The multiscale hybrid-mixed method for the maxwell equations in heterogeneous mediaReport as inadecuate

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* Corresponding author 1 NACHOS - Numerical modeling and high performance computing for evolution problems in complex domains and heterogeneous media CRISAM - Inria Sophia Antipolis - Méditerranée , JAD - Laboratoire Jean Alexandre Dieudonné : UMR6621 2 Instituto de Matematica - Pontificia Universidad Católica de Valparaíso - IMA - PUCV 3 JAD - Laboratoire Jean Alexandre Dieudonné 4 Department of Computational and Applied Mathematics

Abstract : In this work, we address time dependent wave propagation problems with strong multiscale features in space and time. Our goal is to design a family of innovative high performance numerical methods suitable to the simulation of such multiscale problems. Particularly, we extend the Multiscale Hybrid-Mixed finite element method MHM for short for the two-and three-dimensional time-dependent Maxwell equations with heterogeneous coefficients. The MHM method arises from the decomposition of the exact electric and magnetic fields in terms of the solutions of locally independent Maxwell problems tied together with a one-field formulation on top of a coarse-mesh skeleton. The multiscale basis functions, which are responsible for upscaling, are driven by local Maxwell problems with tangential component of the magnetic field prescribed on faces. A high-order discontinuous Galerkin method in space combined with a second-order explicit leapfrog scheme in time discretizes the local problems. This makes the MHM method effective and yields a staggered algorithm within a - divide-and-conquer - framework. Several numerical tests assess the optimal convergence of the MHM method and its capacity to preserve the energy principle, as well as its accuracy to solving heterogeneous media problems on coarse meshes.

Keywords : finite element multiscale Maxwell equations wave model hybrid method

Author: Stéphane Lanteri - Diego Paredes - Claire Scheid - Frédéric Valentin -



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