Comptes Rendus
no. 7
Model reduction, data-based and advanced discretization in computational mechanics
Model order reduction for dynamical systems: A geometric approach
Antonio Falcó1 ; Fernando Sánchez1
1 ESI International Chair@CEU-UCH, Departamento de Matemáticas, Física y Ciencias Tecnológicas, Universidad Cardenal Herrera-CEU, CEU Universities, San Bartolomé 55, 46115 Alfara del Patriarca (Valencia), Spain
Comptes Rendus. Mécanique, Volume 346 (2018) no. 7, pp. 515-523.

The aim of this paper is to ask the question as whether it is possible, for a given dynamical system defined by a vector field over a finite dimensional inner product space, to construct a reduced-order model over a finite dimensional manifold. In order to give a positive answer to this question, we prove that if the manifold under consideration is an immersed submanifold of the vector space, considered as ambient manifold, then it is possible to construct explicitly a reduced-order vector field over this submanifold. In particular, we found that the reduced-order vector field satisfies the variational principle of Dirac–Frenkel and that we can formulate the Proper Orthogonal Decomposition under this framework. Finally, we propose a local-point estimator of the time-dependent error between the original vector field and the reduced-order one.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crme.2018.04.010
Keywords: Proper generalized decomposition, Frequency-dependent parametric models, Harmonic analysis, Modal analysis, Dynamics

Antonio Falcó 1; Fernando Sánchez 1

1 ESI International Chair@CEU-UCH, Departamento de Matemáticas, Física y Ciencias Tecnológicas, Universidad Cardenal Herrera-CEU, CEU Universities, San Bartolomé 55, 46115 Alfara del Patriarca (Valencia), Spain 
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Antonio Falcó; Fernando Sánchez. Model order reduction for dynamical systems: A geometric approach. Comptes Rendus. Mécanique, Volume 346 (2018) no. 7, pp. 515-523. doi : 10.1016/j.crme.2018.04.010. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2018.04.010/

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