Research Article

Three-dimensional discontinuous Galerkin elements with plane waves and Lagrange multipliers for the solution of mid-frequency Helmholtz problems

  1. Radek Tezaur,
  2. Charbel Farhat*

Article first published online: 14 NOV 2005

DOI: 10.1002/nme.1575

Issue

International Journal for Numerical Methods in Engineering

International Journal for Numerical Methods in Engineering

Volume 66, Issue 5, pages 796–815, 30 April 2006

Additional Information

How to Cite

Tezaur, R. and Farhat, C. (2006), Three-dimensional discontinuous Galerkin elements with plane waves and Lagrange multipliers for the solution of mid-frequency Helmholtz problems. International Journal for Numerical Methods in Engineering, 66: 796–815. doi: 10.1002/nme.1575

Author Information

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

*Department of Mechanical Engineering and 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 2006
  2. Article first published online: 14 NOV 2005
  3. Manuscript Accepted: 25 SEP 2005
  4. Manuscript Revised: 22 AUG 2005
  5. Manuscript Received: 9 JUN 2005

Funded by

  • Office of Naval Research. Grant Number: N00014-05-1-0204-1

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Keywords:

  • acoustic scattering;
  • discontinuous Galerkin;
  • Helmholtz;
  • Lagrange multipliers;
  • medium frequency;
  • plane waves

Abstract

Recently, a discontinuous Galerkin finite element method with plane wave basis functions and Lagrange multiplier degrees of freedom was proposed for the efficient solution in two dimensions of Helmholtz problems in the mid-frequency regime. In this paper, this method is extended to three dimensions and several new elements are proposed. Computational results obtained for several wave guide and acoustic scattering model problems demonstrate one to two orders of magnitude solution time improvement over the higher-order Galerkin method. Copyright © 2005 John Wiley & Sons, Ltd.

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