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The fictitious domain method

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Abstract

An improved bound is derived on the rate of convergence of the standard difference scheme for solving the Dirichlet problem for the Helmholtz equation in domains of arbitrary shape. The scheme is based on the fictitious domain method. An application of the fictitious domain method and the grid method for solving one nonlinear boundary-value problem is considered. A rate of convergence bound is obtained for the proposed method.

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Literature cited

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Translated from Vychislitel'naya i Prikladnaya Matematika, No. 59, pp. 10–15, 1986

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Voitsekhovskii, S.A. The fictitious domain method. J Math Sci 60, 1437–1441 (1992). https://doi.org/10.1007/BF01095736

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Keywords

  • Standard Difference
  • Difference Scheme
  • Dirichlet Problem
  • Helmholtz Equation
  • Arbitrary Shape