Details
| Original language | English |
|---|---|
| Pages (from-to) | 740-759 |
| Number of pages | 20 |
| Journal | International Journal for Numerical Methods in Engineering |
| Volume | 106 |
| Issue number | 9 |
| Publication status | Published - 19 Oct 2015 |
Abstract
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.
Keywords
- Adaptive strategy, BFGS, Galerkin projection, Model order reduction, Nonlinear dynamic analysis, POD
ASJC Scopus subject areas
- Mathematics(all)
- Numerical Analysis
- Engineering(all)
- General Engineering
- Mathematics(all)
- Applied Mathematics
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In: International Journal for Numerical Methods in Engineering, Vol. 106, No. 9, 19.10.2015, p. 740-759.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - An adaptive model order reduction with Quasi-Newton method for nonlinear dynamical problems
AU - Nigro, P. S.B.
AU - Anndif, M.
AU - Teixeira, Y.
AU - Pimenta, P. M.
AU - Wriggers, P.
PY - 2015/10/19
Y1 - 2015/10/19
N2 - 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.
AB - 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.
KW - Adaptive strategy
KW - BFGS
KW - Galerkin projection
KW - Model order reduction
KW - Nonlinear dynamic analysis
KW - POD
UR - http://www.scopus.com/inward/record.url?scp=84948167100&partnerID=8YFLogxK
U2 - 10.1002/nme.5145
DO - 10.1002/nme.5145
M3 - Article
AN - SCOPUS:84948167100
VL - 106
SP - 740
EP - 759
JO - International Journal for Numerical Methods in Engineering
JF - International Journal for Numerical Methods in Engineering
SN - 0029-5981
IS - 9
ER -