Transactions of the Japan Society for Industrial and Applied Mathematics
Online ISSN : 2424-0982
ISSN-L : 0917-2246
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Volume 31, Issue 1
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Theory
  • Method of Fundamental Solutions for Doubly-Periodic Potential Problems
    Hidenori Ogata
    2021 Volume 31 Issue 1 Pages 1-19
    Published: 2021
    Released on J-STAGE: March 25, 2021
    DOIhttps://doi.org/10.11540/jsiamt.31.1_1
    JOURNAL FREE ACCESS
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    Abstract. We propose a method of fundamental solutions for two-dimensional potential problems, especially potential flow problems, with double periodicity. It is difficult to approximate the solution of these problems by the conventional method because the solution involves a periodic function. In our method, the solution is approximated by a linear combination of the periodic potentials, which is constructed using the Weierstrass elliptic functions. Our method inherits the advantanges of the conventional method, and, furthermore, it has the periodicity of the exact solution. Numerical examples show the effectiveness of our method.

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