An inverse problem for time-harmonic electromagnetic currents in a smoothly layered medium.
An optimum design problem in magnetostatics
In this paper, we are interested in finding the optimal shape of a magnet. The criterion to maximize is the jump of the electromagnetic field between two different configurations. We prove existence of an optimal shape into a natural class of domains. We introduce a quasi-Newton type algorithm which moves the boundary. This method is very efficient to improve an initial shape. We give some numerical results.
An Optimum Design Problem in Magnetostatics
In this paper, we are interested in finding the optimal shape of a magnet. The criterion to maximize is the jump of the electromagnetic field between two different configurations. We prove existence of an optimal shape into a natural class of domains. We introduce a quasi-Newton type algorithm which moves the boundary. This method is very efficient to improve an initial shape. We give some numerical results.
Analysis of a coaxial waveguide with finite-length impedance loadings in the inner and outer conductors.
Analysis of an algorithm for computing electromagnetic Bloch modes using Nedelec spaces.
Analysis of integral equations attached to skin effect
Analysis of the potential formulation for the eddy current problem in a bounded domain.
Anisotropic inverse problems and Carleman estimates
This note reports on recent results on the anisotropic Calderón problem obtained in a joint work with Carlos E. Kenig, Mikko Salo and Gunther Uhlmann [8]. The approach is based on the construction of complex geometrical optics solutions to the Schrödinger equation involving phases introduced in the work [12] of Kenig, Sjöstrand and Uhlmann in the isotropic setting. We characterize those manifolds where the construction is possible, and give applications to uniqueness for the corresponding anisotropic...
Applications of the Dirac sequences in mechanics.
Applied Mathematics and the Imaging of the Brain
Approximation by generalized impedance boundary conditions of a transmission problem in acoustic scattering
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
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 of magnetic lines using the Lie transformation. (Approximation des lignes magnétiques utilisant la transformation Lie.)
Asymptotic analysis, in a thin multidomain, of minimizing maps with values in
Asymptotic analysis of an approximate model for time harmonic waves in media with thin slots
In this article, we derive a complete mathematical analysis of a coupled 1D-2D model for 2D wave propagation in media including thin slots. Our error estimates are illustrated by numerical results.
Asymptotic analysis of magnetic induction with high frequency for solid conductors
Asymptotic formulas for perturbations in the electromagnetic fields due to the presence of inhomogeneities of small diameter
Asymptotic formulas for perturbations in the electromagnetic fields due to the presence of inhomogeneities of small diameter
We consider solutions to the time-harmonic Maxwell's Equations of a TE (transverse electric) nature. For such solutions we provide a rigorous derivation of the leading order boundary perturbations resulting from the presence of a finite number of interior inhomogeneities of small diameter. We expect that these formulas will form the basis for very effective computational identification algorithms, aimed at determining information about the inhomogeneities from electromagnetic boundary measurements. ...
Asymptotic models for scattering from unbounded media with high conductivity
We analyze the accuracy and well-posedness of generalized impedance boundary value problems in the framework of scattering problems from unbounded highly absorbing media. We restrict ourselves in this first work to the scalar problem (E-mode for electromagnetic scattering problems). Compared to earlier works, the unboundedness of the rough absorbing layer introduces severe difficulties in the analysis for the generalized impedance boundary conditions, since classical compactness arguments are no...
Asymptotics for large time of solutions to nonlinear system associated with the penetration of a magnetic field into a substance
The nonlinear integro-differential system associated with the penetration of a magnetic field into a substance is considered. The asymptotic behavior as of solutions for two initial-boundary value problems are studied. The problem with non-zero conditions on one side of the lateral boundary is discussed. The problem with homogeneous boundary conditions is studied too. The rates of convergence are given. Results presented show the difference between stabilization characters of solutions of these...