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非对称稀疏线性方程组的快速外存解法及其在无网格法计算中的应用

苑维然 陈璞 刘凯欣

苑维然, 陈璞, 刘凯欣. 非对称稀疏线性方程组的快速外存解法及其在无网格法计算中的应用[J]. 应用数学和力学, 2006, 27(10): 1173-1181.
引用本文: 苑维然, 陈璞, 刘凯欣. 非对称稀疏线性方程组的快速外存解法及其在无网格法计算中的应用[J]. 应用数学和力学, 2006, 27(10): 1173-1181.
YUAN Wei-ran, CHEN Pu, LIU Kai-xin. High Performance Sparse Solver for Unsymmetrical Linear Equations With Out-of-Core Strategies and Its Application on Meshless Methods[J]. Applied Mathematics and Mechanics, 2006, 27(10): 1173-1181.
Citation: YUAN Wei-ran, CHEN Pu, LIU Kai-xin. High Performance Sparse Solver for Unsymmetrical Linear Equations With Out-of-Core Strategies and Its Application on Meshless Methods[J]. Applied Mathematics and Mechanics, 2006, 27(10): 1173-1181.

非对称稀疏线性方程组的快速外存解法及其在无网格法计算中的应用

基金项目: 国家自然科学基金资助项目(10232040;10572002;10572003)
详细信息
    作者简介:

    苑维然(1980- ),男,辽宁人,博士生;陈璞(1962- ),男,重庆人,副教授,博士(联系人.Tel:+86-10-62751828;E-mail:chenpu@pku.edu.cn);刘凯欣,(1956- ),吉林人,教授,博士.

  • 中图分类号: O241.6

High Performance Sparse Solver for Unsymmetrical Linear Equations With Out-of-Core Strategies and Its Application on Meshless Methods

  • 摘要: 针对局部Petrov-Galerkin无网格法(MLPG)等无网格方法的计算所产生的大型非对称稀疏线性方程组,介绍了一种新的直接解法.与一般非对称求解过程不同,该解法从现有的对称正定解法中演变出来,其分解过程在矩阵的上、下三角阵中对称进行.新的矩阵分解算法可以通过修改对称矩阵分解算法的代码来实现,这提供了从对称解法到非对称解法的快捷转换.还针对MLGP法以及有限元法所产生的方程组开发了多块外存算法(multi-blocked out-of-core strategy)来扩大求解规模.测试结果证明该方法大幅度提高了大型非对称稀疏线性方程组的求解速度.
  • [1] CHEN Pu,Runesha H,Nguyen D T,et al. Sparse algorithms for indefinite systems of linear equations[J].Comput Mech J,2000,25(1):33—42. doi: 10.1007/s004660050013
    [2] Damhaug A C,Reid J,Bergseth A.The impact of an efficient linear solver on finite element analysis[J].Comput Struct,1999,72(4/5):594—604.
    [3] Weinberg D J.A performance assessment of NE/Nastran's new sparse direct and iterative solvers[J].Adv Engng Software,2000,31(8/9):547—554. doi: 10.1016/S0965-9978(00)00016-8
    [4] Wilson E L,Bathe K J,Doherty W P.Direct solution of large system of linear equations[J].Comput Struct,1974,4(2):363—372. doi: 10.1016/0045-7949(74)90063-7
    [5] Atluri S N,Zhu T.A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics[J].Comput Mech,1998,22(2):117—127. doi: 10.1007/s004660050346
    [6] Atluri S N,Zhu T.The meshless local Petrov-Galerkin (MLPG) approach for solving problems in elasto-statics[J].Comput Mech,2000,25(2/3):169—179. doi: 10.1007/s004660050467
    [7] Ng E G,Peyton B W.Block sparse Cholesky algorithm on advanced uniprocessor computers[J].SIAM J Sci Comput,1993,14(5):1034—1055. doi: 10.1137/0914063
    [8] Pissanetzky S.Sparse Matrix Technology[M].London,Orlando:Academic Press,1984.
    [9] Demmel W J,Eisenstat C S,Gilbert J R,et al.A supernodal approach to sparse partial pivoting[J].SIAM J Matrix Anal Appl,1999,20(3):720—755. doi: 10.1137/S0895479895291765
    [10] Li S X.An overview of superLU:algorithms,implementation, and user interface[J].ACM Trans Math Software,2005,31(3):302—325. doi: 10.1145/1089014.1089017
    [11] Runesha H B,Nguyen D T.Vector-sparse solver for unsymmetrical matrices[J].Adv Engng Software,2000,31(8/9):563—569. doi: 10.1016/S0965-9978(00)00024-7
    [12] Sherman A H.On the efficient solution of sparse systems of linear and nonlinear equations[D].Rept No.46.Ph D Dissertation.New York:Dept of Computer Science, Yale University, 1975.
    [13] CHEN Pu,ZHENG Dong,SUN Shu-li,et al. High performance sparse static solver in finite element analyses with loop-unrolling[J].Adv Engng Software,2003,34(4):203—215. doi: 10.1016/S0965-9978(02)00128-X
    [14] Fellipa C A. Solution of linear equations with skyline-stored symmetric matrix[J].Comput Struct,1975,5(1):13—29. doi: 10.1016/0045-7949(75)90016-4
    [15] Wilson E L,Dovey H H.Solution or reduction of equilibrium equations for large complex structural system[J].Adv Engng Software,1978,1(1):19—26. doi: 10.1016/0141-1195(78)90018-9
    [16] Amestoy R P,Enseeiht-Irit,Davis A T,et al.Algorithm 837 : AMD, an approximate minimum degree ordering algorithm[J].ACM Trans Math Software,2004,30(3):381—388. doi: 10.1145/1024074.1024081
    [17] Karypis G, Kumar V.A fast and high quality multilevel scheme for partitioning irregular graphs[J].SIAM J Sci Comput,1998,20(1):359—392. doi: 10.1137/S1064827595287997
    [18] Zheng D,Chang T Y P.Parallel Cholesky method on MIMD with shared memory[J].Comput Struct,1995,56(1):25—38. doi: 10.1016/0045-7949(94)00534-A
    [19] Dowd K,Severance C R.High Performance Computing[M].2nd ed.Cambridge: Sebastopol, CA O’Reilly & Associates,1998.
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出版历程
  • 收稿日期:  2005-07-25
  • 修回日期:  2006-04-07
  • 刊出日期:  2006-10-15

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