MOYA , Ludovic

An attractive feature of discontinuous Galerkin (DG) spatial discretization is the possibility of using locally refined space grids to handle geometrical details. However, when combined with an explicit integration method to numerically solve a time-dependent partial differential equation, this readily leads to unduly large step size...

An attractive feature of discontinuous Galerkin (DG) spatial discretization is the possibility of using locally refined space grids to handle geometrical details. However, when combined with an explicit integration method to numerically solve a time-dependent partial differential equation, this readily leads to unduly large step size...

This work deals with the time-domain formulation of Maxwell's equations. The main objective is to propose high-order finite element type methods for the discretization of Maxwell's equations and efficient time integration methods on locally refined meshes. We consider Discontinuous Galerkin Time-Domain (DGTD) methods relying on an arbitrary...

In this note we study the temporal convergence of a locally implicit discontinuous Galerkin (DG) method for Maxwell's equations modeling electromagnetic wave propagation. Particularly, we wonder whether the method retains its second-order ordinary differential equation (ODE) convergence under stable simultaneous space-time grid refinement...

An attractive feature of discontinuous Galerkin (DG) spatial discretization is the possibility of using locally refined space grids to handle geometrical details. However, locally refined meshes lead to severe stability constraints on explicit integration methods to numerically solve a time-dependent partial differential equation. If the region...

This paper discusses about the development of high-order locally implicit time integration strategies in a discontinuous Galerkin method for Maxwell's equations.

An attractive feature of discontinuous Galerkin (DG) spatial discretization is the possibility of using locally refined space grids to handle geometrical details. However, locally refined meshes lead to severe stability constraints on explicit integration methods to numerically solve a time-dependent partial differential equation. If the ratio...

This paper discusses about the development of high-order locally implicit time integration strategies in a discontinuous Galerkin method for Maxwell's equations.

This paper is concerned with the approximation 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. We adapt the locally implicit time integration method from [1] and derive a convergence analysis...

We are concerned here with the numerical simulation of electromagnetic wave propagation in biological media. Because of their water content, these media are dispersive i.e. their electromagnetic material characteristics depend of the frequency. In the time-domain, this translates in a time dependency of these parameters that can be taken into...

An attractive feature of discontinuous Galerkin (DG) spatial discretization is the possibility of using locally refined space grids to handle geometrical details. However, locally refined meshes lead to severe stability constraints on explicit integration methods to numerically solve a time-dependent partial differential equation. If the region...

Discontinuous Galerkin (DG) methods have ben extensively studied in the last ten years for the numerical solution of the time-domain Maxwell equations. For the numerical treatment of the frequency-domain Maxwell equations, nodal DG methods can also be considered. However, such DG formulations are highly expensive, especially for the...

During the last ten years, the discontinuous Galerkin time-domain (DGTD) method has progressively emerged as a viable alternative to well established finite-difference time-domain (FDTD) and finite-element time-domain (FETD) methods for the numerical simulation of electromagnetic wave propagation problems in the time-domain. In this paper, we...

This work is concerned with the numerical treatment of the system of three-dimensional frequency-domain (or time-harmonic) Maxwell equations using a high order hybridizable dis-continuous Galerkin (HDG) approximation method combined to domain decomposition (DD) based hybrid iterative-direct parallel solution strategies. The proposed HDG method...

During the last ten years, the discontinuous Galerkin time-domain (DGTD) method has progressively emerged as a viable alternative to well established finite-difference time-domain (FDTD) and finite-element time-domain (FETD) methods for the numerical simulation of electromagnetic wave propagation problems in the time-domain. In this paper, we...