Different time-stepping methods for a nodal high-order discontinuous Galerkin discretisation of the Maxwell equations are discussed. A comparison between the most popular choices of Runge-Kutta (RK) methods is made from the point of view of accuracy and computational work. By choosing the strong-stability-preserving Runge-Kutta (SSP-RK) time-integration method of order consistent with the polynomial order of the spatial discretisation, better accuracy can be attained compared to fixed-order schemes. This comes without a significant increase in the computation work. A numerical Fourier analysis is performed for this Runge-Kutta discontinuous Galerkin (RKDG) discretisation to gain insight into the dispersion and dissipation properties of the complete scheme. The analysis also provides practical information on the convergence of the dissipation and dispersion error, which is important when studying wave propagation phenomena.
|Publisher||Department of Applied Mathematics, University of Twente|