TY - JOUR

T1 - An adaptive model order reduction by proper snapshot selection for nonlinear dynamical problems

AU - Nigro, P. S.B.

AU - Anndif, M.

AU - Teixeira, Y.

AU - Pimenta, P. M.

AU - Wriggers, P.

N1 - Funding Information: The fourth author acknowledges the support by CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico) under the grant 303091/2013-4 as well as expresses his gratitude to the Alexander von Humboldt Foundation for the Georg Forster Research Award that made possible his stay at the University of Duisburg-Essen and the Leibniz University of Hannover. Funding Information: The first author acknowledges the support by CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico) under the grant 201656/2012-4 that made possible his stay at the Leibniz University of Hannover.

PY - 2016/4

Y1 - 2016/4

N2 - 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).

AB - 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).

KW - Adaptive strategy

KW - Galerkin projection

KW - Model order reduction

KW - Nonlinear dynamic analysis

KW - PSS

KW - Ritz vector

UR - http://www.scopus.com/inward/record.url?scp=84961119235&partnerID=8YFLogxK

U2 - 10.1007/s00466-015-1238-y

DO - 10.1007/s00466-015-1238-y

M3 - Article

AN - SCOPUS:84961119235

VL - 57

SP - 537

EP - 554

JO - Computational mechanics

JF - Computational mechanics

SN - 0178-7675

IS - 4

ER -