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Multigrid method for stability problemsThe problem of calculating the stability of steady state solutions of differential equations is addressed. Leading eigenvalues of large matrices that arise from discretization are calculated, and an efficient multigrid method for solving these problems is presented. The resulting grid functions are used as initial approximations for appropriate eigenvalue problems. The method employs local relaxation on all levels together with a global change on the coarsest level only, which is designed to separate the different eigenfunctions as well as to update their corresponding eigenvalues. Coarsening is done using the FAS formulation in a nonstandard way in which the right-hand side of the coarse grid equations involves unknown parameters to be solved on the coarse grid. This leads to a new multigrid method for calculating the eigenvalues of symmetric problems. Numerical experiments with a model problem are presented which demonstrate the effectiveness of the method.
Document ID
19890055724
Acquisition Source
Legacy CDMS
Document Type
Reprint (Version printed in journal)
External Source(s)
Authors
Ta'asan, Shlomo
(NASA Langley Research Center Hampton, VA; Weizmann Institute of Science, Rehovot, Israel)
Date Acquired
August 14, 2013
Publication Date
September 1, 1988
Publication Information
Publication: Journal of Scientific Computing
Volume: 3
ISSN: 0885-7474
Subject Category
Numerical Analysis
Accession Number
89A43095
Funding Number(s)
CONTRACT_GRANT: NAS1-18107
CONTRACT_GRANT: AF-AFOSR-86-0127
Distribution Limits
Public
Copyright
Other

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