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

Abstract

The double Column block method applies to solute of large sparse linear simultaneous equations in finite element analysis.At present the partitioned 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-seal FE problems, especially the three-dimensional problems.This difficulty has-been overcome by the doulbe column block method, completely independent of the bandwidth, by means Of our method the coefficient matrix is partitioned according to the 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 te be applied to calculations in large-scale FE problems.