A Discontinuous Coarse Space (DCS) Algorithm for Cell Centered Finite Volume Based Domain Decomposition Methods: The DCS-RJMin Algorithm
In this paper, we introduce a new coarse space algorithm, the “Discontinuous Coarse Space Robin Jump Minimizer” (DCS-RJMin), to be used in conjunction with one-level domain decomposition methods (DDMs). This new algorithm makes use of Discontinuous Coarse Spaces (DCS), and is designed for DDM that naturally produce discontinuous iterates such as Optimized Schwarzs Methods (OSM). This algorithm is suitable both at the continuous level and for cell-centered finite volume discretizations. At the continuous level, we prove, under some conditions on the parameters of the algorithm, that the difference between two consecutive iterates goes to 0. We also provide numerical results illustrating the convergence behavior of the DCS-RJMin algorithm.
This study has been carried out with financial support from the French State, managed by the French National Research Agency (ANR) in the frame of the “Investments for the future” Programme IdEx Bordeaux—CPU (ANR-10-IDEX-03-02).
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