Dissipative terms and local time-stepping improvements in a spatial high order Discontinuous Galerkin scheme for the time-domain Maxwell’s equations E. Montseny 1 , S. Pernet 2 , X. Ferrières 3 , G. Cohen 4 Abstract In this paper, we present some improvements, in terms of accuracy and speed-up, for a particular well adapted Discontinuous Galerkin method devoted to the time- domain Maxwell equations. First, to reduce spurious modes on very distorted meshes, the addition of dissipative terms as penalization in the numerical scheme is stud- ied and compared on examples. Second, in order to increase the efficiency of the method, a multi-class local time-stepping strategy is presented and its validation and advantages are highlighted on different examples. Key words: Maxwell’s equations, Discontinuous Galerkin method, local time-stepping 1 Introduction In order to limit dispersive and dissipative errors [1] generated by classical schemes used to solve the time-domain Maxwell equations like FDTD [2] [3] or FVTD [4],[5],[6], some other methods as Discontinuous Galerkin (DG) meth- ods [7], using high order spatial approximation of the fields in each cell, have been studied. Such methods are generally used with unstructured meshes and naturally allow spatial refinements when necessary, as for example near walls or in presence of materials with high dielectric contrasts. We have developed for the Maxwell equations a DG method based on a leap-frog scheme in time 1 ONERA, currently LAAS-CNRS, 7 av. du Colonel Roche, 31077 Toulouse, France 2 CERFACS, 42 avenue Gaspard Coriolis, 31507 Toulouse, France 3 ONERA, 2 avenue Edouard Belin, 31055 Toulouse, France 4 INRIA, Domaine de Voluceau, BP-105 Rocquencourt, Le Chesnay cedex Preprint submitted to Elsevier Science 16 September 2008