POD–ISAT: An efficient POD‐based surrogate approach with adaptive tabulation and fidelity regions for parametrized steady‐state PDE discrete solutions

Bui, Dung C.; Hamdaoui, Mohamed; Vuyst, Florian De

doi:10.1002/nme.4468

Cited by 2 publications

(3 citation statements)

References 55 publications

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“…This extension is obtained by increasing the distance of a centroid cluster to its boundary. Alternatively, to generate smooth transitions between clusters, ellipsoids of accuracy can be computed as in [32].…”

Section: Reduced-order Model Combined With Gnat Framework and Localizmentioning

confidence: 99%

Adaptive training of local reduced bases for unsteady incompressible Navier–Stokes flows

Hetmaniuk

2015

Numerical Meth Engineering

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SUMMARYThis report presents a numerical study of reduced-order representations for simulating incompressible Navier-Stokes flows over a range of physical parameters. The reduced-order representations combine ideas of approximation for nonlinear terms, of local bases, and of least-squares residual minimization. To construct the local bases, temporal snapshots for different physical configurations are collected automatically until an error indicator is reduced below a user-specified tolerance. An adaptive time-integration scheme is also employed to accelerate the generation of snapshots as well as the simulations with the reduced-order representations. The accuracy and efficiency of the different representations is compared with examples with parameter sweeps.

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Section: Reduced-order Model Combined With Gnat Framework and Localizmentioning

confidence: 99%

Adaptive training of local reduced bases for unsteady incompressible Navier–Stokes flows

Hetmaniuk

2015

Numerical Meth Engineering

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“…The first property (36) comes from the Legendre transformation (14). The property (37) comes from Equation (19).…”

Section: The Constitutive Relation Error and Its Partitionmentioning

confidence: 99%

“…Such an approach enables certification of outputs of interest [7], or error estimation of predictions obtained by using Reduced-Order Models [7][8][9][10][11]. Moreover, error estimation is mandatory in many model reduction of parametric Partial Differential Equations, when one needs to evaluate, in the parameter space, a trust region or a validity domain related to Reduced-Basis accuracy [12][13][14]. Error estimation is also mandatory to perform a priori model reduction by using greedy algorithms [15,16] or the A Priori Hyper-reduction method [4].…”

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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POD–ISAT: An efficient POD‐based surrogate approach with adaptive tabulation and fidelity regions for parametrized steady‐state PDE discrete solutions

Cited by 2 publications

References 55 publications

Adaptive training of local reduced bases for unsteady incompressible Navier–Stokes flows

Adaptive training of local reduced bases for unsteady incompressible Navier–Stokes flows

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

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