Modified Eigenvalue Problems, with Applicatin to Structural Dynamic Re-Analysis on Parallel Computers

本研究项目将集中在修正特征值问题的有效求解方法上，并应用于并行计算环境下的结构动态再分析。以下是具体的任务：1.并行实现一种改进的求解器线性方程组：2.评价子空间迭代法和lanczos法对动力学问题的适用性。重新分析；3.研究低阶修正的可行性。一些(不是全部)本征值的方法。这项研究将致力于开发实用的、可用于解决结构动力重分析修正特征值问题的有效方法，这只需要结构系统的几个典型的固有频率和振型。将特别注意开发适合于并行MIMD计算机的并行动态求解程序。

This research project will focus on the efficient solution methods for the modified eigenvalue problem, with application to dynamic re- analysis of structures on parallel computing environments. The following are the specific task: 1. parallel implementation of solvers for a modified system oflinear equations: 2. evaluating the applicability of subspace iteration and Lanczos methods for dynamic reanalysis; 3. study the feasibility of low rank modification methods for some (not all) eigenvalues. The research will be directed towards the development of practical, effective methods that can be used in solving the modified eignevalue problems arising from structural dynamic re-analysis, which require only a few representative natural frequencies and modal shapes of a structural system. Particular attention will be given to developing parallel dynamic solution procedures that are suitable for parallel MIMD computer.