Multilevel solution procedures for structural dynamics eigenvalue problems
Hwang, Tsanhuei
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Permalink
https://hdl.handle.net/2142/21020
Description
Title
Multilevel solution procedures for structural dynamics eigenvalue problems
Author(s)
Hwang, Tsanhuei
Issue Date
1991
Doctoral Committee Chair(s)
Parsons, I. Dennis
Department of Study
Civil and Environmental Engineering
Discipline
Civil Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Civil
Computer Science
Language
eng
Abstract
Three multigrid algorithms are described that can solve the symmetric generalized eigenvalue problem encountered in structural dynamics. First, the multigrid algorithm for solving linear matrix equations is incorporated into the subspace iteration and block Lanczos methods to produce implicit subspace and Lanczos multigrid methods. The nested iteration technique is adopted to produce the initial trial vectors. Second, the basic multigrid idea of fine mesh relaxation followed by a coarse mesh correction is explicitly applied to the eigenvalue problem to produce an explicit multigrid method. The nested iteration technique is also used to provide information on the coarse meshes and to produce good initial approximations to the fine mesh eigensolutions.
Particular attention is paid to the implementation of these methods on vector and shared memory parallel supercomputers. Several large-scale problems are used to study the convergence behavior and computational performance of the methods. The vector and parallel performance of the algorithms are tested using an Alliant FX/80, a Convex C240, and a Cray Y-MP8/832. For example, the first eigensolution of a plate problem with 3,151,875 degrees-of-freedom is solved in 670 seconds with 370 Mbytes of in-core storage on the Convex. In addition, a computation rate of 950 Mflops and a speedup of 6.5 (96.7% of parallelism) are measured on the Cray.
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