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

2013 ◽  
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.

scholarly journals The use of POD–DEIM model order reduction for the simulation of nonlinear hygrothermal problems

2020 ◽  
Vol 172 ◽  
pp. 04002
Author(s):  
Tianfeng Hou ◽  
Karl Meerbergen ◽  
Staf Roels ◽  
Hans Janssen
Keyword(s):  
Interpolation Method ◽  
Computational Cost ◽  
Order Reduction ◽  
Illustrative Case ◽  
Hygrothermal Simulation ◽  
Discrete Empirical Interpolation Method ◽  
Empirical Interpolation Method ◽  
Illustrative Case Study ◽  
Volume Method ◽  
Proper Orthogonal

In this paper, the discrete empirical interpolation method (DEIM) and the proper orthogonal decomposition (POD) method are combined to construct a reduced order model to lessen the computational expense of hygrothermal simulation. To investigate the performance of the POD-DEIM model, HAMSTAD benchmark 2 is selected as the illustrative case study. To evaluate the accuracy of the POD-DEIM model as a function of the number of construction modes and interpolation points, the results of the POD-DEIM model are compared with a POD and a Finite Volume Method (FVM). Also, as the number of construction modes/interpolation points cannot entirely represent the computational cost of different models, the accuracies of the different models are compared as function of the calculation time, to provide a fair comparison of their computational performances. Further, the use of POD-DEIM to simulate a problem different from the training snapshot simulation is investigated. The outcomes show that with a sufficient number of construction modes and interpolation points the POD-DEIM model can provide an accurate result, and is capable of reducing the computational cost relative to the POD and FVM.

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