Complex geometrical optics solutions for Lipschitz conductivities.
Computation of the demagnetizing potential in micromagnetics using a coupled finite and infinite elements method
This paper is devoted to the practical computation of the magnetic potential induced by a distribution of magnetization in the theory of micromagnetics. The problem turns out to be a coupling of an interior and an exterior problem. The aim of this work is to describe a complete method that mixes the approaches of Ying [12] and Goldstein [6] which consists in constructing a mesh for the exterior domain composed of homothetic layers. It has the advantage of being well suited for catching the decay...
Computation of the demagnetizing potential in micromagnetics using a coupled finite and infinite elements method
This paper is devoted to the practical computation of the magnetic potential induced by a distribution of magnetization in the theory of micromagnetics. The problem turns out to be a coupling of an interior and an exterior problem. The aim of this work is to describe a complete method that mixes the approaches of Ying [12] and Goldstein [6] which consists in constructing a mesh for the exterior domain composed of homothetic layers. It has the advantage of being well suited for catching the...
Computation of the fundamental solution of electrodynamics for anisotropic materials
A new method for computation of the fundamental solution of electrodynamics for general anisotropic nondispersive materials is suggested. It consists of several steps: equations for each column of the fundamental matrix are reduced to a symmetric hyperbolic system; using the Fourier transform with respect to space variables and matrix transformations, formulae for Fourier images of the fundamental matrix columns are obtained; finally, the fundamental solution is computed by the inverse Fourier transform....
Computational issues in Electrical Impedence Tomography
Computer simulation of magnetic phase portraits and geometric dynamics around piecewise rectilinear circuits.
Computing guided modes for an unbounded stratified medium in integrated optics
We present a finite element method to compute guided modes in a stratified medium. The major difficulty to overcome is related to the unboundedness of the stratified medium. Our method is an alternative to the use of artificial boundary conditions and to the use of integral representation formulae. The domain is bounded in such a way we can write the solution on its lateral boundaries in terms of Fourier series. The series is then truncated for the computations over the bounded domain. The problem...
Computing guided modes for an unbounded stratified medium in integrated optics
We present a finite element method to compute guided modes in a stratified medium. The major difficulty to overcome is related to the unboundedness of the stratified medium. Our method is an alternative to the use of artificial boundary conditions and to the use of integral representation formulae. The domain is bounded in such a way we can write the solution on its lateral boundaries in terms of Fourier series. The series is then truncated for the computations over the bounded domain. The problem...
Conditions aux limites approchées pour les couches minces périodiques
Conditions aux limites approchées pour les couches minces périodiques
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.
Confining quantum particles with a purely magnetic field
We consider a Schrödinger operator with a magnetic field (and no electric field) on a domain in the Euclidean space with a compact boundary. We give sufficient conditions on the behaviour of the magnetic field near the boundary which guarantees essential self-adjointness of this operator. From the physical point of view, it means that the quantum particle is confined in the domain by the magnetic field. We construct examples in the case where the boundary is smooth as well as for polytopes; These...
Conical diffraction by multilayer gratings: A recursive integral equation approach
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 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...
Consistent models for electrical networks with distributed parameters
A system of one-dimensional linear parabolic equations coupled by boundary conditions which include additional state variables, is considered. This system describes an electric circuit with distributed parameter lines and lumped capacitors all connected through a resistive multiport. By using the monotony in a space of the form , one proves the existence and uniqueness of a variational solution, if reasonable engineering hypotheses are fulfilled.
Contributo allo studio dei fenomeni di trasporto della carica minoritaria in regioni quasi neutre di semiconduttori fortemente e disuniformemente drogati. Riduzione del problema ad equazioni integrali
Transport phenomena of minority carriers in quasi neutral regions of heavily doped semiconductors are considered for the case of one-dimensional stationary flow and their study is reduced to a Fredholm integral equation of the second kind, the kernel and the known term of which are built from known functions of the doping arbitrarily distributed in space. The advantage of the method consists, among other things, in having all the coefficients of the differential equations and of the boundary conditions...
Contrôle et stabilisation d'ondes électromagnétiques
Contrôle et stabilisation d'ondes électromagnétiques
We consider the exact controllability and stabilization of Maxwell equation by using results on the propagation of singularities of the electromagnetic field. We will assume geometrical control condition and use techniques of the work of Bardos et al. on the wave equation. The problem of internal stabilization will be treated with more attention because the condition divE=0 is not preserved by the system of Maxwell with Ohm's law.
Convergence analysis of a Fourier-based solution method of the Laplace equation for a model of magnetic recording.
Convergence and stability of a discontinuous Galerkin time-domain method for the 3D heterogeneous Maxwell equations on unstructured meshes
A Discontinuous Galerkin method is used for to the numerical solution of the time-domain Maxwell equations on unstructured meshes. The method relies on the choice of local basis functions, a centered mean approximation for the surface integrals and a second-order leap-frog scheme for advancing in time. The method is proved to be stable for cases with either metallic or absorbing boundary conditions, for a large class of basis functions. A discrete analog of the electromagnetic energy is conserved...
Convergence and stability of a discontinuous Galerkin time-domain method for the 3D heterogeneous Maxwell equations on unstructured meshes
A Discontinuous Galerkin method is used for to the numerical solution of the time-domain Maxwell equations on unstructured meshes. The method relies on the choice of local basis functions, a centered mean approximation for the surface integrals and a second-order leap-frog scheme for advancing in time. The method is proved to be stable for cases with either metallic or absorbing boundary conditions, for a large class of basis functions. A discrete analog of the electromagnetic energy is conserved...
Convergence of a constrained finite element discretization of the Maxwell Klein Gordon equation
As an example of a simple constrained geometric non-linear wave equation, we study a numerical approximation of the Maxwell Klein Gordon equation. We consider an existing constraint preserving semi-discrete scheme based on finite elements and prove its convergence in space dimension 2 for initial data of finite energy.