Dipoles formulation for the method of fundamental solutions applied to potential problems

Abstract

This paper generalizes and extends the traditional source formulation within the method of fundamental solutions (MFS) to use dipoles (or even series of multi-poles). In this paper, two-dimensional potential problems are considered. The present formulation is formulated by taking the limiting case of two adjacent sources. The necessary kernels are derived in explicit forms. Some numerical examples, covering different cases of boundary conditions and geometry, are solved. Several parametric studies are presented to demonstrate different configurations for placement of sources (monopoles or dipoles). The accuracy of the presented new formulation is verified by comparing its results to those obtained from other numerical and analytical methods. The main advantage of the present formulation lies in decreasing the oscillation in the sources intensity and reducing the number of sources required which is useful especially in concave and narrow geometries.