Ultra-weak variational formulation for heterogeneous Maxwell problem in the context of high performance computing

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 one variational formulation which can be obtained either by upwind fluxes or Riemann traces. We associate to this variational formulation an iterative Trefftz Krylov 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.