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This paper develops a Dirichlet-Neumann (D-N) alternating algorithm to solve the mixed boundary value problem of Laplace equation in an infinite domain, and analyses the convergence of the algorithm. By choosing a circle surrounding the original boundary as an artificial boundary to divide the unbounded domain into two sub-domains, we can make use of the natural boundary reduction (NBR) method in the infinite subdomain to solve a Dirichlet boundary value problem while use the finite element method in the finite sub-domain to solve a mixed boundary value problem. We prove that the algorithm is convergent geometrically for any relaxation factor between 0 and 1. The numerical experiment results also display that the sequence of iterative solutions is geometrically convergent, the convergence rate is independent of the finite element mesh size h , and the maximum nodal error on 1  is roughly of 2 ( ) O h . Keywords-exterior Laplace problem; mixed boundary value conditions; D-N alternating algorithm; natural boundary reduction; Convergence analysis

A D-N Alternating Algorithm for Exterior Laplace Problem with Mixed Boundary Value Conditions