Adaptive Time-Integration for Discontinuous Galerkin Time-Domain Simulations of Maxwell’s Equations
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Date
2013Type
- Other Conference Item
ETH Bibliography
yes
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Abstract
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 [1]. In order to match the accurate spatial discretization one typically also requires an efficient higher-order time integration method. In practice, explicit low-storage Runge-Kutta (LSRK) schemes were shown to offer an excellent compromise of accuracy, performance and memory consumption. Here, we will present several new low-storage Runge-Kutta methods which significantly improve both the efficiency and the accuracy of DG time-domain simulations of Maxwell’s equations. First, we present novel LSRK schemes in the 2N formulation with up to 22 stages. Besides optimized schemes of 4th order [2], we also discuss new methods of 5th order. In addition, we also demonstrate embedded Runge-Kutta pairs in the low-storage 3S* formulation [3] with optimized stability contours for both the main and the embedded schemes. Using the embedded scheme for error estimation then allows us to automatically adapt the timestep in large scale DG calculations. Show more
Publication status
publishedBook title
Book of Abstracts - Femtec 2013Pages / Article No.
Publisher
University of NevadaEvent
Organisational unit
02635 - Institut für Elektromagnetische Felder / Electromagnetic Fields Laboratory
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