The hp-local discontinuous Galerkin method for low-frequency time-harmonic Maxwell equations

Solution of the time-harmonic Maxwell equations using discontinuous Galerkin methods

This work is concerned with the numerical solution of the time-harmonic Maxwell equations discretized by discontinuous Galerkin methods on unstructured meshes. Our motivation for using a discontinuous Galerkin method is the enhanced flexibility compared to the conforming edge element method [12]: for instance, dealing with non-conforming meshes is straightforward and the choice of the local app...

A domain decomposition strategy for solving time-harmonic Maxwell’s equations discretized by a discontinuous Galerkin method

A domain decomposition strategy is introduced in order to solve time-harmonic Maxwell’s equations discretized by a discontinuous Galerkin method. Its principles are explained for a 2D model problem and its efficacy is demonstrated on 2D and 3D examples.

Resolution of the time-harmonic Maxwell equations using discontinuous Galerkin methods and domain decomposition algorithms

We present numerical results relative to the resolution of the time-harmonic Maxwell equations discretized by discontinuous Galerkin methods. First, a numerical study of the convergence of discontinuous Galerkin methods which compares different strategies proposed in the literature for the elliptic Maxwell equations, is performed in the two-dimensional case. We also introduce a Schwarz-type dom...

Error analysis of Trefftz-discontinuous Galerkin methods for the time-harmonic Maxwell equations

In this paper, we extend to the time-harmonic Maxwell equations the p–version analysis technique developed in [R. Hiptmair, A. Moiola and I. Perugia, Plane wave discontinuous Galerkin methods for the 2D Helmholtz equation: analysis of the p-version, SIAM J. Numer. Anal., 49 (2011), 264-284] for Trefftz-discontinuous Galerkin approximations of the Helmholtz problem. While error estimates in a me...

Optimized Schwarz method for solving time-harmonic Maxwell's equations discretized by a discontinuous Galerkin method