Accurate reanalysis of structures by a preconditioned conjugate gradient method

• Published in: International journal for numerical methods in engineering Vol. 55; no. 2; pp. 233 - 251
• Main Authors: Kirsch, Uri, Kocvara, Michal, Zowe, Jochem
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 20.09.2002
• Subjects: preconditioned conjugate gradients; structural reanalysis
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.496

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.