Find file
Fetching contributors…
Cannot retrieve contributors at this time
35 lines (21 sloc) 2.06 KB
\title{Efficient Time-Integration for Discontinuous Galerkin Discretizations of Maxwell's Equations}
\tocauthor{J. Niegemann} \author{} \institute{}
{\large Jens Niegemann}\\
Laboratory for Electromagnetic Fields and Microwave Electronics, Swiss Federal Institute of Technology (ETH), Z\"urich, Switzerland\\
In recent years, the discontinuous Galerkin (DG) approach has gained considerable attention as an efficient and accurate method for solving Maxwell's equations in time-domain. Its ability to allow explicit time integration while offering a higher-order spatial discretization on unstructured meshes makes it a very attractive method for complex electromagnetic systems \cite{Koenig11}. In order to match the accurate spatial discretization one also requires an efficient higher-order time integration
method. In practice, explicit low-storage Runge-Kutta (LSRK) schemes have been shown to offer an excellent compromise of accuracy, performance and memory consumption.
Here, we will discuss a numeric approach to generate new LSRK schemes with specifically tailored stability domains \cite{Niegemann12}. It will be demonstrated that such schemes can provide performance enhancements of up to 50\% over the best previously known schemes. In addition we will show how such optimized methods can be combined with a multistep Adams integrator \cite{Hochbruck11} to allow for a very efficient local timestepping in strongly refined meshes.
{\sc K. Busch and M. K\"onig and J. Niegemann}. {Discontinuous Galerkin methods in nanophotonics}. Laser Photonics Rev. 5, 773-809 (2011).
{\sc J. Niegemann and R. Diehl and K. Busch}. {Efficient low-storage Runge-Kutta schemes with optimized stability regions}. J. Comput. Phys. 231, 364-372 (2012) .
{\sc M. Hochbruck and A. Ostermann}. {Exponential multistep methods of Adams-type}. BIT Numer. Math. 51, 889-908 (2011).