Research Article

The discontinuous enrichment method for elastic wave propagation in the medium-frequency regime

  1. Lin Zhang1,2,
  2. Radek Tezaur1,2,
  3. Charbel Farhat1,2,*

Article first published online: 13 JAN 2006

DOI: 10.1002/nme.1619

Issue

International Journal for Numerical Methods in Engineering

International Journal for Numerical Methods in Engineering

Volume 66, Issue 13, pages 2086–2114, 25 June 2006

Additional Information

How to Cite

Zhang, L., Tezaur, R. and Farhat, C. (2006), The discontinuous enrichment method for elastic wave propagation in the medium-frequency regime. International Journal for Numerical Methods in Engineering, 66: 2086–2114. doi: 10.1002/nme.1619

Author Information

  1. 1

    Department of Mechanical Engineering, Stanford University, Mail Code 3035, Stanford, CA 94305-3035, U.S.A.

  2. 2

    Institute for Computational and Mathematical Engineering, Stanford University, Mail Code 3035, Stanford, CA 94305-3035, U.S.A.

*Institute for Computational and Mathematical Engineering, Stanford University, Building 500, Room 501S, Mail Code 3035, Stanford, CA 94305-3035, U.S.A.

Publication History

  1. Issue published online: 23 MAY 2006
  2. Article first published online: 13 JAN 2006
  3. Manuscript Accepted: 13 NOV 2005
  4. Manuscript Received: 2 NOV 2005

Funded by

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

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Keywords:

  • elastic wave propagation;
  • discontinuous Galerkin;
  • Lagrange multipliers;
  • medium frequency;
  • plane waves

Abstract

The discontinuous enrichment method (DEM) is specified and developed for the solution of two-dimensional elastic wave propagation problems in the frequency domain. The classical finite element polynomial approximation of the displacement field is enriched by the superposition of discontinuous pressure and shear wave functions. The continuity of the solution across the element interfaces is weakly enforced by suitable Lagrange multipliers. Higher-order rectangular DEM elements are constructed and benchmarked against the standard higher-order polynomial Galerkin elements for two-dimensional problems in the medium frequency regime. In general, it is found that for such applications, DEM can achieve the same accuracy as the p finite element method using a similar computational complexity but with about 10 times fewer degrees of freedom. This highlights the potential of this hybrid method for problems where the scale of vibrations is very small compared to the characteristic dimension of the physical medium. Copyright © 2006 John Wiley & Sons, Ltd.

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