求解结构特征值问题的前置共轭梯度子空间迭代法

本文采用前置共轭梯度法与移轴迁移子空间迭代法相结合求解结构特征值问题，结构的单元并不按常规的组装过程组集总刚度阵和总质量阵，在大多数工程问题的有限元分析中，很多单元具有相同的类型及尺度，因此采用本文方法能降低对计算机存储容量的需求，且计算模型的节点可以按任意方式排列，此外，在移轴迁移中空间迭代法的基础上，引入自动收集初始迭代向量以及可变子空间维数的技术以加速收敛性。

PRECONDITIONED CONJUGATE GRADIENT-SUBSPACE ITERATION METHOD FOR SOLVING EIGENPROBLEMS OF STRUCTURES

A combination of preconditioned conjugate gradient method and shifted progressive subspace iteration method is proposed for solving eigenproblems of structures. All the finite elements of the structures are arranged in groups without the conventional assemblage process. Since in the finite element analysis of engineering problems many elements are of the same type and same size, therefore the computer storage requirement may be lowered and the nodes of the computational model could be numbered in an arbitrary way. On the basis of shifted progressive subspace iteration method the automatic collection of initial iteration vectors and the changeable subspace dimension technique are introduced in this paper to accelerate the convergence. It implies that the finite element analysis of large scale dynamic problems could be carried out on microcomputers. As the application of this method, some numerical examples are presented to demonstrate the lower storage requirement and the higher copmutational efficiency of the proposed method.