Author(s)

A. Tadeu, L. Godinho & C. S. Chen

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. Keywords: Kansa’s method, MFS, BEM, performance, wave equation. 1 Introduction The scattering and diffraction of waves by inclusions is a research area used in many fields of engineering, including seismology and non-destructive testing techniques. Analytical solutions are only known for very simple problems such as those involving circular cylindrical inclusions. Thus, over the years, different numerical schemes have been proposed to study the propagation of waves in acoustic and elastic media in unbounded, semi-finite and confined media.

Keywords

Kansa’s method, MFS, BEM, performance, wave equation