结构力学中广义单步单算子算法收敛率的注记

A note on the convergence rate of the generalized single step single solve algorithms in structural dynamics

针对线性结构力学问题中的广义单步单算子算法,通过局部截断误差分析方法,给出了三个主变量即位移、速度和加速度取得二阶精度的充分必要条件,对广义单步单算子算法的主变量相容性的概念进行了深入探讨,并且解释了某些流行的算法中加速度一阶精度的问题。数值实验验证了理论结果。

The convergence analysis of the generalized single step single solve algorithms for the linear structural dynamics problems is made.Through the mathematical local truncation error analysis,the sufficient and necessary conditions of the second order convergence of the three primary variables,namely the displacement,the velocity and the acceleration,are obtained.The consistency of the primary variables in the generalized single step single solve algorithms is discussed thoroughly and the first order accuracy of the acceleration in some popular algorithms is explained.Numerical examples testify theoretical results.