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Dynamic relaxation method based on Lanczos algorithm
Author(s) -
Namadchi Amir Hossein,
Alamatian Javad
Publication year - 2017
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.5565
Subject(s) - lanczos resampling , lanczos algorithm , algorithm , relaxation (psychology) , dynamic relaxation , computer science , mathematics , mathematical optimization , physics , geometry , eigenvalues and eigenvectors , medicine , quantum mechanics
Summary This paper tries to accelerate the convergence rate of the general viscous dynamic relaxation method. For this purpose, a new automated procedure for estimating the critical damping factor is developed by employing a simple variant of the Lanczos algorithm, which does not require any re‐orthogonalization process. All of the computational operations are performed by simple vector–matrix multiplication without requiring any matrix factorization or inversion. Some numerical examples with geometric nonlinear behavior are analyzed by the proposed algorithm. Results show that the suggested procedure could effectively decrease the total number of convergence iterations compared with the conventional dynamic relaxation algorithms. Copyright © 2017 John Wiley & Sons, Ltd.