改进的EBE预条件矩阵及其在有限元方程组求解中的应用

A Modified EBE Preconditioner and its Application in the Finite System

结构分析中的有限元法一般归结为线性方程组的求解,依据EBE(Element-by-Element)策略,有限元方程组的系数矩阵(即系统的总刚度矩阵)可以表示成低秩的单元级矩阵的和。针对这类形式的线性方程组,本文在EBE策略的基础上给出了改进的预条件矩阵,称其为MEBE预条件矩阵;结合共轭梯度法,可在不显式形成总刚度矩阵的情形下,得出适合于并行计算的MEBE-PCG算法,并在网络机群(COW)并行计算环境下结合实例对算法的效率进行了验证。

A larger system of linear equations will always be found in structural finite element analysis. With the EBE strategy, its coefficient matrix (system's stiffness matrix) can be expressed as the addition of several low-rank matrices. In this paper, a new modified preconditioner suitable for such structural linear system, which names as MEBE preconditioner, is presented. In combination with the algorithm of conjugate gradients, a new parallel algorithm, MEBE-PCG, is obtained in the absence of the formation of the system's stiffness matrix. Under the COW parallel environment, a structural analysis problem is solved by the use of this MEBE-PCG algorithm and its parallel efficiency is discussed.