The collocation points of the fundamental solution method for the potential problem

We propose an algorithm for computing harmonic functions in a two dimensional domain with prescribed Dirichlet data. Our algorithm is a variant of what is called a “Fundamental Solution Method” [1–3]. This method requires us to select 2N points in the two-dimensional plane, N of which are called collocation points and the remaining N are called charge points representing the position of the singularities of the fundamental solution. It is known that there exists a set of 2N points by which the error is exponentially small [1,3–6]. However, these papers are concerned mainly with existence, and, as far as the authors know, few fast and reliable algorithms are known for good position of the points. In this paper, we propose a new rule for the position of the points and examine its efficiency by numerical experiments. The new rule uses FFT effectively.