Transparent boundary conditions for wave propagation on unbounded domains

  • Authors:

  • Dorin-Cezar Ionescu;Heiner Igel

  • Affiliations:

  • Queensland University Advanced Centre for Earthquake Studies, The University of Queensland, Brisbane, QLD, Australia;Department für Geo- und Umweltwissenschaften, Ludwig-Maximilians-Universität, München, Germany

  • Venue:
  • ICCS'03 Proceedings of the 2003 international conference on Computational science: PartIII
  • Year:
  • 2003

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Abstract

The numerical solution of the time dependent wave equation in an unbounded domain generally leads to a truncation of this domain, which requires the introduction of an artificial boundary with associated boundary conditions. Such nonreflecting conditions ensure the equivalence between the solution of the original problem in the unbounded region and the solution inside the artificial boundary. We consider the acoustic wave equation and derive exact transparent boundary conditions that are local in time and can be directly used in explicit methods. These conditions annihilate wave harmonics up to a given order on a spherical artificial boundary, and we show how to combine the derived boundary condition with a finite difference method. The analysis is complemented by a numerical example in two spatial dimensions that illustrates the usefulness and accuracy of transparent boundary conditions.