The Application of Hypersingular Meshless Method for 3D Potential and Exterior Acoustic Problems
Date Issued
2007
Date
2007
Author(s)
Liu, Tzu-Yumg
DOI
en-US
Abstract
In this thesis, a hypersingular meshless method is developed to solve the potential and exterior acoustic problems in three dimensions for arbitrary shapes. The solutions are represented by a distribution of double layer potentials instead of the single layer potentials as generally used in the conventional method of fundamental solutions. By using the desingularization technique to regularize the singularity and hypersingularity of double layer potentials, the source points can be located on the real boundary to avoid the sensitivity of locating fictitious boundary as used by the conventional method of fundamental solutions, and therefore the diagonal terms of influence matrices are determined. The main difficulty of the coincidence of the source and collocation points thus can be overcome. The numerical evidences of the proposed meshless method demonstrate the accuracy of the solutions after comparing with the results of analytical solution, the method of fundamental solutions, finite element method, boundary element method and local differential quadrature method for the Dirichlet, Neumann and mix-type boundary conditions problems with simple and complicated boundaries. The numerical results have demonstrated the validity and accuracy in solving a number of testing cases for potential and exterior acoustic problems after comparing with analytical solution and other numerical methods.
Subjects
含超強奇異性無網格法
基本解法
雙層勢能核函數
徑向基底函數
去除奇異性技術
聲學散射
三維
hypersingular meshless method
method of fundamental solutions
double layer potential
radial basis function
desingularized technique
acoustic scattering
3D
Type
thesis