Regularized meshless method for multiply-connected-domain Laplace problems

In this paper, the regularized meshless method (RMM) is developed to solve two-dimensional Laplace problem with multiply-connected domain. The solution is represented by using the double-layer potential. The source points can be located on the physical boundary by using the proposed technique to regularize the singularity and hypersingularity of the kernel functions. The troublesome singularity in the traditional methods is avoided and the diagonal terms of influence matrices are easily determined. The accuracy and stability of the RMM are verified in numerical experiments of the Dirichlet, Neumann, and mixed-type problems under a domain having multiple holes. The method is found to perform pretty well in comparison with the boundary element method.