求解Maxwell线性棱元鞍点系统的并行Uzawa算法  

A Parallel Uzawa Algorithm for Solving the Maxwell Saddle-Point System of Linear Edge Elements

作　　者：王俊仙[1] 舒适[1] 冯春生[1] 

机构地区：[1]湘潭大学数学与计算科学学院,湖南湘潭411105

出　　处：《计算机工程与科学》2009年第11期110-112,131,共4页Computer Engineering & Science

基　　金：国家自然科学基金资助项目(10771178);高性能科学计算研究资助项目(2005CB321702);湘潭大学一般项目(08XZX04)

摘　　要：本文针对一类Maxwell方程组鞍点问题的第一类N啨d啨lec线性棱元离散系统,设计了一种基于节点辅助空间预条件子的并行Uzawa算法(HX-Uzawa-p)。数值实验结果表明,不论是对光滑系数还是对有无浮动子区域及有无内交叉点的跳系数情形,我们所设计的并行算法HX-Uzawa-p的迭代次数都基本不依赖于网格规模及系数跳幅,且具有很好的并行可扩展性。In this paper, we design a preconditioned parallel Uzawa algorithm （HX-Uzawa-p） for solving the saddlepoint system generated by the lowest order edge element discretization of the Maxwell equations. In the Uzawa algorithm, we use the HX preconditioner for the primal variable. The numerical results indicate that the new algorithm has good parallelization scalability and the iteration counts are independent of the mesh size and the jump range as for the floating subdomains and interior cross-points.

关 键 词：Maxwell鞍点系统 辅助空间预条件子 UZAWA算法 跳系数 并行可扩展性 

分 类 号：O241.82[理学—计算数学] O246[理学—数学]