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A general perturbation formula for electromagnetic fields in presence of low volume scatterers

Roland Griesmaier (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

In several practically interesting applications of electromagnetic scattering theory like, e.g., scattering from small point-like objects such as buried artifacts or small inclusions in non-destructive testing, scattering from thin curve-like objects such as wires or tubes, or scattering from thin sheet-like objects such as cracks, the volume of the scatterers is small relative to the volume of the surrounding medium and with respect to the wave length of the applied electromagnetic fields. This...

A general perturbation formula for electromagnetic fields in presence of low volume scatterers

Roland Griesmaier (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

In several practically interesting applications of electromagnetic scattering theory like, e.g., scattering from small point-like objects such as buried artifacts or small inclusions in non-destructive testing, scattering from thin curve-like objects such as wires or tubes, or scattering from thin sheet-like objects such as cracks, the volume of the scatterers is small relative to the volume of the surrounding medium and with respect to the wave length of the applied electromagnetic fields. This...

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

Sébastien Pernet (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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.

Approximation by generalized impedance boundary conditions of a transmission problem in acoustic scattering

Xavier Antoine, Hélène Barucq (2005)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

This paper addresses some results on the development of an approximate method for computing the acoustic field scattered by a three-dimensional penetrable object immersed into an incompressible fluid. The basic idea of the method consists in using on-surface differential operators that locally reproduce the interior propagation phenomenon. This approach leads to integral equation formulations with a reduced computational cost compared to standard integral formulations coupling both the transmitted...

Approximation by generalized impedance boundary conditions of a transmission problem in acoustic scattering

Xavier Antoine, Hélène Barucq (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

This paper addresses some results on the development of an approximate method for computing the acoustic field scattered by a three-dimensional penetrable object immersed into an incompressible fluid. The basic idea of the method consists in using on-surface differential operators that locally reproduce the interior propagation phenomenon. This approach leads to integral equation formulations with a reduced computational cost compared to standard integral formulations coupling both the transmitted...

Cloaking via anomalous localized resonance for doubly complementary media in the quasistatic regime

Hoai-Minh Nguyen (2015)

Journal of the European Mathematical Society

This paper is devoted to the study of cloaking via anomalous localized resonance (CALR) in the two- and three-dimensional quasistatic regimes. CALR associated with negative index materials was discovered by Milton and Nicorovici [21] for constant plasmonic structures in the two-dimensional quasistatic regime. Two key features of this phenomenon are the localized resonance, i.e., the fields blow up in some regions and remain bounded in some others, and the connection between the localized resonance...

Conditions aux limites approchées pour les couches minces périodiques

Habib Ammari, Chiraz Latiri-Grouz (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Nous écrivons et nous justifions des conditions aux limites approchées pour des couches minces périodiques recouvrant un objet parfaitement conducteur en polarisation transverse électrique et transverse magnétique.

Conical diffraction by multilayer gratings: A recursive integral equation approach

Gunther Schmidt (2013)

Applications of Mathematics

The paper is devoted to an integral equation algorithm for studying the scattering of plane waves by multilayer diffraction gratings under oblique incidence. The scattering problem is described by a system of Helmholtz equations with piecewise constant coefficients in 2 coupled by special transmission conditions at the interfaces between different layers. Boundary integral methods lead to a system of singular integral equations, containing at least two equations for each interface. To deal with...

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