Localized Discrete Empirical Interpolation Method

AbstractWe present a subsampling strategy for the offline stage of the Reduced Basis Method. The approach is aimed at bringing down the considerable offline costs associated with using a finely-sampled training set. The proposed algorithm exploits the potential of the pivoted QR decomposition and the discrete empirical interpolation method to identify important parameter samples. It consists of two stages. In the first stage, we construct a low-fidelity approximation to the solution manifold over a fine training set. Then, for the available low-fidelity snapshots of the output variable, we apply the pivoted QR decomposition or the discrete empirical interpolation method to identify a set of sparse sampling locations in the parameter domain. These points reveal the structure of the parametric dependence of the output variable. The second stage proceeds with a subsampled training set containing a by far smaller number of parameters than the initial training set. Different subsampling strategies inspired from recent variants of the empirical interpolation method are also considered. Tests on benchmark examples justify the new approach and show its potential to substantially speed up the offline stage of the Reduced Basis Method, while generating reliable reduced-order models.

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Nonlinear Aerodynamic and Aeroelastic Model Reduction Using a Discrete Empirical Interpolation Method

AIAA Journal ◽

10.2514/1.j055143 ◽

2017 ◽

Vol 55 (2) ◽

pp. 624-637 ◽

Cited By ~ 12

Author(s):

W. Yao ◽

S. Marques

Keyword(s):

Model Reduction ◽

Interpolation Method ◽

Aeroelastic Model ◽

Discrete Empirical Interpolation Method ◽

Empirical Interpolation Method ◽

Nonlinear Aerodynamic ◽

Discrete Empirical Interpolation

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A Modified Discrete Empirical Interpolation Method for Reducing Non-Linear Structural Finite Element Models

Volume 7B: 9th International Conference on Multibody Systems, Nonlinear Dynamics, and Control ◽

10.1115/detc2013-13280 ◽

2013 ◽

Cited By ~ 8

Author(s):

Paolo Tiso ◽

Rob Dedden ◽

Daniel Rixen

Keyword(s):

Finite Element ◽

Interpolation Method ◽

Computational Cost ◽

Order Reduction ◽

Galerkin Projection ◽

Alternative Formulation ◽

Discrete Empirical Interpolation Method ◽

Empirical Interpolation Method ◽

The Cost ◽

Discrete Empirical Interpolation

Model Order Reduction (MOR) in nonlinear structural analysis problems in usually carried out by a Galerkin projection of the primary variables on a sensibly smaller space. However, the cost of computing the nonlinear terms is still of the order of the full system. The Discrete Empirical Interpolation Method (DEIM) is an effective algorithm to reduce the computational cost of the nonlinear terms of the discretized governing equations. However, its efficiency is diminished when applied to a Finite Element (FE) framework. We present here an alternative formulation of the DEIM that suits FE discretized problems and preserves the efficiency and the accuracy of the original DEIM method.

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