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MULTILEVEL AGGREGATION METHOD FOR SOLVING LARGE‐SCALE GENERALIZED EIGENVALUE PROBLEMS IN STRUCTURAL DYNAMICS
Author(s) -
BULGAKOV V. E.,
BELYI M. V.,
MATHISEN K. M.
Publication year - 1997
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/(sici)1097-0207(19970215)40:3<453::aid-nme74>3.0.co;2-2
Subject(s) - multigrid method , preconditioner , finite element method , truss , mathematics , eigenvalues and eigenvectors , stiffness matrix , iterative method , subspace topology , matrix (chemical analysis) , mathematical optimization , computer science , algorithm , mathematical analysis , structural engineering , partial differential equation , physics , materials science , quantum mechanics , engineering , composite material
In this paper a novel iterative method of multilevel type for solving large‐scale generalized eigenvalue problems encountered in structural dynamics is presented. A preconditioned iterative technique, which can be viewed as a modification of the Subspace Iteration method, is used for simultaneous calculation of a group of lowest modes and frequencies. The paper demonstrates that a coarse aggregation model can be employed in the hierarchical structure of the preconditioner in order to provide a good resemblance of the latter to the stiffness matrix of the finite element approximation with respect to low‐frequency modes. This leads to a fast convergent procedure of subspace iterations. As opposed to the coarse grid used in methods of multigrid type, this model allows for solving problems with different finite elements including reticulated structures in the framework of large comprehensive finite element software systems. Numerical experiments performed for three‐dimensional truss, frame and solid structures demonstrate an excellent performance of the method. © 1997 by John Wiley & Sons, Ltd.