Numerical Investigation on Convergence Rate of Singular Boundary Method

The singular boundary method (SBM) is a recent boundary-type collocation scheme with the merits of being free of mesh and integration, mathematically simple, and easy-to-program. Its essential technique is to introduce the concept of the source intensity factors to eliminate the singularities of fundamental solutions upon the coincidence of source and collocation points in a strong-form formulation. In recent years, several numerical and semianalytical techniques have been proposed to determine source intensity factors. With the help of these latest techniques, this short communication makes an extensive investigation on numerical efficiency and convergence rates of the SBM to an extensive variety of benchmark problems in comparison with the BEM. We find that in most cases the SBM and BEM have similar convergence rates, while the SBM has slightly better accuracy than the direct BEM. And the condition number of SBM is lower than BEM. Without mesh and numerical integration, the SBM is computationally more efficient than the BEM.