An Explicit Nodal Space-Time Discontinuous Galerkin Method for Maxwell’s Equations

A novel implicit nodal Space-Time Discontinuous Galerkin (STDG) method is proposed in this paper. An eigenvalue analysis is performed and compared with that for a DG scheme solved with a 4th-Order Runge-Kutta time integrator. We show that STDG offers a significant improvement of dissipative and dispersive properties and allows larger time steps, regardless of the spatial hp-refinement. A domain-decomposition technique is used to introduce an explicit formulation of the method in order to render it computationally efficient.This work is partially funded by the National Projects TEC2010-20841- C04-04, TEC2013-48414-C3-01, CSD2008-00068, P09-TIC-5327, P12-TIC- 1442, and from the GENIL excellence network

A domain decomposition method for solving the three-dimensional time-harmonic Maxwell equations discretized by discontinuous Galerkin methods

We present here a domain decomposition method for solving the three-dimensional time-harmonic Maxwell equations discretized by a discontinuous Galerkin method. In order to allow the treatment of irregularly shaped geometries, the discontinuous Galerkin method is formulated on unstructured tetrahedral meshes. The domain decomposition strategy takes the form of a Schwarz-type algorithm where a continuity condition on the incoming characteristic variables is imposed at the interfaces between neighboring subdomains. A multifrontal sparse direct solver is used at the subdomain level. The resulting domain decomposition strategy can be viewed as a hybrid iterative/direct solution method for the large, sparse and complex coefficients algebraic system resulting from the discretization of the time-harmonic Maxwell equations by a discontinuous Galerkin method