Method of Fundamental Solutions for Doubly-Periodic Potential Problems

Abstract

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.