AbstractBy using the natural boundary reduction an overlapping domain decomposition method is designed to solve some exterior two‐dimensional time‐dependent parabolic problems. The governing equation is first discretized in time, leading to a sequence of boundary value problems with respect to time step in an unbounded domain. Then artificial boundaries are introduced. For each time level, an overlapping domain decomposition method, which is based on the natural boundary reduction, is constructed to solve the exterior elliptic boundary value problem on a two‐dimensional domain. It is shown that the algorithm is equivalent to Schwarz alternating method. The convergence of this algorithm is given. The contraction factor for the exterior circular domain is also discussed. In the end of this paper, some numerical examples are presented, which illustrate the feasibility and the effectiveness of the proposed methods in this paper. Copyright © 2004 John Wiley & Sons, Ltd.