Formulation Variationnelle Ultra Faible pour les équations de Maxwell hétérogènes dans le contexte du calcul haute performance

Abstract

Electromagnetic simulations on large domains require a huge memory consumption. Domain decomposition methods, based on Trefftz methods, could be an answer to this issue. In this paper, we associate to heterogeneous three-dimensional Maxwell equations two equivalent variational formulations. One is based on upwind fluxes and the other one is based on fluxes introduced by O. Cessenat and B. Després. We associate to these variational formulations an iterative Trefftz GMRES solver. The poor conditioning due to the use of plane wave basis functions is bypassed thanks to a compression strategy. Moreover, the developed iterative solver is accelerated thanks to a left preconditioner. The considered numerical cases illustrate the performance of this basis reduction, which leads to the consideration of an industrial case of more than 750 millions of degrees of freedom