Spectral Difference method On Structured-Grids for Maxwell's Equations in Time Domain

Abstract

International audienceThis article introduces a new way to discretize Maxwell's equations. It is a discontinuous highorder method based on local polynomial interpolations, named the Spectral Difference method. This approach mainly differs from the standard Discontinuous Galerkin method by solving the strong form of the equation, instead of the weak form. This article gives the main lines of the Spectral Difference method for a 1D conservation law and explains how it applies to transient Maxwell's equations. The method is then evaluated on a test-case with well-known analytical solution