Krylov subspace techniques for reduced-order modeling of large-scale dynamical systems
Applied Numerical Mathematics
Survey A review of methods for input/output selection
Automatica (Journal of IFAC)
Computation of POD basis functions for fluid flows with lanczos methods
Mathematical and Computer Modelling: An International Journal
Adaptive model reduction for sensitivity analysis
SMO'06 Proceedings of the 6th WSEAS International Conference on Simulation, Modelling and Optimization
Skipping steps in deformable simulation with online model reduction
ACM SIGGRAPH Asia 2009 papers
Proper general decomposition (PGD) for the resolution of Navier-Stokes equations
Journal of Computational Physics
Multiparametric analysis within the proper generalized decomposition framework
Computational Mechanics
Review: A priori hyper-reduction method for coupled viscoelastic-viscoplastic composites
Computers and Structures
Structural and Multidisciplinary Optimization
Hi-index | 31.46 |
Model reduction methods are usually based on preliminary computations to build the shape function of the reduced order model (ROM) before the computation of the reduced state variables. They are a posteriori approaches. Most of the time these preliminary computations are as complex as the simulation which we want to simplify by the ROM. The reduction method we propose avoids such preliminary computations. It is an a priori approach based on the analysis of some state evolutions, such that all the state evolutions needed to perform the model reduction are described by an approximate ROM. The ROM and the state evolution are simultaneously improved by the method, thanks to an adaptive strategy. Obviously, an initial set of known shape functions can be used to define the ROM to adapt. But it is not necessary. The adaptive procedure includes extensions of the subspace spanned by the shape functions of the ROM and selections of the most relevant shape functions in order to represent the state evolution. The hyperreduction is achieved by selecting a part of the integration points of the finite element model to forecast the evolution of the reduced state variables. Hence both the number of degrees of freedom and the number of integration points are reduced. To perform the adaptive procedure, different computational strategies can be developed. In this paper, we propose an incremental algorithm involving adaptive periods. During these adaptive periods the incremental computation is restarted until a quality criterion is satisfied. This approach is compatible with classical formulations of the equations.