Nigro, P. S. B.; Anndif, M.; Teixeira, Y.; Pimenta, P. M.; Wriggers, P. An adaptive model order reduction with quasi-Newton method for nonlinear dynamical problems. (English) Zbl 1352.65184 Int. J. Numer. Methods Eng. 106, No. 9, 740-759 (2016). 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. Cited in 2 Documents MSC: 65L05 Numerical methods for initial value problems involving ordinary differential equations Keywords:model order reduction; POD; BFGS; nonlinear dynamic analysis; Galerkin projection; adaptive strategy Software:OPTIMA PDFBibTeX XMLCite \textit{P. S. B. Nigro} et al., Int. J. Numer. 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