Boundary integral equations with the generalized Neumann kernel for Laplace’s equation in multiply connected regions

This paper presents a new boundary integral method for the solution of Laplace’s equation on both bounded and unbounded multiply connected regions, with either the Dirichlet boundary condition or the Neumann boundary condition. The method is based on two uniquely solvable Fredholm integral equations of the second kind with the generalized Neumann kernel. Numerical results are presented to illustrate the efficiency of the proposed method.