A modified version of regularized meshless method for three dimensional potential problem

In this study, three-dimensional potential problem is solved using a novel meshless method. Due to the singularity of the kernel functions, the diagonal terms of the influence matrices in the method of fundamental solutions (MFS) are unobtainable. A proposed approach in the literature of the past decade, namely regularized meshless method (RMM), is proposed to overcome such difficulties by using the proposed desingularization (subtracting and adding-back) technique. The main difficulty for the coincidence of the source and collocation points then disappears. However, the disadvantage of RMM is the order of precision of obtained solution is lower than other numerical methods. In this study, we present a novel technique to promote the order of precision of diagonal term; therefore, we can obtain a more precise solution. Finally, we introduce a typical 3-D numerical example to illustrate the technique. The numerical result is compared with those obtained by the RMM; and a more precise result is obtained.