An algorithmic comparison of the Hyper-Reduction and the Discrete Empirical Interpolation Method for a nonlinear thermal problem

Felix Fritzen (1) , Bernard Haasdonk (1) , David Ryckelynck (2) , Sebastian Schöps (3)

1 University of Stuttgart
2 CDM - Centre des Matériaux
3 TU Darmstadt - Technische Universität Darmstadt - Technical University of Darmstadt

A novel algorithmic discussion of the methodological and numerical differences of competing parametric model reduction techniques for nonlinear problems are presented. First, the Galerkin reduced basis (RB) formulation is presented which fails at providing significant gains with respect to the computational efficiency for nonlinear problems. Renown methods for the reduction of the computing time of nonlinear reduced order models are the Hyper-Reduction and the (Discrete) Empirical Interpolation Method (EIM, DEIM). An algorithmic description and a methodological comparison of both methods are provided. The accuracy of the predictions of the hyper-reduced model and the (D)EIM in comparison to the Galerkin RB is investigated. All three approaches are applied to a simple uncertainty quantification of a planar nonlinear thermal conduction problem. The results are compared to computationally intense finite element simulations.

Mots clés: model order reduction (MOR); reduced basis model order reduction (RB MOR); uncertainty quantification (UQ); (discrete) empirical interpolation method (EIM DEIM); hyper-reduction (HR)

Domaines: Physique mathématique [math-ph]; Analyse numérique [cs.NA]

Felix Fritzen, Bernard Haasdonk, David Ryckelynck, Sebastian Schöps. An algorithmic comparison of the Hyper-Reduction and the Discrete Empirical Interpolation Method for a nonlinear thermal problem. Mathematical and computational applications, 2018, 23 (11), pp.8. ⟨10.3390/mca23010008⟩. ⟨hal-01759176⟩