Open Access

ARTICLE

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

Chein-Shan Liu¹

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(2), 145-162. https://doi.org/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 can be adopted easily to derive the meshless numerical method. Several numerical examples are tested showing that the new method is powerful.

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Keywords

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