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A multigrid method for the generalized symmetric eigenvalue problem: Part I—algorithm and implementation
Author(s) -
Hwang T.,
Parsons I. D.
Publication year - 1992
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620350807
Subject(s) - multigrid method , polygon mesh , eigenvalues and eigenvectors , mathematics , relaxation (psychology) , algorithm , regular polygon , sequence (biology) , mathematical optimization , computer science , partial differential equation , geometry , mathematical analysis , psychology , social psychology , physics , quantum mechanics , biology , genetics
A multigrid method is described that can solve the generalized eigenvalue problem encountered in structural dynamics. The algorithm combines relaxation on a fine mesh with the solution of a singular equation on a coarse mesh. A sequence of coarser meshes may be used to quickly solve this singular equation using another multigrid method. The hierarchy of increasingly finer meshes can be further exploited using a nested iteration scheme, whereby initial approximations to the fine mesh eigenvectors are computed using interpolated coarse mesh eigenvectors. The solution of some simple plate problems on a Convex C240 demonstrates the efficiency of a vectorized version of the multigrid algorithm.