矩阵重排序算法在结构分析快速求解中的应用

Application of improved RCM algorithm in fast solution of structural analysis

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.

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 floating point operation.In this paper,by using graph theory,some improvements on RCM algorithm are provided according to the characteristics of one-dimensional variant-banded storage scheme to reduced the bandwidth and profile of total stiffness matrix.Numerical examples show that solving large scale linear equations in structural finite element program with fast solution techology of improved RCM algorithm is more efficient,and the program used in the paper is stable and reliable.