Jeng-Tzong Chen1,2, Jia-Nan Ke1, Huan-Zhen Liao1
CMC-Computers, Materials & Continua, Vol.9, No.2, pp. 93-110, 2009, DOI: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… More >
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