航空学报 > 2008, Vol. 29 Issue (3): 645-650

迭代动力缩聚法的收敛性分析

汪晓虹1;曹立娟2;刘慧1;陈怀海2   

  1. 1.南京航空航天大学 理学院 2.南京航空航天大学 航空宇航学院
  • 收稿日期:2008-01-17 修回日期:2008-04-07 出版日期:2008-05-20 发布日期:2008-05-20
  • 通讯作者: 汪晓虹1

Convergence Analysis of Dynamic Condensation Methods

Wang Xiaohong1, Cao Lijuan2, Liu Hui1, Chen Huaihai2   

  1. 1.College of Science, Nanjing University of Aeronautics and Astronautics 2.College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics
  • Received:2008-01-17 Revised:2008-04-07 Online:2008-05-20 Published:2008-05-20
  • Contact: Wang Xiaohong1

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。

关键词: 动力缩聚, 迭代法, 矩阵方程, 有限元法, 建模

Abstract:

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.

Key words: dynamic , condensation,  , iterative , method,  , matrix , equation,  , finite , element , method,  , modeling

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