Research Article

Improved accuracy for the Helmholtz equation in unbounded domains

  1. Eli Turkel1,‡,*,
  2. Charbel Farhat2,
  3. Ulrich Hetmaniuk2,†

Article first published online: 26 MAR 2004

DOI: 10.1002/nme.882

Issue

International Journal for Numerical Methods in Engineering

International Journal for Numerical Methods in Engineering

Volume 59, Issue 15, pages 1963–1988, 21 April 2004

Additional Information

How to Cite

Turkel, E., Farhat, C. and Hetmaniuk, U. (2004), Improved accuracy for the Helmholtz equation in unbounded domains. International Journal for Numerical Methods in Engineering, 59: 1963–1988. doi: 10.1002/nme.882

Author Information

  1. 1

    Department of Mathematics, Tel Aviv University, Tel Aviv, Israel

  2. 2

    Department of Aerospace Sciences, University of Colorado at Boulder, Boulder, Colorado, U.S.A.

  1. †

    Computational and Mathematics Algorithms Department, Sandia National Laboratory, Albuquerque, New Mexico, U.S.A.

  1. ‡

    Work done while visiting the University of Colorado at Boulder

*Department of Mathematics, Tel Aviv University, Ramat Aviv Tel Aviv 69978, Israel

Publication History

  1. Issue published online: 26 MAR 2004
  2. Article first published online: 26 MAR 2004
  3. Manuscript Accepted: 29 APR 2003
  4. Manuscript Received: 3 FEB 2003

Funded by

  • Office of Naval Research. Grant Number: N-00014-01-0356

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Keywords:

  • Helmholtz equation;
  • preconditioning;
  • unbounded domain;
  • absorbing boundary conditions

Abstract

Based on properties of the Helmholtz equation, we derive a new equation for an auxiliary variable. This reduces much of the oscillations of the solution leading to more accurate numerical approximations to the original unknown. Computations confirm the improved accuracy of the new models in both two and three dimensions. This also improves the accuracy when one wants the solution at neighbouring wavenumbers by using an expansion in k. We examine the accuracy for both waveguide and scattering problems as a function of k, h and the forcing mode l. The use of local absorbing boundary conditions is also examined as well as the location of the outer surface as functions of k. Connections with parabolic approximations are analysed. Copyright © 2004 John Wiley & Sons, Ltd.

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