A pseudospectral Chebychev method for the 2D wave equation with domain stretching and absorbing boundary conditions

Rosemary Renaut, Jochen Fröhlich

Research output: Contribution to journalArticle

32 Scopus citations

Abstract

In this paper we develop a method for the simulation of wave propagation on artificially bounded domains. The acoustic wave equation is solved at all points away from the boundaries by a pseudospectral Chebychev method. Absorption at the boundaries is obtained by applying one-way wave equations at the boundaries, without the use of damping layers. The theoretical reflection coefficient for the method is compared to theoretical estimates of reflection coefficients for a Fourier model of the problem. These estimates are confirmed by numerical results. Modification of the method by a transformation of the grid to allow for better resolution at the center of the grid reduces the maximum eigenvalues of the differential operator. Consequently, for stability the maximum timestep is O(1/N) as compared to O(1/N2) for the standard Chebychev method. Therefore, the Chebychev method can be implemented with efficiency comparable to that of the Fourier method. Moreover, numerical results presented demonstrate the superior performance of the new method.

Original languageEnglish (US)
Pages (from-to)324-336
Number of pages13
JournalJournal of Computational Physics
Volume124
Issue number2
DOIs
StatePublished - Mar 15 1996

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

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