Mathematical Sciences: Iterative Methods for Generalized and Modified Eigenvalue Problems on Parallel Computers

研究者和他的同事分析、发展和实现了摄动广义特征值问题的计算方法。本课题主要分为三个部分：a)研究广义系统的几个（极值）特征值及相关特征向量解方案的数学基础；b)为广义和修正特征值问题开发实用的计算机求解程序；c)设计在MIMD分布式存储计算机环境下的高效实现。这些问题出现在结构的动力分析中。在结构动力学分析完成、固有频率和振型计算完成后，如何在分析和设计中考虑结构的变化是一个经常遇到的问题。研究人员开发了健壮、准确和快速的算法来解决各种这样的问题。

The investigator and his colleague analyze, develop, and implement computational methods for perturbed generalized eigenvalue problems. The project has three main parts: a) Study the mathematical foundation of solution schemes for the calculation of a few (extreme) eigenvalues and associated eigenvectors of generalized systems; b) Develop practical computer solution procedures for the generalized and modified eigenvalue problem; and c) Devise efficient implementation in MIMD distributed memory computer environments. These problems arise in the dynamic analysis of structures. A frequently encountered problem is how to take into account in analysis and design changes introduced after the structural dynamics analysis has been completed, and the natural frequencies and modes have been computed. The investigators develop robust, accurate and fast algorithms for solving a variety of such problems.