Single layer regularized meshless method for three dimensional Laplace problem

The subtraction and adding-back technique for Regularized Meshless Method (RMM) has been proposed by Young et al. (2005) [8] on 2-D Laplace problem and extended to 3-D Laplace problem by Young et al. (2009) [13], where the kernel functions of double layer potentials were adopted to desingularize fundamental solution singularity while the source points are overlapped on the physical points. Here the Single Layer Regularized Meshless Method (SRMM) is proposed. The solutions are represented by single layer potential. The singularity of the fundamental solution is desingularized by the carefully chosen particular solution in the null-fields of the boundary integral equation using the subtraction and adding-back technique for the Dirichlet boundary condition. The double layer potential is adopted for the Neumann boundary condition. The numerical examples show that the convergence trend and accuracy of the SRMM are better than those of using other methods (RMM, IBDS) by one or two orders of magnitude.