Third M.I.T. Conference on Computational Fluid and Solid Mechanics June 14–17, 2005  

High-order RKDG methods for computational electromagnetics

Min-Hung Chen*, Bernardo Cockburn, Fernando Reitich
University of Minnesota, School of Mathematics, Minneapolis, MN 55455, USA

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We introduce a new Runge-Kutta discontinuous Galerkin (RKDG) method for problems of wave propagation that achieves full high-order convergence in time and space. For the time integration it uses an mth-order, m-stage, low storage strong stability preserving Runge–Kutta (SSP–RK) scheme which is an extension to a class of non-autonomous linear systems of a recently designed method for autonomous linear systems. This extension allows for a high-order accurate treatment of the inhomogeneous, time-dependent terms that enter the semi-discrete problem on account of the physical boundary conditions. Thus, if polynomials of degree k are used in the space discretization, the (RKDG) method is of overall order m = k + 1, for any k > 0. Numerical results in two space dimensions are presented that confirm the predicted convergence properties.

Keywords:  Discontinuous Galerkin methods; Wave propagation; Maxwell equations

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