Discontinuous Galerkin methods with Trefftz approximations

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:270

Article; Proceedings Paper

Kretzschmar, Fritz^1,2  Schnepp, Sascha M.³  Tsukerman, Igor⁴  Weiland, Thomas² 

[1] Tech Univ Darmstadt, Grad Sch Computat Engn, D-64293 Darmstadt, Germany

[2] Tech Univ Darmstadt, Inst Theorie Elektromagnet Felder, D-64289 Darmstadt, Germany

[3] Swiss Fed Inst Technol, Lab Electromagnet Fields & Microwave Elect, CH-8092 Zurich, Switzerland

[4] Univ Akron, Dept Elect & Comp Engn, Akron, OH 44325 USA

关键词: Discontinuous Galerkin method;    Finite element method;    Trefftz method;    Higher order time integration;    Electrodynamics;    Wave propagation;   

DOI  :  10.1016/j.cam.2014.01.033

来源: Elsevier

【 摘 要 】

We present a novel Discontinuous Galerkin Finite Element Method for wave propagation problems. The method employs space-time Trefftz basis functions that satisfy the underlying partial differential equations and the respective interface boundary conditions exactly in an element-wise fashion. The basis functions can be of arbitrarily high order and we demonstrate spectral convergence in the space-time L-2-norm. Therefore high order time integration is an inherent property of the method and clearly sets it apart from methods that employ a high order approximation in space only. (C) 2014 Elsevier B.V. All rights reserved.

【 授权许可】

Free