Method of Fundamental Solutions for Doubly Periodic Potential Problems

In this paper, we propose a method of fundamental solution for two-dimensional doubly periodic problems, especially potential flow problems with a doubly periodic array of obstacles. In the proposed method, we approximate the solution, which involves doubly periodic functions, by a linear combination of the logarithmic potentials consisting of the theta functions. The method inherits the efficiency of the ordinary method of fundamental solutions and gives an approximate solution that has the same periodicity as the one of the exact solution. Numerical examples show the efficiency of the presented method.