An operator-splitting approach to nonoverlapping domain decomposition methods

The Robin-Robin method is an iterative substructuring method to solve boundary-value problems (b.v.p.) on domains partitioned into nonoverlapping subdomains. It involves mixed-type boundary conditions on the interface, which depend on suitable weighting coefficients in order to maximize the convergence rate. In this paper we interpret this algorithm as an alternating direction iterative method to compute the solution of the Steklov-Poincaré equation associated to the given b.v.p. . This interpretation allows the characterization of new preconditioners for the interface problem and provides a strategy to compute optimal relaxation parameters. Some numerical examples are presented.


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