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  • Open Access

    ABSTRACT

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

    Chein-Shan Liu1

    The International Conference on Computational & Experimental Engineering and Sciences, Vol.3, No.2, pp. 57-68, 2007, DOI:10.3970/icces.2007.003.057

    Abstract A new method is developed to solve the interior and exterior Dirichlet problems for the two-dimensional Laplace equation, namely the meshless regularized integral equation method (MRIEM), 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 very complex boundary shape and with boundary noise. More >

  • Open Access

    ARTICLE

    A MRIEM for Solving the Laplace Equation in the Doubly-Connected Domain

    Chein-Shan Liu1

    CMES-Computer Modeling in Engineering & Sciences, Vol.19, No.2, pp. 145-162, 2007, DOI:10.3970/cmes.2007.019.145

    Abstract A new method is developed to solve the Dirichlet problems for the two-dimensional Laplace equation in the doubly-connected domains, namely the meshless regularized integral equations method (MRIEM), which consists of three portions: Fourier series expansion, the Fredholm integral equations, and linear equations to determine the unknown boundary conditions onartificial circles. The boundary integral equations on artificial circles are singular-free and the kernels are degenerate. When boundary-type methods are inefficient to treat the problems with complicated domains, the new method can be applicable for such problems. The new method by using the Fourier series and the Fourier coefficients More >

  • Open Access

    ARTICLE

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

    Chein-Shan Liu 1

    CMES-Computer Modeling in Engineering & Sciences, Vol.19, No.1, pp. 99-110, 2007, DOI: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. More >

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