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Eigenproperties of large‐scale structures by finite element partitioning and homotopy continuation
Author(s) -
Zhang Yan,
Harichandran Ronald S.
Publication year - 1989
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.1620280909
Subject(s) - finite element method , homotopy , tracing , conjugate gradient method , mathematics , scale (ratio) , continuation , rayleigh–ritz method , algorithm , mathematical optimization , mathematical analysis , computer science , boundary value problem , structural engineering , engineering , physics , quantum mechanics , pure mathematics , programming language , operating system
Finite element partitioning (or substructuring) is employed to estimate the eigenproperties of large‐scale structural systems. A homotopy equation is constructed and its solutions are characterized by a number of curves which connect the eigensolutions of the partitions with those of the complete system. A step‐by‐step tracing procedure is developed to follow these curves. At each step, prediction and correction are performed. The Rayleigh–Ritz procedure and the conjugate gradient method are used as predictor and corrector, respectively. Compared with the sole use of either the Rayleigh–Ritz or gradient methods, the proposed method is more reliable and more efficient for large‐scale problems. Numerical implementation is well suited for supercomputers.