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Construction of Green's function using null-field integral approach for Laplace problems with circular boundaries

Jeng-Tzong Chen1,2, Jia-Nan Ke1, Huan-Zhen Liao1
Department of Harbor and River Engineering, National Taiwan Ocean University, Keelung, Taiwan
Department of Mechanical and Mechatronic Engineering, National Taiwan Ocean University, Keelung, Taiwan. Email: jtchen@mail.ntou.edu.tw

Computers, Materials & Continua 2009, 9(2), 93-110. https://doi.org/10.3970/cmc.2009.009.093

Abstract

A null-field approach is employed to derive the Green's function for boundary value problems stated for the Laplace equation with circular boundaries. The kernel function and boundary density are expanded by using the degenerate kernel and Fourier series, respectively. Series-form Green's function for interior and exterior problems of circular boundary are derived and plotted in a good agreement with the closed-form solution. The Poisson integral formula is extended to an annular case from a circle. Not only an eccentric ring but also a half-plane problem with an aperture are demonstrated to see the validity of the present approach. Besides, a half-plane problem with a circular hole subject to Dirichlet and Robin boundary conditions and a half-plane problem with a circular hole and a semi-circular inclusion are solved. Good agreement is made after comparing with the Melnikov's results.

Keywords

degenerate kernel, Fourier series, Green's function, null-field approach and Poisson integral formula.

Cite This Article

J. . Chen, J. . Ke and H. . Liao, "Construction of green's function using null-field integral approach for laplace problems with circular boundaries," Computers, Materials & Continua, vol. 9, no.2, pp. 93–110, 2009.



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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