瞬态动力问题的遂单元矩阵分裂和逐步积分方法

Element-by-element Matrix decomposition and Step-by-Step Integration Method for Transient Dynamic Problems

本文对瞬态动力问题，结合逐步积分方法提出了一类广义的矩阵分裂和逐单元松弛算法，摆脱了有限元法通常需形成总体刚度矩阵，总体质量矩阵和求解大型稀疏方程组的工作，理论分析和计算实例表明，本文的广义矩阵分裂是最优的分裂方案。本文的算法物理意义明确，便于编写程序推广应用。

In this paper,a general matrix decomposition scheme as well as an element-by-element relaxation algorithm combined with step-by-step in integration method is presented for transient dynamic problems.thus the finite element method can be free forming global stiffness matrix, global mass matrix as well assolving large-scale sparse squations. Theory analysis and numerical results show that the present matrix decomposition scheme is the optimal one. The present algorithm has clear physical meaning and be easily applied to finite element.