基于分段Legendre多项式的齐次扩容分块精细算法  

Homogenized Precise Integration Methods Based on Piecewise Legendre Polynomial Series

作　　者：汪帜辉[1] 汪梦甫[1] 

机构地区：[1]湖南大学土木工程学院,长沙410082

出　　处：《力学季刊》2012年第3期398-403,共6页Chinese Quarterly of Mechanics

基　　金：国家自然科学基金项目(50978091)

摘　　要：本文将非齐次函数在各时间步长内应用分段Legendre多项式进行模拟,并由此对非齐次线性定常系统扩容,形成基于分段Legendre多项式的齐次扩容方程。借鉴已有齐次扩容方程精细求解的思想,考虑Legendre多项式的性质和扩容后矩阵的特点,对指数矩阵进行分块计算,建立指数矩阵中各分块矩阵计算的加法定理。本算法不仅具有齐次扩容方程精细积分法无需矩阵求逆的优点,而且计算时矩阵维数更小,计算效率更高。数值算例证实了本文算法的高精度与高效率。Non-linearly varying loadings within the time intervals are simulated by using Legendre polynomial series before a direct integration method is performed. Based on homogenized precise integration method, and the mathematic feature of the Legendre polynomial series, an efficient algorithm for compu- ting matrix exponential is given, a partitioning homogenized precise integration method based on piece- wise Legendre polynomial series（HPIM-LP） is presented. HPIM-LP is able to avoid the matrix operation, and dimensional expanding is not required. The accuracy of the time integration schemes are studied and compared with those of the commonly used method. The result shows that the HPIM-LP has arbitrary or- der of accuracy, wider application and less time-consuming. A numerical example is presented to demon- strate the applicability of the HPIM-LP.

关 键 词：精细积分法 非齐次动力系统 齐次扩容分块精细算法 加法定理 

分 类 号：TU311.3[建筑科学—结构工程]