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Novel meshless method for solving the potential problems with arbitrary domain. (English) Zbl 1073.65139
Summary: 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 the exact solution, the conventional method of fundamental solutions and the boundary element method for the Dirichlet, Neumann and mix-type boundary conditions of interior and exterior problems with simple and complicated boundaries. Good agreements with exact solutions are observed.

65N38 Boundary element methods for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
Full Text: DOI
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