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Journal of Software:2013.24(2):391-404

非结构网格的并行多重网格解算器
李宗哲,王正华,姚路,曹维
(国防科学技术大学 计算机学院 软件研究所,湖南 长沙 410073)
Parallel Multigrid Solver for Unstructured Grid
LI Zong-Zhe,WANG Zheng-Hua,YAO Lu,CAO Wei
(Institute of Software, College of Computer, National University of Defense Technology, Changsha 410073, China)
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Received:February 23, 2011    Revised:April 20, 2012
> 中文摘要: 多重网格方法作为非结构网格的高效解算器,其串行与并行实现在时空上都具有优良特性.以控制方程离散过程为切入点,说明非结构网格在并行数值模拟的流程,指出多重网格方法主要用于求解时间推进格式产生的大规模代数系统方程,简述了算法实现的基本结构,分析了其高效性原理;其次,综述性地概括了几何多重网格与代数多种网格研究动态,并对其并行化的热点问题进行重点论述.同时,针对非结构网格的实际应用,总结了多重网格解算器采用的光滑算子;随后列举了非结构网格应用的部分开源项目软件,并简要说明了其应用功能;最后,指出并行多重网格解算器在非结构网格应用中的若干关键问题和未来的研究方向.
Abstract:As an unstructured-grid high efficient solver, the multigrid algorithm, with its serial and parallel application, can achieve the optimal properties of being on time and having space complexity. To illustrate the numerical simulation process of an unstructured grid, this paper begins with the discretization of governing equations and points out that the multigrid algorithm is mainly used for solving large scale algebraic equation, which is derived from the time marching scheme. For the multigrid algorithm, the study briefly describes its basic structure and efficient principle. Secondly, the paper reviews research that trend about the geometric multigrid and algebraic multigrid and discusses the basic design principles and hot topics on parallelization. At the same time, for the practical application of unstructured grid, the paper summarizes and classifies many smoothers, followed by examples of open source software about unstructured grid industrial application. Finally, some applications and key problems in this field are highlighted, as well as the future progress of parallel multigrid solver on unstructured grid.
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基金项目:国家重点基础研究发展计划(973)(2009CB723803) 国家重点基础研究发展计划(973)(2009CB723803)
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李宗哲,王正华,姚路,曹维.非结构网格的并行多重网格解算器.软件学报,2013,24(2):391-404

LI Zong-Zhe,WANG Zheng-Hua,YAO Lu,CAO Wei.Parallel Multigrid Solver for Unstructured Grid.Journal of Software,2013,24(2):391-404