Regularized formulation of potential field gradients in singular boundary method

The main difficulty of the singular boundary method (SBM) is the calculation of the origin intensity factors introduced to remove the singularity of fundamental solution. This work presents an extension of the previous SBM formation. The new contribution of the present method is that the origin intensity factors for potential field gradients are derived, so that the boundary derivatives of the potential at any direction, not limited to the normal derivative, can now be calculated. The accuracy and efficiency of the present method are verified through several numerical examples. All the numerical results demonstrate that the method performs well in comparisons with the exact solution, the method of fundamental solutions (MFS) and boundary element method (BEM).