Research Article

A space–time discontinuous Galerkin method for the solution of the wave equation in the time domain

  1. Steffen Petersen,
  2. Charbel Farhat*,
  3. Radek Tezaur

Article first published online: 5 NOV 2008

DOI: 10.1002/nme.2485

Issue

International Journal for Numerical Methods in Engineering

International Journal for Numerical Methods in Engineering

Volume 78, Issue 3, pages 275–295, 16 April 2009

Additional Information

How to Cite

Petersen, S., Farhat, C. and Tezaur, R. (2009), A space–time discontinuous Galerkin method for the solution of the wave equation in the time domain. International Journal for Numerical Methods in Engineering, 78: 275–295. doi: 10.1002/nme.2485

Author Information

  1. Department of Mechanical Engineering, Institute for Computational and Mathematical Engineering, Stanford University, Mail Code 3035, Stanford, CA 94305, U.S.A.

*Department of Mechanical Engineering, Institute for Computational and Mathematical Engineering, Stanford University, Mail Code 3035, Stanford, CA 94305, U.S.A.

Publication History

  1. Issue published online: 27 MAR 2009
  2. Article first published online: 5 NOV 2008
  3. Manuscript Accepted: 12 SEP 2008
  4. Manuscript Revised: 8 SEP 2008
  5. Manuscript Received: 31 OCT 2007

Funded by

  • German Academic Exchange Service (DAAD). Grant Number: D/06/44695
  • Office of Naval Research (ONR). Grant Number: N00014-05-1-0204-1

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Keywords:

  • wave equation;
  • discontinuous Galerkin;
  • Lagrange multipliers;
  • medium frequency;
  • wave basis functions;
  • space–time finite elements

Abstract

In recent years, the focus of research in the field of computational acoustics has shifted to the medium frequency regime and multiscale wave propagation. This has led to the development of new concepts including the discontinuous enrichment method. Its basic principle is the incorporation of features of the governing partial differential equation in the approximation. In this contribution, this concept is adapted for the simulation of transient problems governed by the wave equation. We present a space–time discontinuous Galerkin method with Lagrange multipliers, where the shape approximation in space and time is based on solutions of the homogeneous wave equation. The use of hierarchical wave-like basis functions is enabled by means of a variational formulation that allows for discontinuities in both the spatial and the temporal discretizations. Numerical examples in one space dimension demonstrate the outstanding performance of the proposed method compared with conventional space–time finite element methods. Copyright © 2008 John Wiley & Sons, Ltd.

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