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A parallel method of eigenvalue analysis using dynamic substructuring and homotopy continuation
Author(s) -
Jang YoungSoon,
Youn SungKie
Publication year - 1998
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(19981015)43:3<409::aid-nme419>3.0.co;2-w
Subject(s) - eigenvalues and eigenvectors , continuation , homotopy analysis method , feti , homotopy , mathematics , substructure , degrees of freedom (physics and chemistry) , simple (philosophy) , algorithm , computer science , finite element method , domain decomposition methods , pure mathematics , structural engineering , engineering , philosophy , physics , epistemology , quantum mechanics , programming language
A parallel method to solve large eigenvalue problems using dynamic substructuring and homotopy continuation is presented. Unlike the conventional approaches in substructuring, the non‐linear term is not neglected for improved accuracy. Therefore, instead of solving the approximated condensed problems, full exact condensed forms are treated. Homotopy continuation method is introduced to solve the non‐linear reduced eigenvalue problem. In the process small number of substructure modes are used to reduce the original eigenvalue problem, and additional degrees of freedom, besides those at interfaces, are selected. The whole procedures are implemented to workstation cluster using PVM. To show how the method works, simple two‐dimensional numerical examples are solved. It is demonstrated that the method yields highly accurate results and good parallel efficiency. © 1998 John Wiley & Sons, Ltd.

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