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A multigrid method for the generalized symmetric eigenvalue problem: Part II—performance evaluation
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.1620350808
Subject(s) - multigrid method , polygon mesh , convergence (economics) , eigenvalues and eigenvectors , regular polygon , mathematics , degrees of freedom (physics and chemistry) , mathematical optimization , computer science , mathematical analysis , geometry , partial differential equation , physics , quantum mechanics , economics , economic growth
The behaviour of the multigrid method is studied by solving some simple test problems. Optimum choices for some of the parameters are discussed, together with effective techniques for solving the coarse mesh correction equation. The effects of ill‐conditioning on the performance of the algorithm are examined. In particular, thin shells and non‐uniform meshes are observed to slow convergence. The solution of practical, large scale problems demonstrates the utility and speed of the proposed multigrid method. For example, the first 10 eigensolutions of a stiffened plate problem with 193 536 degrees‐of‐freedom were computed in 1.6 CPU hours using 42 Mbytes of memory on a Convex C240.