LANTERI , Stephane

In this paper, we discuss the formulation, stability and validation of a high-order non-dissipative discontinuous Galerkin (DG) method for solving Maxwell's equations on non-conforming simplex meshes. The proposed method combines a centered approximation for the numerical fluxes at inter element boundaries, with either a second-order or a...

Existing numerical methods for the solution of the time domain Maxwell equations often rely on explicit time integration schemes and are therefore constrained by a stability condition that can be very restrictive on highly refined or unstructured meshes. The present study aims at investigating the applicability of an implicit time integration...

This study is concerned with the solution of the time domain Maxwell's equations in a dispersive propagation media by a Discontinuous Galerkin Time Domain (DGTD) method. The Debye model is used to describe the dispersive behaviour of the media. The resulting system of equations is solved using a centered flux discontinuous Galerkin formulation...

In this work, we discuss the formulation, stability, convergence and numerical validation of a high-order leap-frog based non-dissipative discontinuous Galerkin time-domain (DGTD) method for solving Maxwell's equations on non-conforming simplicial meshes. This DGTD method makes use of a nodal polynomial interpolation method for the...

Discontinuous Galerkin (DG) methods have been the subject of numerous research activities in the last 15 years and have been successfully developed for various physical contexts modeled by elliptic, mixed hyperbolic-parabolic and hyperbolic systems of PDEs. One major drawback of high order DG methods is their intrinsic cost due to the very...

This work is about the numerical solution of the time-domain Maxwell's equations in dispersive propagation media by a discontinuous Galerkin time-domain method. The Debye model is used to describe the dispersive behaviour of the media. The resulting system of differential equations is solved using a centred-flux discontinuous Galerkin...

This work is about the numerical solution of the time-domain Maxwell's equations in dispersive propagation media by a discontinuous Galerkin time-domain method. The Debye model is used to describe the dispersive behaviour of the media. The resulting system of differential equations is solved using a centred-flux discontinuous Galerkin...

Nous présentons dans ce rapport une méthode Galerkin discontinue pour la résolution numérique des équations de Maxwell en domaine temporel sur des maillages hybrides. Nous formulons les schémas de discrétisation en trois dimensions d'espace (3D) pour des maillages hybrides alors tétraédriques / hexaédriques, en utilisant une approximation...

The numerical solution of the three-dimensional time-harmonic Maxwell equations using high order methods such as discontinuous Galerkin formulations require efficient solvers. A domain decomposition strategy is introduced for this purpose. This strategy is based on optimized Schwarz methods applied to the first order form of the Maxwell system...

We present here a domain decomposition method for solving the three-dimen\-sional time-harmonic Maxwell equations discretized by a discontinuous Galerkin method. In order to allow the treatment of irregularly shaped geometries, the discontinuous Galerkin method is formulated on unstructured tetrahedral meshes. The domain decomposition strategy...

This contribution consists of two main parts: non-local dispersion models and the numerical modeling of single electron beams. Both subjects are discussed in the context of computational nanophotonics for metallic nano-structures. Non-local dispersion models take into account the non-local nature of mutual electron interaction in the electron...

We study the numerical solution of 3d time-harmonic Maxwell's equations by a hybridizable discontinuous Galerkin method. A hybrid term representing the tangential component of the numerical trace of the magnetic field is introduced. The global system to solve only involves the hybrid term as unknown. We show that the reduced system has...

Numerical methods for solving the time domain Maxwell equations often rely on cartesian meshes and are variants of the finite difference time domain method originating in the seminal work of Yee [6]. In the recent years, there has been an increasing interest in discontinuous Galerkin time domain methods dealing with unstructured meshes since...

Ce rapport traite de la résolution des équations de Maxwell en régime harmonique par une méthode de type Galerkin discontinu. Il rappelle tout d'abord la formulation du problème et propose quelques éléments de discussion pour le choix du flux numérique utilisé dans la méthode de discrétisation. Il présente ensuite quelques pistes pour la...

This work is concerned with the design of a hp-like discontinuous Galerkin (DG) method for solving the 2D time-domain Maxwell's equations on non-conforming locally refined triangular meshes. The proposed DG method allows non-conforming meshes with arbitrary-level hanging nodes. This method combines a centered approximation for the evaluation of...

Numerical methods for solving the time-domain Maxwell equations often rely on cartesian meshes and are variants of the finite difference time-domain (FDTD) method due to Yee. In the recent years, there has been an increasing interest in discontinuous Galerkin time-domain (DGTD) methods dealing with unstructured meshes since the latter are...

Recent advances in fabrication technologies of metallic nanostructures have opened a new branch of nanophotonics. Those structures show significantly different behaviour compared to the mi- crowave regime due to the negative refraction index of noble metals at optical frequencies. Popular applications are for example light harvesting, cancer...

On étudie la stabilité d'une méthode Galerkin discontinu pour la résolution numérique des équations de Maxwell 2D en domaine temporel sur des maillages triangulaires non-conformes. Cette méthode combine l'utilisation d'une approximation centrée pour l'évaluation des flux aux interfaces entre éléments voisins du maillage, á un schéma...

We present an explicit hybridizable discontinuous Galerkin (HDG) method for numerically solving the system of three-dimensional (3D) time-domain Maxwell equations. The method is fully explicit similarly to classical so-called DGTD (Discontinuous Galerkin Time-Domain) methods that have been extensively studied during the last 15 years for the...

Ces dernières années, les méthodes Galerkin discontinues ont fait l'objet de plusieurs travaux visant à leur mise au point pour la résolution numérique des équations de Maxwell instationnaires. Dans la grande majorité de ces travaux, les composantes du champ électromagnétique sont approchées au sein de chaque élément du maillage par une...

In this paper, we are concerned with the numerical modelling of the propagation of electromagnetic waves in dispersive materials for nanophotonics applications. We focus on a generalized model that allows for the description of a wide range of dispersive media. The underlying differential equations are recast into a generic form, and we...

We present a high performance computing methodology for the simulation of electromagnetic wave propagation in biological tissues and its application to the numerical evaluation of radio frequency absorption in head tissues as they are exposed to radiation from a cellular phone. For this purpose, the system of time-domain Maxwell equations is...

Programming non-embarrassingly parallel scientific computing applications such as those involving the numerical resolution of system of PDEs using mesh based methods for grid computing environments is a complex and important issue. This work contributes to this goal by proposing some MPI extensions to let programmers deal with the hierarchical...

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We present a high-order discontinuous Galerkin method for the simulation of P-SV seismic wave propagation in heterogeneous media and two dimensions of space. The first-order velocity-stress system is obtained by assuming that the medium is linear, isotropic and viscoelastic, thus considering intrinsic attenuation. The associated stress-strain...