This paper considers the preconditioned block conjugate gradient method for solving the algebraic, generalized partial eigenvalue problem, which arises when the finite element method is applied to dynamic analysis in structural and solid mechanics. The focus is on the development of an algorithm that keeps constant the iterable subspace dimension, independently of the number of eigenpairs required. Novelties in this approach include a preconditioning strategy based on block incomplete factorization of the shifted stiffness matrix, and analysis of unremovable errors, which accumulate with increasing numbers of eigenpairs.

中文翻译：

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模态结构分析中的块子空间投影预处理共轭梯度法

本文考虑了预处理的块共轭梯度法，用于解决代数广义广义特征值问题，这种问题是在有限元方法应用于结构和固体力学动力学分析时出现的。重点是开发一种算法，该算法使可迭代子空间维保持不变，而与所需本征对的数量无关。这种方法的新颖性包括基于位移刚度矩阵的块不完全分解的预处理策略，以及不可移动误差的分析，这些误差随着特征对数目的增加而累积。