2.12) to get an equation with a unique solution. The derivations of some of these equations can be found for example in [4].…”

Section: Remark 22mentioning

confidence: 99%

A well-conditioned integral equation for iterative solution of scattering problems with a variable Leontovitch boundary condition

Pernet¹

2010

ESAIM: M2AN

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Abstract. The construction of a well-conditioned integral equation for iterative solution of scattering problems with a variable Leontovitch boundary condition is proposed. A suitable parametrix is obtained by using a new unknown and an approximation of the transparency condition. We prove the well-posedness of the equation for any wavenumber. Finally, some numerical comparisons with well-tried method prove the efficiency of the new formulation.Mathematics Subject Classification. 65R20, 15A12, 65N38, 65F10, 65Z05.

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“…A first uses an integral formulation which only ensure the IBC when the convergence (i.e., when the spatial step tends toward zero) is achieved [9]. A second is to impose the IBC via a Lagrange multiplier [7]. Unfortunately, these equations generally degenerate to an Electric Field Integral Equation (EFIE) when η = 0, i.e., for perfectly metallic part of Γ. Consequently, some problems can appear when one wants to treat partially coated objects for example.…”

Section: Introductionmentioning

confidence: 99%

Boundary-Integral Methods for Iterative Solution of Scattering Problems With Variable Impedance Surface Condition

Collino¹,

Millot²,

Pernet³

2008

PIER

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Abstract-We present an efficient boundary element method to solve electromagnetic scattering problems relative to an impedance boundary condition on an obstacle of arbitrary shape in the frequency domain. In particular, the technique is based on a Combined Field Integral Equation (CFIE) and is well adapted to treat the partially coated objects. Some methods are then proposed in order to eliminate the magnetic current and to treat correctly the rotation operator n × · (where n is the unit outward normal). After discretization, the final system is solved by an iterative method coupled with the Fast Multipole Method (FMM). Finally, a numerical comparison with a well-tried method to solve this kind of problem proves that we have proposed an attractive technique in terms of memory storage and CPU time.

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A boundary-element solution of the Leontovitch problem

Cited by 44 publications

References 20 publications

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

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

A well-conditioned integral equation for iterative solution of scattering problems with a variable Leontovitch boundary condition

Boundary-Integral Methods for Iterative Solution of Scattering Problems With Variable Impedance Surface Condition

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