Research Article

Fast direct solution of the Helmholtz equation with a perfectly matched layer or an absorbing boundary condition

  1. Erkki Heikkola*,
  2. Tuomo Rossi,
  3. Jari Toivanen

Article first published online: 12 JUN 2003

DOI: 10.1002/nme.752

Issue

International Journal for Numerical Methods in Engineering

International Journal for Numerical Methods in Engineering

Volume 57, Issue 14, pages 2007–2025, 14 August 2003

Additional Information

How to Cite

Heikkola, E., Rossi, T. and Toivanen, J. (2003), Fast direct solution of the Helmholtz equation with a perfectly matched layer or an absorbing boundary condition. International Journal for Numerical Methods in Engineering, 57: 2007–2025. doi: 10.1002/nme.752

Author Information

  1. Department of Mathematical Information Technology, University of Jyväskylä, P.O. Box 35 (Agora), FIN-40014 University of Jyväskylä, Finland

*Department of Mathematical Information Technology, University of Jyväskylä, P.O. Box 35 (Agora), FIN-40014 University of Jyväskylä, Finland

Publication History

  1. Issue published online: 12 JUN 2003
  2. Article first published online: 12 JUN 2003
  3. Manuscript Accepted: 18 NOV 2002
  4. Manuscript Revised: 7 NOV 2002
  5. Manuscript Received: 13 FEB 2002

Funded by

  • The Academy of Finland. Grant Numbers: #43066, #49006, #53588, #66407

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Keywords:

  • Helmholtz equation;
  • perfectly matched layer;
  • absorbing boundary conditions;
  • finite-element discretization;
  • fast direct solver

Abstract

We consider the efficient numerical solution of the Helmholtz equation in a rectangular domain with a perfectly matched layer (PML) or an absorbing boundary condition (ABC). Standard bilinear (trilinear) finite-element discretization on an orthogonal mesh leads to a separable system of linear equations for which we describe a cyclic reduction-type fast direct solver. We present numerical studies to estimate the reflection of waves caused by an absorbing boundary and a PML, and we optimize certain parameters of the layer to minimize the reflection. Copyright © 2003 John Wiley & Sons, Ltd.

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