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SCD SEMINAR:

High-Order RKDG Methods for

Computational Electromagnetics

Min-Hung Chen
School of Mathematics

University of Minnesota

Friday, February 11, 2005

Chapman Room, NCAR Mesa Lab

2 – 3 PM

In this talk, we devise a new RKDG method that achieves full high-order convergence in time and space while keeping the time-step proportional to the spatial mesh-size. To this end, we derive an extension to non-autonomous linear systems of the mth-order, m-stage strong stability preserving Runge-Kutta (SSP-RK) scheme with low storage described in Gottlieb et al (SIAM, 2000). With this time-integration scheme, and if polynomials of degree k are used in the space discretization, our RKDG method can be made to converge with overall order m = k + 1, for any k > 0. In particular, the scheme 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. Therefore, we can implement the exact non-reflecting boundary conditions derived by Grote, Keller (JCP, 1998) and Sofronov (J Appl M, 1998). Numerical results in two space dimensions are presented that confirm the predicted convergence properties.