An accelerated domain decomposition procedure based on robin transmission conditions
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A domain decomposition procedure based on Robin transmission conditions applicable to elliptic boundary problems was first introduced by P. L. Lions and later discussed by a number of authors. In all of these discussions, the weighting of the flux and the trace of the solution were independent of the iterative step number. For some model problems we introduce a cycle of weights and prove that an acceleration of the convergence rate similar to that occurring for alternating-direction iteration using a cycle of pseudo-time steps results. In some discrete cases, the cycle length can be taken to be independent of the mesh spacing.
AMS subject classification65N55
Key wordsDomain decomposition elliptic boundary problem Robin transmission condition acceleration of convergence
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