| 外推瀑布式多网格法的OpenMP并行化 |
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| 引用本文： | 潘克家,胡宏伶,陈传淼,汤井田.外推瀑布式多网格法的OpenMP并行化[J].计算数学,2012,34(4):425-436. |
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| 作者姓名： | 潘克家 胡宏伶 陈传淼 汤井田 |
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| 作者单位： | 1. 中南大学有色金属成矿预测教育部重点实验室, 地球科学与信息物理学院, 长沙 410083;
2. 中南大学数学与统计学院, 长沙 410075;
3. 高性能计算与随机信息处理省部共建教育部重点实验室, 长沙 410081;
4. 湖南师范大学数学与计算机科学 学院, 长沙 410081 |
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| 基金项目： | 国家自然科学基金(41204082, 11071067)、中央高校基本科研业务费专项资金(2011QNZT102)、中国博士后科学基金(2011M501295)和中南大学博士后科学基金资助项目、湖南省教育厅资助科研项目(11C0831) |
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| 摘 要： | 基于外推瀑布式多网格法(EXCMG)程序的性能分析, 采用共享存储编程标准OpenMP对EXCMG法的Fortran程序进行了并行处理,极大地提高了原串行程序的计算效率.在双核PC机和机群的一个八核SMP节点上分别进行了数值试验.结果表明: 在不改变串行程序结构的前提下, 仅对EXCMG程序中最耗时的三个子程序并行处理, 双核下并行效率可高达90%;八核下两分钟内可求解上亿个未知数的椭圆边值问题, 精度达到10-10.
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| 关 键 词： | 外推瀑布式多网格法 OpenMP 并行编程 共轭梯度法 加速比 |
| 收稿时间： | 2012-01-12; |
PARALLELIZATION OF EXTRAPOLATION CASCADIC MULTIGRID METHOD USING OPENMP |
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| Pan Kejia,Hu Hongling,Chen Chuanmiao,Tang Jingtian.PARALLELIZATION OF EXTRAPOLATION CASCADIC MULTIGRID METHOD USING OPENMP[J].Mathematica Numerica Sinica,2012,34(4):425-436. |
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| Authors: | Pan Kejia Hu Hongling Chen Chuanmiao Tang Jingtian |
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| Institution: | Pan Kejia (Key Laboratory of Metallogenic Prediction of Nonferrous Metals,Ministry of Education,School of Geosciences and Info-Physics,Central South University,Changsha 410083,China; School of Mathematics and Statistics,Central South University,Changsha 410075,China; Key Laboratory of High Performance Computing and Stochastic Information Processing,Ministry of Education,Changsha 410081,China) Hu Hongling Chen Chuanmiao (College of Mathematica and Computer Science,Hunan Normal University,Changsha 410081,China; Key Laboratory of High Performance Computing and Stochastic Information Processing,Ministry of Education,Changsha 410081,China) Tang Jingtian (Key Laboratory of Metallogenic Prediction of Nonferrous Metals,Ministry of Education,School of Geosciences and Info-Physics,Central South University,Changsha 410083,China) |
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| Abstract: | Based on the performance analysis of Extrapolation Cascadic Multigrid (EXCMG) method, the Fortran program of EXCMG algorithm is parallelized with OpenMP shared memory programming interface, which greatly improves the computational efficiency of the original sequential program. Numerical experiments are carried out on a dual-core personal computer and a SMP node with eight-core of a cluster, respectively. The results show that: if the sequential program’s structure remains unchanged and only the three most time consuming subroutines are parallelized, the parallel efficiency in 2 cores will up to 90%, and in 8 cores elliptic boundary value problems discretized with hundreds of millions of unknowns can be solved in two minutes with accuracy less than 10?10. |
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| Keywords: | Extrapolation Cascadic Multigrid Method OpenMP Parallel Programming Conjugate Gradient Methods Speedup |
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