| 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 |
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| 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 |
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| 作者姓名： | 苑维然 陈璞 刘凯欣 |
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| 作者单位： | 北京大学 力学与空间技术系,湍流与复杂系统国家重点实验室, 北京 100871;2.北京大学 工程研究院,北京 100871 |
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| 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．
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| 关 键 词： | 稀疏矩阵 线性方程组 无网格法 高性能计算 |
| 文章编号： | 1000-0887（2006）10-1173-09 |
| 收稿时间： | 2005-07-25 |
| 修稿时间： | 2006-04-07 |
High Performance Sparse Solver for Unsymmetrical Linear Equations With Out-of-Core Strategies and Its Application on Meshless Methods |
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| 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 |
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| Authors: | YUAN Wei-ran CHEN Pu LIU Kai-xin |
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| Affiliation: | LTCS & Department of Mechanics and Aerospace Engineering, Peking University, Beijing 100871, P. R. China; |
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| Abstract: | A new direct method for solving unsymmetrical sparse linear systems(USLS) arising from meshless methods was introduced.Computation of certain meshless methods such as meshless local Petrov-Galerkin(MLPG) method need to solve large USLS.The proposed solution method for unsymmetrical case performs factorization processes symmetrically on the upper and lower portion of matrix,which differs from previous work based on general unsymmetrical process,and attains higher performance.It is shown that the solution algorithm for USLS can be simply derived from the existing approaches for the symmetrical case.The new matrix factorization algorithm in the method can be implemented easily by modifying a standard JKI symmetrical matrix factorization code.Multi-blocked out-of-core strategies were also developed to expand the solution scale.The approach convincingly increases the speed of the solution process,as is demonstrated with the numerical tests. |
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| Keywords: | sparse matrices linear equations meshless methods high performance computation |
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