Null-field equation approach as a tool for computing Green's function for Laplace operator with circular holes and/or inclusions

Abstract

Null-field equation approach is employed to derive the Green's function for boundary value problems stated for Laplace equations with circular holes and/or inclusions. 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 eccentric ring but also a half plane problem with an aperture and inclusions are demonstrated to see the validity of the present approach. Good agreement is made after comparing with the Melnikov's results.