High Order Finite Element Schemes and Domain Decomposition Solvers for Large-scale Simulations in Electromagnetics

We report on our work aiming at enabling large-scale simulations of frequency-domain electromagnetic wave propagation based on a recently developed innovative simulation software combining a high order finite element discretization scheme formulated on an unstructured tetrahedral grid, and scalable sparse linear solvers. The enabling numerical tool is a domain decomposition solution strategy for the sparse system of linear equations resulting from the spatial discretization of the underlying PDEs (Partial Differential Equations), that can be either a purely algebraic algorithm working at the matrix operator level (i.e. a black-box solver), or a tailored algorithm designed at the continuous PDE level (i.e. a PDE-based solver). The PDEs at hand here are the frequency-domain (or time-harmonic) Maxwell equations. Two concrete and different applications are considered for illustrating the modeling capabilities of the simulation software and assessing its parallel performances on the road to Exascale: the scattering of a plane wave by an aircraft, and the interaction of an electromagnetic wave with a heterogeneous model of head tissues