一种用于基于单元中心有限体积方法的域分解方法的不连续粗空间（DCS）算法：DCS-RJMin算法
A Discontinuous Coarse Spaces (DCS) Algorithm for Cell Centered Finite Volumes based Domain Decomposition Methods: the DCS-RJMin algorithm
AI总结：
本文提出DCS-RJMin算法，用于单层域分解方法，通过不连续粗空间提升收敛性，适用于连续层和单元中心有限体积离散化，并证明迭代差收敛至零。
摘要：
本文介绍了一种新的粗空间算法，称为“不连续粗空间Robin跳跃最小化”（DCS-RJMin），用于与单层域分解方法（DDM）结合使用。该算法利用不连续粗空间（DCS），适用于自然产生不连续迭代的DDM，如优化Schwarz方法（OSM）。该算法适用于连续层和单元中心有限体积离散化。在连续层上，我们证明，在某些算法参数条件下，连续迭代之间的差异趋于0。我们还提供了数值结果，以说明DCS-RJMin算法的收敛行为。
英文摘要：
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 (DDM). This new algorithm makes use of Discontinuous Coarse Spaces(DCS), and is designed for DDM that naturally produce discontinuous iterates such as Optimized Schwarz 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.
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