A Two-level Additive Schwarz Preconditioning Algorithm for the Weak Galerkin Method for the Second-order Elliptic Equation
首发时间:2015-12-21
Abstract:This paper study a two-level additive Schwarz preconditioning algorithmfor the weak Galerkin approximation of the second-order elliptic equation.In the algorithm, a $P_1$ conforming finite element space is defined on the coarse mesh,and an stable intergrid transfer operator is proposed to exchange the information between the problems on the coarse mesh and the fine mesh.With the framework of the Schwarz method, it is proved that the algorithm is quasi-optimal, that is, the condition number of the preconditioned system only logarithmically depends on the rate of the coarse and fine mesh size.Some numerical experiments are carried out to verify the theoretical results.
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求解弱Galerkin有限元离散二阶椭圆问题的一种两水平Schwarz预处理算法
摘要:本文研究了弱Galerkin有限元离散二阶椭圆问题的两水平加性Schwarz预处理算法. 该预处理方法, 在粗网格上采用$P_1$协调元方法求解, 粗细网格之间的信息通过一个特殊的具有稳定性和逼近性网格转移算子进行交换. 借助经典的Schwarz框架, 文章证明了预处理后系统的条件数仅对数依赖于粗网格和细网格的尺寸比, 因此算法是拟最优的. 文章最后给出了一些数值试验来验证算法的拟最优性.
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No.4670905110901814****
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求解弱Galerkin有限元离散二阶椭圆问题的一种两水平Schwarz预处理算法
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