迭代动力缩聚法的收敛性分析  

Convergence Analysis of Iterative Dynamic Condensation Methods

作　　者：汪晓虹[1] 曹立娟[2] 刘慧[1] 陈怀海[2] 

机构地区：[1]南京航空航天大学理学院,江苏南京210016 [2]南京航空航天大学航空宇航学院,江苏南京210016

出　　处：《航空学报》2008年第3期645-650,共6页Acta Aeronautica et Astronautica Sinica

基　　金：国家自然科学基金(10672078);航空支撑科技基金(05D52009);国家“863”计划(2006AA706103)

摘　　要：利用Lyapunov矩阵方程和Riccati矩阵方程解的理论,对迭代动力缩聚法的收敛性进行了分析证明,并给出了迭代收敛的充分条件。揭示了动力缩聚法与经典的子空间迭代法的内在关系,阐明了各自的优缺点。迭代动力缩聚法实质上是子空间迭代法的变形,它需要人为选择主辅自由度,而子空间迭代法需要人为选定初始迭代向量。从理论上讲,只有主辅自由度选择满足收敛的充分条件要求,才能保证迭代结果收敛到理论上的精确解。给出了一个数值算例,对几种算法进行了对比,并验证了本文的论点。Based on the theory of solution to the Lyapunov and Riccati matrix equations,in this paper an in-depth analysis of the convergence of iterative dynamic condensation methods is provided and the sufficient conditions for their convergence are introduced.The relationship between the iterative dynamic condensation methods and the classical subspace iterative method is uncovered.In fact,the iterative dynamic condensation methods are a transformed kind of the subspace iterative method.One must select the master and slave degrees of freedom in the iterative dynamic condensation algorithms or the initial iterative vectors in the subspace iterative algrithm.Theoretically,if the selection of the master and slave degrees of freedom meet the demand of the sufficient conditions,the iterative dynamic condensation algorithms will obtain an accurate result.A numerical example is presented in the end of the paper.The results by the various algorithms are compared,and the idea of the paper is verified.

关 键 词：动力缩聚 迭代法 矩阵方程 有限元法 建模 

分 类 号：V214.1[航空宇航科学与技术—航空宇航推进理论与工程]