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

作者：Nigro P S B^*; A***if M; Teixeira Y; Pimenta P M; Wriggers P

来源：International Journal for Numerical Methods in Engineering, 2016, 106(9): 740-759.

DOI：10.1002/nme.5145

• model order reduction
• POD
• BFGS
• nonlinear dynamic analysis
• Galerkin projection
• adaptive strategy

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.

• 出版日期2016-6-1