A two-level additive Schwarz preconditioning algorithm for the weak Galerkin method for the second-order elliptic equation
A two-level additive Schwarz preconditioning algorithm for the weak Galerkin method for the second-order elliptic equation
复制标题
二阶椭圆方程弱伽辽金法的两级加性Schwarz预处理算法
DOI：
10.1155/2016/2685659
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发表时间：
2016
影响因子：
--
通讯作者：
Feng Wang
中科院分区：
文献类型：
--
作者：
Fangfang Qin;Min Zha;Feng Wang
针对二阶椭圆方程的弱Galerkin逼近，提出了一种两级加性Schwarz预处理算法。该算法在粗网格上定义了一致的有限元空间，并提出了稳定的网格间传递算子来实现粗网格与细网格空间间的信息交换。在Schwarz方法的框架下，证明了预条件系统的条件数仅取决于粗网格大小和重叠大小的比率。通过数值实验验证了理论结果。
This paper proposes a two-level additive Schwarz preconditioning algorithm for the weak Galerkin approximation of the second-order elliptic equation. In the algorithm, a conforming finite element space is defined on the coarse mesh, and a stable intergrid transfer operator is proposed to exchange the information between the spaces on the coarse mesh and the fine mesh. With the framework of the Schwarz method, it is proved that the condition number of the preconditioned system only depends on the rate of the coarse mesh size and the overlapping size. Some numerical experiments are carried out to verify the theoretical results.