Model Reduction for Heat Conduction with Radiative Boundary Conditions using the Modal Identification Method

Balima, O.; Favennec, Yann; Petit, Daniel

doi:10.1080/10407790701347357

Cited by 25 publications

(17 citation statements)

References 12 publications

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“…MIM uses concepts stemming from the automatics community and has been developed in heat transfer to identify low-order models in linear thermal diffusion processes from experimental data [29], and then has been extended to non-linear heat transfer [30,31]. An extension of the method to fluid flows has been proposed [32,33], the identification method being reformulated using the adjoint state method to compute the gradient of the cost function to be minimized [34].…”

Section: Nomenclaturementioning

confidence: 99%

Model reduction by the Modal Identification Method in forced convection: Application to a heated flow over a backward-facing step

Rouizi

Girault

Favennec

et al. 2010

International Journal of Thermal Sciences

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Section: Nomenclaturementioning

confidence: 99%

Model reduction by the Modal Identification Method in forced convection: Application to a heated flow over a backward-facing step

Rouizi

Girault

Favennec

et al. 2010

International Journal of Thermal Sciences

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“…On the one hand, the Proper Orthogonal Method coupled with the Galerkin projection (POD-G) has proved to be very efficient on fluid-type nonlinear problems where turbulence plays a non-negligible role [7][8][9]. On the other hand, the Modal Identification Method (MIM) has proved to be very efficient on diffusion-type nonlinear problems [10][11][12]. A comparison on a particular nonlinear diffusive problem between both the POD-Galerkin method and the Modal Identification Method recently proved that both methods are accurate and robust and that both can be formulated equivalently although the general ideas behind those two are completely different [13].…”

Section: Introductionmentioning

confidence: 99%

Numerical model reduction of 2D steady incompressible laminar flows: Application on the flow over a backward-facing step

Rouizi¹,

Favennec²,

Ventura³

et al. 2009

Journal of Computational Physics

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“…They reduce the computational complexity of optimization procedures or parametric analyses [1][2][3].…”

Section: Introductionmentioning

confidence: 99%

Estimation of the validity domain of hyper-reduction approximations in generalized standard elastoviscoplasticity

Ryckelynck

Gallimard

Jules

2015

Adv. Model. and Simul. in Eng. Sci.

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Background:We propose an a posteriori estimator of the error of hyper-reduced predictions for elastoviscoplastic problems. For a given fixed mesh, this error estimator aims to forecast the validity domain in the parameter space, of hyper-reduction approximations. This error estimator evaluates if the simulation outputs generated by the hyper-reduced model represent a convenient approximation of the outputs that the finite element simulation would have predicted. We do not account for the approximation error related to the finite element approximation upon which the hyper-reduction approximation is introduced. Methods: We restrict our attention to generalized standard materials. Upon use of incremental variational principles, we propose an error in constitutive relation. This error is split into three terms including a tailored norm of the hyper-reduction approximation error. This error norm is defined by using the convexity of an incremental potential introduced to state the constitutive equations. The second term of the a posteriori error is related to the stress recovery technique that generates stresses fulfilling the finite element equilibrium equations. The last term is a coupling term between the hyperreduction approximation error at each time step and the errors committed before this time step. Unfortunately, this last term prevents error certification. In this paper, we restrict our attention to outputs extracted by a Lipschitz function of the displacements. Results: In the proposed numerical examples, we show very good preliminary results in predicting the validity domain of hyper-reduction approximations. The average computational time of the predictions obtained by hyper reduction, is accelerated by a factor of 6 compared to that of finite element simulations. This speed-up incorporates the computational time devoted to the error estimation. Conclusions: The numerical implementation of the proposed error estimator is straightforward. It does not require the computation of the incremental potential. In the numerical results, the estimated validity domain of hyper-reduced approximations is inside the reference validity domain. This paper is a first attempt for a posteriori error estimation of hyper-reduction approximations.

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Model Reduction for Heat Conduction with Radiative Boundary Conditions using the Modal Identification Method

Cited by 25 publications

References 12 publications

Model reduction by the Modal Identification Method in forced convection: Application to a heated flow over a backward-facing step

Model reduction by the Modal Identification Method in forced convection: Application to a heated flow over a backward-facing step

Numerical model reduction of 2D steady incompressible laminar flows: Application on the flow over a backward-facing step

Estimation of the validity domain of hyper-reduction approximations in generalized standard elastoviscoplasticity

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