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On a Fourier Method of Embedding Domains Using an Optimal Distributed Control

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Abstract

We propose a domain embedding method to solve second order elliptic problems in arbitrary two-dimensional domains. This method can be easily extended to three-dimensional problems. The method is based on formulating the problem as an optimal distributed control problem inside a rectangle in which the arbitrary domain is embedded. A periodic solution of the equation under consideration is constructed easily by making use of Fourier series. Numerical results obtained for Dirichlet problems are presented. The numerical tests show a high accuracy of the proposed algorithm and the computed solutions are in very good agreement with the exact solutions.

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Authors and Affiliations

  1. Institute of Mathematics, Romanian Academy of Sciences, P.O. Box 1-764, RO-70700, Bucharest, Romania

    Lori Badea

  2. Department of Mathematics, Texas A&M University, College Station, TX-, 77843, USA

    Prabir Daripa

Authors
  1. Lori Badea
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  2. Prabir Daripa
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Badea, L., Daripa, P. On a Fourier Method of Embedding Domains Using an Optimal Distributed Control. Numerical Algorithms 32, 261–273 (2003). https://doi.org/10.1023/A:1024002802603

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