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### A mixed–FEM and BEM coupling for a three-dimensional eddy current problem

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

We study in this paper the electromagnetic field generated in a conductor by an alternating current density. The resulting interface problem (see Bossavit (1993)) between the metal and the dielectric medium is treated by a mixed–FEM and BEM coupling method. We prove that our BEM-FEM formulation is well posed and that it leads to a convergent Galerkin method.

### A mixed–FEM and BEM coupling for a three-dimensional eddy current problem

ESAIM: Mathematical Modelling and Numerical Analysis

We study in this paper the electromagnetic field generated in a conductor by an alternating current density. The resulting interface problem (see Bossavit (1993)) between the metal and the dielectric medium is treated by a mixed–FEM and BEM coupling method. We prove that our BEM-FEM formulation is well posed and that it leads to a convergent Galerkin method.

### A new H(div)-conforming p-interpolation operator in two dimensions

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

In this paper we construct a new H(div)-conforming projection-based p-interpolation operator that assumes only Hr(K) $\cap$$\stackrel{˜}{𝐇}$-1/2(div, K)-regularity (r &gt; 0) on the reference element (either triangle or square) K. We show that this operator is stable...

### A new H(div)-conforming p-interpolation operator in two dimensions

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper we construct a new H(div)-conforming projection-based p-interpolation operator that assumes only Hr(K) $\cap$$\stackrel{˜}{𝐇}$-1/2(div, K)-regularity (r > 0) on the reference element (either triangle or square) K. We show that this operator is stable with...

### Conical diffraction by multilayer gratings: A recursive integral equation approach

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 ${ℝ}^{2}$ 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...

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

ESAIM: Mathematical Modelling and Numerical Analysis

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...

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

ESAIM: Mathematical Modelling and Numerical Analysis

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...

### Exact and numerical solutions of Poisson equation for electrostatic potential problems.

Mathematical Problems in Engineering

### Modèle effectif de couche mince rugueuse périodique sur une structure semi-infinie

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

Nous étudions l’effet d’une couche mince rugueuse périodique déposée sur une structure semi-infinie, dans le contexte Helmholtz bi-dimensionnel. Formellement, nous obtenons des conditions de transmission équivalentes à l’ordre 1, par des techniques de type homogénéisation. Suivent alors la résolution du problème du milieu effectif éclairé par une onde plane, et le calcul de la fonction de Green effective ; le tout par analyse de Fourier. Dans un deuxième temps, nous considérons le problème de diffraction...

### Tangential fields in mathematical model of optical diffraction

Programs and Algorithms of Numerical Mathematics

We present the formulation of optical diffraction problem on periodic interface based on vector tangential fields, for which the system of boundary integral equations is established. Obtained mathematical model is numerically solved using boundary element method and applied to sine interface profile.

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