Single layer regularized meshless method for three dimensional exterior acoustic problem

The Regularized Meshless Method (RMM) is a meshless boundary method. Its source points and physical points are overlapped. The substraction and adding-back technique is utilized to avoid the singularity of the fundamental solution. It is simple and easy to be programmed. But the double layer potential should be adopted in the desingularity technique. Here the single layer potential is employed to circumvent the singularity. The substraction and adding-back technique is succeeded, but the careful selection of particular solution for the null-fields boundary integral equation is chosen to derive the diagonal elements for the Laplace Dirichlet problem. By this particular solution, the diagonal elements can be represented by the single layer potential. Here it is extended to the exterior Helmholtz problem by relationships between Laplace and Helmholtz singularities. The fictitious frequencies are avoided by the Burton-Miller type formula and Dual Surface technique. The accuracy of these methods are shown by three typical examples.