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Accurate reanalysis of structures by a preconditioned conjugate gradient method
Author(s) -
Kirsch Uri,
Kocvara Michal,
Zowe Jochem
Publication year - 2002
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.496
Subject(s) - conjugate gradient method , derivation of the conjugate gradient method , conjugate residual method , eigenvalues and eigenvectors , range (aeronautics) , convergence (economics) , nonlinear conjugate gradient method , mathematics , matrix (chemical analysis) , algorithm , gradient method , computer science , mathematical optimization , gradient descent , physics , artificial intelligence , materials science , quantum mechanics , artificial neural network , economics , composite material , economic growth
Abstract A preconditioned conjugate gradient (PCG) method that is most suitable for reanalysis of structures is developed. The method presented provides accurate results efficiently. It is easy to implement and can be used in a wide range of applications, including non‐linear analysis and eigenvalue problems. It is shown that the PCG method presented and the combined approximations (CA) method developed recently provide theoretically identical results. Consequently, available results from one method can be applied to the other method. Effective solution procedures developed for the CA method can be used for the PCG method, and various criteria and error bounds developed for conjugate gradient methods can be used for the CA method. Numerical examples show that the condition number of the selected preconditioned matrix is much smaller than the condition number of the original matrix. This property explains the fast convergence and accurate results achieved by the method. Copyright © 2002 John Wiley & Sons, Ltd.