A Practical Algorithm for Determining the Optimal Pseudo-Boundary in the Method of Fundamental Solutions

One of the main difficulties in the application of the method offundamental solutions (MFS) is the determination of the position ofthe pseudo-boundary on which are placed the singularities in termsof which the approximation is expressed. In this work, we propose asimple practical algorithm for determining an estimate of thepseudo-boundary which yields the most accurate MFS approximationwhen the method is applied to certain boundary value problems.Several numerical examples are provided.