Solution of exterior problem using ellipsoidal artificial boundary

  • Authors:

  • Hongying Huang;Dongjie Liu;Dehao Yu

  • Affiliations:

  • School of Mathematics, Physics and Information Science, Zhejiang Ocean University, Zhoushan, Zhejiang, 316004, China;Department of Mathematics, College of Sciences, Shanghai University, Shanghai, 200444, China;LSEC, ICMSEC, Academy of Mathematics and System Sciences, The Chinese Academy of Sciences, Beijing, 100190, China

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2009

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Abstract

In this paper, we present a general ellipsoidal artificial boundary method for three-dimensional exterior problem. The exact artificial boundary condition, which is expressed explicitly by the series concerning the ellipsoidal harmonic functions, is derived and then an equivalent problem in a bounded domain is presented. The error estimates show that the convergence rate depends on the mesh parameter, the number of terms used in the exact artificial boundary condition, and the location of the artificial boundary.