Derivation of Green's function using addition theorem

Abstract

Following the success of null-field integral equation to solve the BVP of the Laplace equation, this paper employs the addition theorem and superposition technique to revisit the Green’s function of Laplace problems with circular boundaries. The Green’s function is decomposed into two parts, one is the fundamental solution and the other is an infinite plane of circular boundaries subject to the specified boundary conditions derived from the addition theorem. After superimposing the two solutions, the governing equation and boundary condition are both satisfied. Some examples are demonstrated to see the validity of the present method.