An adaptive model order reduction with Quasi-Newton method for nonlinear dynamical problems

Summary Model Order Reduction (MOR) methods are extremely useful to reduce processing time, even nowadays, when parallel processing is possible in any personal computer. This work describes a method that combines Proper Orthogonal Decomposition (POD) and Ritz vectors to achieve an efficient Galerkin...

Full description

Saved in:
Bibliographic Details
Published in:International journal for numerical methods in engineering 2016-06, Vol.106 (9), p.740-759
Main Authors: Nigro, P. S. B., Anndif, M, Teixeira, Y., Pimenta, P. M., Wriggers, P.
Format: Article
Language:English
Subjects:
adaptive strategy
BFGS
Convergence
Galerkin projection
Mathematical analysis
Mathematical models
model order reduction
nonlinear dynamic analysis
Nonlinearity
Numerical analysis
Order reduction
POD
Projection
Strategy
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Summary Model Order Reduction (MOR) methods are extremely useful to reduce processing time, even nowadays, when parallel processing is possible in any personal computer. This work describes a method that combines Proper Orthogonal Decomposition (POD) and Ritz vectors to achieve an efficient Galerkin projection, which changes during nonlinear solving (online analysis). It is supported by a new adaptive strategy, which analyzes the error and the convergence rate for nonlinear dynamical problems. This model order reduction is assisted by a secant formulation which is updated by the Broyden‐Fletcher‐Goldfarb‐Shanno (BFGS) formula to accelerate convergence in the reduced space, and a tangent formulation when correction of the reduced space is needed. Furthermore, this research shows that this adaptive strategy permits correction of the reduced model at low cost and small error. Copyright © 2015 John Wiley & Sons, Ltd.
ISSN:0029-5981
1097-0207
DOI:10.1002/nme.5145