Performance Of The BEM, MFS,And RBF Collocation Method InA 2.5D Wave Propagation Analysis

Abstract

This paper compares the solutions provided by the boundary element method (BEM), the method of fundamental solutions (MFS) and the radial basis functions (RBF) collocation method (Kansa’s Method) for the 2.5D vector wave equation (elastic problem) in the frequency domain. The BEM requires only boundary meshing, but it involves the integration of singular functions, which is not trivial, particularly for high-dimensional problems. The MFS and Kansa’s methods require neither domain nor surface discretization, and no integration is required. In the case of the RBF collocation method, various globally supported radial basis functions are used, such as MQ ( 2 2 r c + ), 7 r and 9 r . Circular cylindrical domains are modeled to illustrate the efficiency of these three formulations, since analytical solutions are available.