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

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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.