Abstract: Some new domain decomposition methods based on natural boundary reduction are suggested for overlapping and non-overlapping domains. A two-dimensional scalar wave equation is taken as a model to illustrate these methods. The governing equation is discretized in time, leading to time-stepping scheme, where an exterior elliptic problem has to be solved in each time step. The Dirichlet-Neumann method and Schwartz alternating method are proposed respectively. For the Schwartz alternating method, the convergence of the algorithm and the contraction factor for exterior circular domain are given. Finally, some numerical examples are devoted to illustrate these methods.

Key words: wave equation, natural boundary reduction, domain decomposition method (DDM), exterior problem