一种类似不连续伽辽金的粗空间校正方法用于具有连续局部空间的域分解方法：DCS-DGLC算法
A Discontinuous Galerkin like Coarse Space correction for Domain Decomposition Methods with continuous local spaces : the DCS-DGLC Algorithm
AI总结：
本文提出DCS-DGLC算法，通过不连续伽辽金形式计算不连续粗空间校正，以补偿OSM在邻域子域间引入的不连续性，适用于单层DDM。
摘要：
本文研究了一种新的粗空间校正算法DCS-DGLC，用于优化Schwarz方法。主要思想是使用类似不连续伽辽金的公式计算不连续粗空间校正。尽管局部空间保持连续，粗空间应不连续以补偿OSM在邻域子域间引入的不连续性。该算法不仅能用于OSM，还能用于任何产生不连续迭代的单层DDM。尽管计算粗校正时借鉴了不连续伽辽金的思想，但DCS-DGLC算法的最终目标是并行计算经典非不连续有限元问题的离散解。
英文摘要：
In this paper, we are interested in scalable Domain Decomposition Methods (DDM). To this end, we introduce and study a new Coarse Space Correction algorithm for Optimized Schwarz Methods(OSM) : the DCS-DGLC algorithm. The main idea is to use a Discontinuous Galerkin like formulation to compute a discontinuous coarse space correction. While the local spaces remain continuous, the coarse space should be discontinuous to compensate the discontinuities introduced by the OSM at the interface between neighboring subdomains. The discontinuous coarse correction algorithm can not only be used with OSM but also be used with any one-level DDM that produce discontinuous iterates. While ideas from Discontinuous Galerkin(DG) are used in the computation of the coarse correction, the final aim of the DCS-DGLC algorithm is to compute in parallel the discrete solution to the classical non-DG finite element problem.
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