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A preconditioned conjugate gradient approach to structural reanalysis for general layout modifications
Author(s) -
Li Zhengguang,
Wu Baisheng
Publication year - 2006
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.1889
Subject(s) - preconditioner , conjugate gradient method , conjugate , computer science , convergence (economics) , matrix (chemical analysis) , conjugate residual method , degrees of freedom (physics and chemistry) , incomplete cholesky factorization , algorithm , mathematics , stiffness matrix , factorization , stiffness , mathematical optimization , matrix decomposition , iterative method , mathematical analysis , gradient descent , eigenvalues and eigenvectors , engineering , structural engineering , artificial intelligence , physics , materials science , economic growth , composite material , quantum mechanics , artificial neural network , economics
This paper presents a preconditioned conjugate gradient approach to structural static reanalysis for general layout modifications. It is suitable for all types of layout modifications, including the general case in which some original members and nodes are deleted and other new members and nodes are added concurrently. The approach is based on the preconditioned conjugate gradient technique. The preconditioner is constructed, and an efficient implementation for applying the preconditioner is presented, which requires the factorization of the stiffness matrix corresponding to the newly added degrees of freedom only. In particular, the approach can adaptively monitor the accuracy of approximate solutions. Numerical examples show that the condition number of the preconditioned matrix is remarkably reduced. Therefore, the fast convergence and accurate results can be achieved by the approach. Copyright © 2006 John Wiley & Sons, Ltd.