Performance Of The BEM, MFS,
And RBF Collocation Method In
A 2.5D Wave Propagation Analysis
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
Related Book
Other papers in this volume
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