Shape derivatives of boundary integral operators in electromagnetic scattering

We develop the shape derivative analysis of solutions to the problem of scattering of time-harmonic electromagnetic waves by a bounded penetrable obstacle. Since boundary integral equations are a classical tool to solve electromagnetic scattering problems, we study the shape differentiability properties of the standard electromagnetic boundary integral operators. Using Helmholtz decomposition, we can base their analysis on the study of scalar integral operators in standard Sobolev spaces, but we then have to study the G\^ateaux differentiability of surface differential operators. We prove that the electromagnetic boundary integral operators are infinitely differentiable without loss of regularity and that the solutions of the scattering problem are infinitely shape differentiable away from the boundary of the obstacle, whereas their derivatives lose regularity on the boundary. We also give a characterization of the first shape derivative as a solution of a new electromagnetic scattering problem

Shape derivatives of boundary integral operators in electromagnetic scattering. Part I: Shape differentiability of pseudo-homogeneous boundary integral operators

In this paper we study the shape differentiability properties of a class of boundary integral operators and of potentials with weakly singular pseudo-homogeneous kernels acting between classical Sobolev spaces, with respect to smooth deformations of the boundary. We prove that the boundary integral operators are infinitely differentiable without loss of regularity. The potential operators are infinitely shape differentiable away from the boundary, whereas their derivatives lose regularity near the boundary. We study the shape differentiability of surface differential operators. The shape differentiability properties of the usual strongly singular or hypersingular boundary integral operators of interest in acoustic, elastodynamic or electromagnetic potential theory can then be established by expressing them in terms of integral operators with weakly singular kernels and of surface differential operators

Shape derivatives of boundary integral operators in electromagnetic scattering. Part II : Application to scattering by a homogeneous dielectric obstacle

We develop the shape derivative analysis of solutions to the problem of scattering of time-harmonic electromagnetic waves by a bounded penetrable obstacle. Since boundary integral equations are a classical tool to solve electromagnetic scattering problems, we study the shape differentiability properties of the standard electromagnetic boundary integral operators. The latter are typically bounded on the space of tangential vector fields of mixed regularity TH\sp{-1/2}(\Div_{\Gamma},\Gamma). Using Helmholtz decomposition, we can base their analysis on the study of pseudo-differential integral operators in standard Sobolev spaces, but we then have to study the G\^ateaux differentiability of surface differential operators. We prove that the electromagnetic boundary integral operators are infinitely differentiable without loss of regularity. We also give a characterization of the first shape derivative of the solution of the dielectric scattering problem as a solution of a new electromagnetic scattering problem.Comment: arXiv admin note: substantial text overlap with arXiv:1002.154

On the Kleinman-Martin integral equation method for electromagnetic scattering by a dielectric body

The interface problem describing the scattering of time-harmonic electromagnetic waves by a dielectric body is often formulated as a pair of coupled boundary integral equations for the electric and magnetic current densities on the interface $\Gamma$. In this paper, following an idea developed by Kleinman and Martin \cite{KlMa} for acoustic scattering problems, we consider methods for solving the dielectric scattering problem using a single integral equation over $\Gamma$ for a single unknown density. One knows that such boundary integral formulations of the Maxwell equations are not uniquely solvable when the exterior wave number is an eigenvalue of an associated interior Maxwell boundary value problem. We obtain four different families of integral equations for which we can show that by choosing some parameters in an appropriate way, they become uniquely solvable for all real frequencies. We analyze the well-posedness of the integral equations in the space of finite energy on smooth and non-smooth boundaries

Qu’est-ce qu’une communauté ?

Depuis quelques années maintenant, le constat de la communautarisation est devenu un classique de l’analyse sociologique et politique d’Israël. Les sociologues constatent « la pérennité de l’ethnicité juive », tandis que les politologues soulignent « la fragmentation communautaire israélienne ». Beaucoup y voient la fin d’une certaine forme de l’idéologie sioniste ayant présidé à la construction de l’État et aux premières décennies de son existence. Désormais, l’impératif d’unité du peuple ju..

Erminia Chiara Calabrese, Robin Beaumont (dir.), « Chiismes politiques. Pouvoirs, engagements, imaginaires politiques chiites au xxie siècle »

Comme son titre l’indique, ce numéro a pour objectif d’analyser la diversité des usages politiques du chiisme. Le thème de la production de l’imaginaire politique est le principal fil conducteur qui relie entre eux les six articles. Sepideh Parsapajouh et Agnès Devictor s’intéressent au rôle de l’État iranien dans ce processus, dans deux contextes de violence extrême, la guerre Iran-Iraq (1980-1988) d’une part, l’intervention iranienne dans les guerres civiles en Iraq et en Syrie (depuis 2011..

Fast iterative boundary element methods for high-frequency scattering problems in 3D elastodynamics

International audienceThe fast multipole method is an efficient technique to accelerate the solution of large scale 3D scattering problems with boundary integral equations. However, the fast multipole accelerated boundary element method (FM-BEM) is intrinsically based on an iterative solver. It has been shown that the number of iterations can significantly hinder the overall efficiency of the FM-BEM. The derivation of robust preconditioners for FM-BEM is now inevitable to increase the size of the problems that can be considered. The main constraint in the context of the FM-BEM is that the complete system is not assembled to reduce computational times and memory requirements. Analytic preconditioners offer a very interesting strategy by improving the spectral properties of the boundary integral equations ahead from the discretization. The main contribution of this paper is to combine an approximate adjoint Dirichlet to Neumann (DtN) map as an analytic preconditioner with a FM-BEM solver to treat Dirichlet exterior scattering problems in 3D elasticity. The approximations of the adjoint DtN map are derived using tools proposed in [40]. The resulting boundary integral equations are preconditioned Combined Field Integral Equations (CFIEs). We provide various numerical illustrations of the efficiency of the method for different smooth and non smooth geometries. In particular, the number of iterations is shown to be completely independent of the number of degrees of freedom and of the frequency for convex obstacles

Le VOT dans une situation de contact des langues : Étude comparative de la production orale des locuteurs natifs et des apprenants du français

La présente étude préliminaire explore la prononciation des consonnes occlusives par des locuteurs bilingues vivant en situation de contact des langues au sud-ouest de l’Ontario. L’analyse se base sur deux sous-corpus consistant des enregistrements du français par quatre Franco-Ontariens de Windsor qui ont le français comme langue maternelle (L1), par deux apprenants du français de Waterloo qui ont le français comme langue seconde (L2), et des enregistrements de l’anglais par les apprenants du français. Nous examinons le Voice Onset Time (VOT), un des paramètres acoustiques qui caractérise différemment les consonnes occlusives sonores [b, d, g] des sourdes [p, t, k] en français et en anglais, ce qui crée de la confusion chez les locuteurs bilingues ainsi que chez les apprenants du français. Les résultats confirment que les Franco-Ontariens ont deux systèmes phonologiques séparés et que leurs occlusives suivent le patron français et ne subissent pas d’influence de l’anglais, avec l’exception de la plus jeune locutrice qui est affecté par l’anglais. Les résultats montrent aussi que les jeunes locuteurs franco-ontariens sont plus affectés par l’anglais que les âgés, et qu’il y a de la variabilité entre les hommes et les femmes. De l’autre côté, il y a une forte influence de l’anglais chez les apprenants du français car ils n’arrivent pas à maitriser la prononciation des occlusives françaises

What is a community?

For several years now, it has become commonplace for sociological and political analyses of Israel to highlight communalism. Sociologists have drawn attention to “the perennial nature of Jewish ethnicity”, whereas political scientists have stressed “the fragmentation of Israeli society into communities.” This feature has been interpreted by many observers as the swan song for a certain form of Zionist ideology that dominated the construction of the State and the first decades of its existence..