数值计算与计算机应用
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数值计算与计算机应用  2012, Vol. Issue (1): 48-58    DOI:
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一种求解 H(curl)型椭圆问题的高效并行预条件子及并行实现
冯春生, 王俊仙, 舒适
湘潭大学数学与计算科学学院, 科学工程计算与数值仿真湖南省重点实验室, 湖南湘潭 411105
AN EFFICIENT PARALLEL PRECONDITIONER FOR SOLVING H(curl) ELLIPTIC PROBLEM AND PARALLEL IMPLEMENTATION
Feng Chunsheng, Wang Junxian, Shu Shi
School of Mathematics and Computational Science, Xiangtan University,Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan 411105, Hunan, China
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摘要 本文为一类 H(curl) 型椭圆问题的线性棱有限元方程,构造了一种基于节点辅助空间预条件子 (HX 预条件子)和基于简单粗空间的非重叠区域分解相结合的预条件子,并为该预条件子设计了并行算法, 编制了基于 MPI+OpenMP二级并行架构的并行程序. 数值实验结果表明基于该预条件子的并行 PCG法具有良好的算法可扩展能力和并行可扩展能力.
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关键词H(curl) 型椭圆问题   非重叠 DDM   HX 预条件子   并行可扩展能力   算法可扩展能力   MPI+OpenMP     
Abstract: In this paper, we construct a new parallel preconditioner, combining auxiliary space preconditioner(HX preconditioner) with nonoverlapping domain decomposition method, for solving the linear edge finite element discretization of H(curl) elliptic problem. We design the parallel algorithm in detail and make the parallel program based on MPI+OpenMP. Numerical experiment show that the corresponding PCG method has good algorithm scalability and parallel scalability.
Key wordsH(curl) elliptic problem   nonoverlapping DDM   HX preconditioner   algorithm scalability   parallel scalability   MPI+OpenMP   
收稿日期: 2011-09-20;
基金资助:

国家自然科学基金项目(11031006, 91130002, 11171281); 湖南省科学技术厅科技计划重点项目(2011FJ2011); 湖南省教育厅资助科研项目(10C1265, 11C1219); 湘潭大学校级项目(10XZX03)资助.

引用本文:   
. 一种求解 H(curl)型椭圆问题的高效并行预条件子及并行实现[J]. 数值计算与计算机应用, 2012, (1): 48-58.
. AN EFFICIENT PARALLEL PRECONDITIONER FOR SOLVING H(curl) ELLIPTIC PROBLEM AND PARALLEL IMPLEMENTATION[J]. Journal of Numerical Methods and Computer Applicat, 2012, (1): 48-58.
 
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[1] 王俊仙, 胡齐芽, 舒适. 一种求解 H(curl) 型椭圆问题的非重叠 DDM 预条件子[J]. 数值计算与计算机应用, 2010, 32(4): 373-384.
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