The Double Column Block Method, an Effective Solution for Large sparse symmetric System of Linear Equations

Ge Xiurun; Yang Jialing

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The Double Column Block Method, an Effective Solution for Large sparse symmetric System of Linear Equations

更新时间：2026-06-25

- The Double Column Block Method, an Effective Solution for Large sparse symmetric System of Linear Equations
- Vol. 6, Issue 2, (1985)
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- Online First：10 April 2017，
  
  Published：1985
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Ge Xiurun, Yang Jialing. The Double Column Block Method, an Effective Solution for Large sparse symmetric System of Linear Equations[J]. 1985, 6(2).
DOI：

Ge Xiurun, Yang Jialing. The Double Column Block Method, an Effective Solution for Large sparse symmetric System of Linear Equations[J]. 1985, 6(2). DOI：

摘要

双列块法用于有限元分析计算中求解大型线代数方程组。目前在有限元计算中最通常使用的求解大型线代数方程组的方法是分块的三角分解法。由于这种方法对方程组系数矩阵的分块受带宽的限制‘以至目前一般计算机的内存贮量限制了大带宽问题的求解

使一些大型的有限元课题

特别是三维问题的解算难以实现。双列块法解决了这个西难。双列块法对方程组系数矩阵实行按计算机许可的容量划分列块

按列分解

可以完全不受带宽的限制。方法是成功的、有效的。用双列块法在PE-3220小型机上仅用686K字节的内存解算了最大半带宽为1746

系数矩阵存贮量为5000K以上字节的三维(124个20节点等参元

8个16节点等参节理元、831个节点)有限元课题

这种方法使小型和高档微机用于大型有限元的解算成为可能。

Abstract

The double Column block method applies to solute of large sparse linear simultaneous equations in finite element analysis. At present the portioned triangular decomposition method is generally used for solving large systems of linear equations in FE. With the partition of the coefficient matrix dependent on its bandwidth

the solution of problems with a large bandwidth is restricted owing to the computer core storage and hence it is difficult for this method to solve some large-scal FE problems

especially the three-dimensional problems. This difficulty has been overcome by the double column block method

completely independent of the bandwidth

by means of our method the coefficient matrix is partitioned according to computer core storage capacity. It is proved that this approach is successful and effective. Based on this method

the solution has been completed of the three-dimensional FE problem with 124 twenty-node and 8 sixteen-node isoparametric elements

and 831 nodes

having a maximum half-bandwidth of 1746 and global stiffness matrix storage of more than 5000 K bytes. The computation was performed on PE-3220 minicomputer and only a core storage of 685 K bytes was used. The double column block method makes it possible for minicomputer and high-level microcomputer to be applied to calculations in large-scale FE problems.

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