Infinite domain potential problems by a new formulation of singular boundary method

Abstract

This study proposes a new formulation of singular boundary method (SBM) and documents the first attempt to apply this new method to infinite domain potential problems. The essential issue in the SBM-based methods is to evaluate the origin intensity factor. This paper derives a new regularization technique to evaluate the origin intensity factor on the Neumann boundary condition without the need of sample solution and nodes as in the traditional SBM. We also modify the inverse interpolation technique in the traditional SBM to get rid of the perplexing sample nodes in the calculation of the origin intensity factor on the Dirichlet boundary condition. It is noted that this new SBM retains all merits of the traditional SBM being truly meshless, free of integration, mathematically simple, and easy-to-program without the requirement of a fictitious boundary as in the method of fundamental solutions (MFS). We examine the new SBM by the four benchmark infinite domain problems to verify its applicability, stability, and accuracy.