p自适应分析求解快速迭代算法的研究

A Study of the Fast Iterative Method for p Adaptive Computation

提出一种结构系统ｐ自适应有限元分析快速求解算法．该方法以预处理共轭梯度法为基础，采用了逐单元矩阵处理技术和基于单元的分块预处理矩阵技术；提出以高斯消元法求得ｐ＝１或２时问题的解作为高阶问题初始解的求解策略，避免了显式组装系统总体刚度矩阵，具有内存需求少、收敛速度快的优点．

A fast solving method with p adaptive finite element analysis for structure systems is presented. It is based on the preconditioned conjugate gradient method and the element by element matrix handling techniques as well as a blocked preconditioner constructed with the element stiffness matrices have been used. The solving strategy proposed consists in that the solution of a lower order problem, p equals 1 or 2, obtained using Gaussian eliminating method is taken as the initial solution for a higher order one. The explicit packaging of the global stiffness matrix is avoided and less memory is required with a high converging rate.