Novel meshless method for solving the potential problems with arbitrary domain

In this article, a non-singular and boundary-type meshless method in two dimensions is developed to solve the potential problems. The solution is represented by a distribution of the kernel functions of double layer potentials. By using the desingularization technique to regularize the singularity a...

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Bibliographic Details
Published in:Journal of computational physics 2005-10, Vol.209 (1), p.290-321
Main Authors: Young, D.L., Chen, K.H., Lee, C.W.
Format: Article
Language:English
Subjects:
Boundaries
Circulants
Computational techniques
Conventional MFS
Desingularization technique
Dirichlet problem
Double layer potential
Exact sciences and technology
Exact solutions
Finite element method
Hypersingularity
Kernel function
Mathematical analysis
Mathematical methods in physics
Mathematical models
Matrices
Meshless method
Meshless methods
Mixed-type BC
Non-singular
Physics
Singular fundamental solution
Singularity
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Description
Summary:In this article, a non-singular and boundary-type meshless method in two dimensions is developed to solve the potential problems. The solution is represented by a distribution of the kernel functions of double layer potentials. By using the desingularization technique to regularize the singularity and hypersingularity of the kernel functions, the source points can be located on the real boundary and therefore the diagonal terms of influence matrices are determined. The main difficulty of the coincidence of the source and collocation points then disappears. By employing the two-point function, the off-diagonal coefficients of influence matrices are easily obtained. The numerical evidences of the proposed meshless method demonstrate the accuracy of the solutions after comparing with the results of exact solution, conventional MFS and BEM for the Dirichlet, Neumann and mix-type boundary conditions (BCs) of interior and exterior problems with simple and complicated boundaries. Good agreements with exact solutions are observed.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2005.03.007