Une méthode de raffinement de maillage espace-temps pour le système de Maxwell en dimension un

✍ Scribed by Francis Collino; Thierry Fouquet; Patrick Joly

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 426 KB
• Volume: 328
• Category: Article
• ISSN: 0764-4442
• DOI: 10.1016/s0764-4442(99)80132-3

✦ Synopsis

Dans cette Note, nous proposons une methode nouvelle pour le raffinement de grille espace-temps dans l'approximation par differences finies du systeme de Maxwell en dimension un. Notre strategic est fondte sur la conservation d'une Cnergie disc&e. 0 AcadCmie des Sciences/Elsevier, Paris A space-time mesh refinement method for the 1D Maxwell's system We propose a new method for space-time mesh refinement in the finite difference approximation of the 1D Maxwell's system. Our strategy is based on the conservation of a discrete energy. 0 AcadCmie des Sciences/Elsevier, Paris

Abridged English Version

We propose a new approach for a space-time grid refinement method for the time domain finite difference approximation (FDTD) of the Maxwell system (equation ( 1)).

Our basic interior scheme is Yee's scheme 193. Our goal is to use a space step AZ, and a time step At in the half-line .7: > 0; and a space step 2Ax, and a time step 2At in the half-line z < 0, in such a way that in the whole domain the ratio between the space step and the time step remains constant. This avoids the introduction of numerical dispersion in some part of the domain. The corresponding equations are given in (3) and (4). The main difficulty is to obtain a scheme for gluing together the solution in the fine grid and the solution in the coarse grid. Classical techniques based on interpolation in space or time ([33, [S]) generally lead to instability problems [4]. Our approach consists in guaranteeing a priori the stability of the scheme under the same CFL condition as in the case of a uniform mesh. One key point consists in representing twice the line x = 0, one considered as the boundary of the half-space x > 0, the other as the boundary of the half-space .7: < 0. Doing Note pr&ent& par Pierre-Louis LIONS.