High-order RKDG methods for computational electromagnetics

Min Hung Chen, Bernardo Cockburn, Fernando Reitich

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

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.

Original languageEnglish (US)
Title of host publication3rd M.I.T. Conference on Computational Fluid and Solid Mechanics
Pages1069-1071
Number of pages3
StatePublished - Dec 1 2005
Event3rd M.I.T. Conference on Computational Fluid and Solid Mechanics - Boston, MA, United States
Duration: Jun 14 2005Jun 17 2005

Publication series

Name3rd M.I.T. Conference on Computational Fluid and Solid Mechanics

Other

Other3rd M.I.T. Conference on Computational Fluid and Solid Mechanics
CountryUnited States
CityBoston, MA
Period6/14/056/17/05

Keywords

  • Discontinuous Galerkin methods
  • Maxwell equations
  • Wave propagation

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