Comparison of Low-Storage Runge-Kutta Schemes for Discontinuous Galerkin Time-Domain Simulations of Maxwell's Equations

摘要

We present a detailed analysis of several low-storage Runge-Kutta time-stepping schemes for the simulation of Maxwell's equations within a discontinuous Galerkin (DG) finite-element framework that is particularly well-suited for nano-photonic problems. In particular, we discuss the influence of the numerical flux on the spectrum of the DG-operator and demonstrate how to optimize the spectrum for increased computational performance. As a result, we find that a speedup of around 60% can be achieved by combining a partial upwind flux with a properly selected low-storage Runge-Kutta scheme.