A Meshless Regularized Integral Equation Method for Laplace Equation in Arbitrary Interior or Exterior Plane Domains
Chein-Shan Liu

Source CMES: Computer Modeling in Engineering & Sciences, Vol. 19, No. 1, pp. 99-110, 2007
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Keywords Laplace equation, Meshless method, Regularized integral equation, Artificial circle
Abstract A new {\it 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 {\it 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.
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