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A subspace forward iteration method for solving the quadratic eigenproblem associated with the FDE formulation
Author(s) -
Gmuer Thomas E. C.
Publication year - 1990
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.1620290503
Subject(s) - subspace topology , convergence (economics) , quadratic equation , mathematics , monotonic function , finite element method , acceleration , mathematical optimization , scheme (mathematics) , krylov subspace , inertia , algorithm , iterative method , mathematical analysis , geometry , physics , classical mechanics , economics , thermodynamics , economic growth
This paper presents the development of an efficient and numerically stable algorithm for accurately computing the eigensolutions of the quadratic real symmetric eigenproblem arising in the finite dynamic element (FDE) formulation. Closely related to the subspace forward iteration method, the proposed scheme is well suited to extracting the lowest natural frequencies and associated mode shapes of large practical eigenproblems, takes full advantage of the banded configuration of the stiffness, inertia and dynamic correction matrices involved in the eigenproblem and ensures a monotonic convergence from above to the required eigenpairs. A shifting technique for convergence acceleration and an eigenpair verification scheme are also presented. Numerical examples are shown demonstrating the excellent performance of the solution procedure.