An adaptive model order reduction by proper snapshot selection for nonlinear dynamical problems

• Published in: Computational mechanics 2016-04, Vol.57 (4), p.537-554
• Main Authors: Nigro, P. S. B., Anndif, M., Teixeira, Y., Pimenta, P. M., Wriggers, P.
• Format: Article
• Language: English
• Subjects: Classical and Continuum Physics; Computational Science and Engineering; Engineering; Original Paper; Theoretical and Applied Mechanics
• ISSN: 0178-7675; 1432-0924
• DOI: 10.1007/s00466-015-1238-y

Model Order Reduction (MOR) methods are employed in many fields of Engineering in order to reduce the processing time of complex computational simulations. A usual approach to achieve this is the application of Galerkin projection to generate representative subspaces (reduced spaces). However, when strong nonlinearities in a dynamical system are present and this technique is employed several times along the simulation, it can be very inefficient. This work proposes a new adaptive strategy, which ensures low computational cost and small error to deal with this problem. This work also presents a new method to select snapshots named Proper Snapshot Selection (PSS). The objective of the PSS is to obtain a good balance between accuracy and computational cost by improving the adaptive strategy through a better snapshot selection in real time (online analysis). With this method, it is possible a substantial reduction of the subspace, keeping the quality of the model without the use of the Proper Orthogonal Decomposition (POD).