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A Meshless Regularized Integral Equation Method for Laplace Equation in Arbitrary Interior or Exterior Plane Domains

Chein-Shan Liu 1
Department of Mechanical and Mechatronic Engineering, Taiwan Ocean University, Keelung, Taiwan. E-mail: csliu@mail.ntou.edu.tw

Computer Modeling in Engineering & Sciences 2007, 19(1), 99-110. https://doi.org/10.3970/cmes.2007.019.099

Abstract

A new meshless regularized integral equation method (MRIEM) is developed to solve the interior and exterior Dirichlet problems for the two-dimensional Laplace equation, which consists of three parts: Fourier series expansion, the second kind Fredholm integral equation and an analytically regularized solution of the unknown boundary condition on an artificial circle. We find that the new method is powerful even for the problem with complex boundary shape and with random noise disturbing the boundary data.

Keywords

Laplace equation, Meshless method, Regularized integral equation, Artificial circle

Cite This Article

Liu, C. (2007). A Meshless Regularized Integral Equation Method for Laplace Equation in Arbitrary Interior or Exterior Plane Domains. CMES-Computer Modeling in Engineering & Sciences, 19(1), 99–110.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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