PERRUSSEL , Ronan

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...

Purpose - This work is concerned with the development and the numerical investigation of a hybridizable discontinuous Galerkin (HDG) method for the simulation of two-dimensional time-harmonic electromagnetic wave propagation problems. Design/methodology/approach - The proposed HDG method for the discretization of the two-dimensional transverse...

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...

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...

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...

A Schwarz-type domain decomposition method is presented for the solution of the system of 3d time-harmonic Maxwell equations. We introduce a hybridizable discontinuous Galerkin (HDG) scheme for the discretization of the problem based on a tetrahedrization of the computational domain. The discrete system of the HDG method on each subdomain is...

Hybridized discontinuous Galerkin methods preserve the advantages of classical discontinuous Galerkin methods and in addition enable to circumvent the issue of the number of degrees of freedom. The principles of these numerical methods are summed up for 3d time-harmonic Maxwell's equations and basic examples are proposed to assess their efficiency.

Purpose - This work is concerned with the development and the numerical investigation of a hybridizable discontinuous Galerkin (HDG) method for the simulation of two-dimensional time-harmonic electromagnetic wave propagation problems. Design/methodology/approach - The proposed HDG method for the discretization of the two-dimensional transverse...

In this paper, we study a bybridizable discontinuous Galerkin (HDG) method for the numerical solution of 2D time-harmonic Maxwell's equations. The formulations are given, and the relationship between the HDG scheme and the upwind flux DG method is also examined. The presented numerical results show the effectiveness of the proposed HDG method...

L'hybridation entre la WCIP (Wave Concept Iterative Procedure) et des méthodes volumiques comme la FDTLM (Frequency Domain Transmission Line Method), la FEM (Finite Element Method) et la méthode HDG (Hybridizable Discontinuous Galerkin) est présentée dans cet article. Le problème traité est celui de l'équation des ondes dans le domaine...

To study and design complex microwave circuits, we aim at hybridizing the method of moments called the Wave Concept Iterative Procedure with the Hybridizable Discontinuous Galerkin method. The goal is to take advantage of the low number of unknowns provided by the MoM with a surface mesh and to deal with inhomogeneous substrates with the...

Hybridization between the WCIP (Wave Concept Iterative Procedure) and volumic methods like the FDTLM (Frequency Domain Transmission Line Method), the FEM (Finite Element Method) and the HDG (Hybridizable Discontinuous Galerkin) method is presented in 2d in this paper. The considered problem is the Helmholtz equation in the frequency domain. Two...

International audience

We aim at coupling a method of moments, the Wave Concept Iterative Procedure, and the Hybridizable Discontinuous Galerkin (HDG) method to study electromagnetic susceptibility of innovative planar circuits in 3-D. Hybridizing the Wave Concept Iterative Procedure with volumic methods such as the Frequency-Domain Transmission Line Matrix method,...

We aim at coupling a method of moments, the Wave Concept Iterative Procedure, and the Hybridizable Discontinuous Galerkin (HDG) method to study electromagnetic susceptibility of innovative planar circuits in 3-D. Hybridizing the Wave Concept Iterative Procedure with volumic methods such as the Frequency-Domain Transmission Line Matrix method,...

An hybridization between two numerical methods, the 1d Wave Concept Iterative Procedure (WCIP) and the 2d Finite Element Method (FEM), is developed. Using two examples, comparisons are provided between the new hybrid method and an analytic solution, when available, or the WCIP alone.

To study and design complex microwave circuits, we aim at hybridizing the method of moments called the Wave Concept Iterative Procedure with the Hybridizable Discontinuous Galerkin method. The goal is to take advantage of the low number of unknowns provided by the MoM with a surface mesh and to deal with inhomogeneous substrates with the...

Hybridization between the WCIP (Wave Concept Iterative Procedure) and volumic methods like the FDTLM (Frequency Domain Transmission Line Method), the FEM (Finite Element Method) and the HDG (Hybridizable Discontinuous Galerkin) method is presented in 2d in this paper. The considered problem is the Helmholtz equation in the frequency domain. Two...

L'hybridation entre la WCIP (Wave Concept Iterative Procedure) et des méthodes volumiques comme la FDTLM (Frequency Domain Transmission Line Method), la FEM (Finite Element Method) et la méthode HDG (Hybridizable Discontinuous Galerkin) est présentée dans cet article. Le problème traité est celui de l'équation des ondes dans le domaine...

We present numerical results concerning the solution of the time-harmonic Maxwell's equations discretized by discontinuous Galerkin methods. In particular, a numerical study of the convergence, which compares different strategies proposed in the literature for the elliptic Maxwell equations, is performed in the two-dimensional case.

National audience

We report on recent efforts towards the development of a high order, non-conforming, discontinuous Galerkin method for the solution of the system of frequency domain Maxwell's equations in heterogeneous propagation media. This method is an extension of the low order one which was proposed in (http://hal.inria.fr/inria-00155231/en/)

The hybridization between two numerical methods, the 1D Wave Concept Iterative Procedure (WCIP) and the 2D Finite Element Method (FEM), is introduced. Preliminary numerical results are also presented.

We are interested here in the numerical modeling of time-harmonic electromagnetic wave propagation problems in irregularly shaped domains and heterogeneous media. In this context, we are naturally led to consider volume discretization methods (i.e. finite element method) as opposed to surface discretization methods (i.e. boundary element...