Research Article

Overview of the discontinuous enrichment method, the ultra-weak variational formulation, and the partition of unity method for acoustic scattering in the medium frequency regime and performance comparisons

  1. Dalei Wang3,*,
  2. Radek Tezaur1,
  3. Jari Toivanen1,
  4. Charbel Farhat1,2,3

Article first published online: 26 JUL 2011

DOI: 10.1002/nme.3239

Issue

International Journal for Numerical Methods in Engineering

International Journal for Numerical Methods in Engineering

Volume 89, Issue 4, pages 403–417, 27 January 2012

Additional Information

How to Cite

Wang, D., Tezaur, R., Toivanen, J. and Farhat, C. (2012), Overview of the discontinuous enrichment method, the ultra-weak variational formulation, and the partition of unity method for acoustic scattering in the medium frequency regime and performance comparisons. International Journal for Numerical Methods in Engineering, 89: 403–417. doi: 10.1002/nme.3239

Author Information

  1. 1

    Department of Aeronautics and Astronautics, Stanford University, Stanford, U.S.A.

  2. 2

    Department of Mechanical Engineering, Stanford University, Stanford, U.S.A.

  3. 3

    Institute for Computational & Mathematical Engineering, Stanford University, Stanford, U.S.A.

*Dalei Wang, Institute for Computational & Mathematical Engineering, Stanford University, Stanford, CA 94305, U.S.A.
E-mail: daleiw@stanford.edu

Publication History

  1. Issue published online: 14 JAN 2012
  2. Article first published online: 26 JUL 2011
  3. Manuscript Accepted: 8 MAY 2011
  4. Manuscript Revised: 3 MAY 2011
  5. Manuscript Received: 21 MAR 2011

Funded by

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

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Keywords:

  • Discontinuous enrichment method;
  • Helmholtz;
  • medium frequency regime;
  • partition of unity method;
  • ultra-weak variational formulation

SUMMARY

The efficient finite element discretization of the Helmholtz equation becomes challenging in the medium frequency regime because of numerical dispersion, or what is often referred to in the literature as the pollution effect. A number of FEMs with plane wave basis functions have been proposed to alleviate this effect, and improve on the unsatisfactory preasymptotic convergence of the polynomial FEM. These include the partition of unity method, the ultra-weak variational formulation, and the discontinuous enrichment method. A previous comparative study of the performance of such methods focused on the first two aforementioned methods only. By contrast, this paper provides an overview of all three methods and compares several aspects of their performance for an acoustic scattering benchmark problem in the medium frequency regime. It is found that the discontinuous enrichment method outperforms both the partition of unity method and the ultra-weak variational formulation by a significant margin. Copyright © 2011 John Wiley & Sons, Ltd.

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