| 矩阵重排序算法在结构分析快速求解中的应用 |
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| 引用本文： | 于二青,王春江,赵金城.矩阵重排序算法在结构分析快速求解中的应用[J].空间结构,2010,16(1). |
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| 作者姓名： | 于二青 王春江 赵金城 |
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| 作者单位： | 上海交通大学土木工程系,上海,200240 |
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| 摘 要： | 结构有限元分析中最基本的计算是大规模线性方程组的求解,求解方法有直接法和迭代法两种.由于收敛性问题迭代法的应用受到很大限制,而解决求解规模和速度问题是直接法应用的关键.用直接法求解线性方程组,可通过减小矩阵的带宽与轮廓来减少数据存贮量及浮点运算次数,从而提高求解规模和速度.本文基于图论原理并针对结构总刚矩阵的一维变带宽存贮特点,对RCM算法进行了改进,以减少总刚矩阵的轮廓及带宽.算例表明,本文提出的在大规模线性方程组求解中采用改进的RCM算法快速求解技术,其算法是高效的,编制的计算程序是稳定、可靠的.
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| 关 键 词： | 线性方程组求解 图论 矩阵重排序 RCM算法 快速求解 |
Application of improved RCM algorithm in fast solution of structural analysis |
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| YU Er-qing,WANG Chun-jiang,ZHAO Jin-cheng.Application of improved RCM algorithm in fast solution of structural analysis[J].Spatial Structures,2010,16(1). |
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| Authors: | YU Er-qing WANG Chun-jiang ZHAO Jin-cheng |
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| Affiliation: | Department of Civil Engineering/a>;Shanghai Jiao Tong University/a>;Shanghai 200240/a>;China |
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| Abstract: | The solution of large-scale linear equations is the primary calculation in the structural finite element analysis.Direct and iterative methods are two solution methods for linear equations.The application of the iterative method is usually limited for converge problem,while the direct method has key problems of solution scale and efficiency.Direct solution of linear equations can improve the solution scale and efficiency by reducing the bandwidth and profile of matrix to decrease the data storage and floati... |
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| Keywords: | linear equations solution graph theory matrix permutation RCM algorithm fast solution |
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