Efficient hyper reduced-order model (HROM) for parametric studies of the 3D thermo-elasto-plastic calculation

Zhang, Yancheng; Combescure, Alain; Gravouil, Anthony

doi:10.1016/j.finel.2015.04.009

Cited by 18 publications

(27 citation statements)

References 24 publications

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“…In the area of welding simulations, MORs are less successful. Recently, the hyper‐reduction method has been applied to thermo‐elasto‐plastic calculations . The inefficiency due to the nonlinearity is reduced by considering a reduced integration domain.…”

Section: Introductionmentioning

confidence: 99%

“…framework. [2][3][4][5][6][7][8][9] The main drawback of such approaches remains in the loss of efficiency when dealing with nonlinear problems with high parametric dependency, although several approaches, eg, the empirical interpolation method (and its discrete counterpart discrete empirical interpolation method), 10,11 the hyper-reduction methods, 5,12,13 and the asymptotic numerical method [14][15][16] can be introduced to accelerate the computations.…”

mentioning

confidence: 99%

“…Recently, the hyper-reduction method has been applied to thermo-elasto-plastic calculations. 13,33 The inefficiency due to the nonlinearity is reduced by considering a reduced integration domain. Significant reduction of the computational cost has been obtained.…”

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confidence: 99%

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Adaptive sparse grid based HOPGD: Toward a nonintrusive strategy for constructing space‐time welding computational vademecum

Blal

Gravouil

2018

Numerical Meth Engineering

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Summary Simulation‐based engineering usually needs the construction of computational vademecum to take into account the multiparametric aspect. One example concerns the optimization and inverse identification problems encountered in welding processes. This paper presents a nonintrusive a posteriori strategy for constructing quasi‐optimal space‐time computational vademecum using the higher‐order proper generalized decomposition method. Contrary to conventional tensor decomposition methods, based on full grids (eg, parallel factor analysis/higher‐order singular value decomposition), the proposed method is adapted to sparse grids, which allows an efficient adaptive sampling in the multidimensional parameter space. In addition, a residual‐based accelerator is proposed to accelerate the higher‐order proper generalized decomposition procedure for the optimal aspect of computational vademecum. Based on a simplified welding model, different examples of computational vademecum of dimension up to 6, taking into account both geometry and material parameters, are presented. These vademecums lead to real‐time parametric solutions and can serve as handbook for engineers to deal with optimization, identification, or other problems related to repetitive task.

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Section: Introductionmentioning

confidence: 99%

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confidence: 99%

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Adaptive sparse grid based HOPGD: Toward a nonintrusive strategy for constructing space‐time welding computational vademecum

Blal

Gravouil

2018

Numerical Meth Engineering

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“…T r−o gathers both the CPU time required for the training of the ROMs, and the CPU time to advance in time the solution for all the sub-domains. While the training of the ROMs can be optimized through a so-called thin SVD procedure [15,51] in place of the standard one in Eq. (21), the duration of the reduced-order analysis is obviously affected by t end (see Algorithm 1).…”

Section: Numerical Examplesmentioning

confidence: 99%

Coupled domain decomposition–proper orthogonal decomposition methods for the simulation of quasi-brittle fracture processes

Corigliano

Confalonieri

Dossi

et al. 2016

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

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In this paper, we discuss a strategy to reduce the computational costs of the simulation of dynamic fracture processes in quasi-brittle materials, based on a combination of domain decomposition (DD) and model order reduction (MOR) techniques. Fracture processes are simulated by means of three-dimensional finite element models in which use is made of cohesive elements, introduced on-the-fly wherever a cracking criterion is attained. The body is initially subdivided into sub-domains; for each sub-domain MOR is obtained through a proper orthogonal decomposition (POD) of the equations governing its evolution, until when it starts getting cracked. After crack inception within a sub-domain, the solution is switched back to the original full-order model for that sub-domain only. The computational gain attained through the coupled use of DD and POD thus depends on the geometry of the body, on the topology of sub-domains and, on top of all, on the spreading of cracking induced by load conditions. Numerical examples concerning well-established fracture tests are used for validation, and the attainable reduction of the computing time is discussed at varying decomposition into sub-domains, even in the absence of a full exploitation of parallel computing potentialities.

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“…Then the solution of this reduced problem is decomposed using POD and projects the full-order model onto low-dimensional reduced bases [15]. In addition, various interpolation methods are reported to get the adaptive RB for parametric studies [12,[16][17][18]. However, the accuracy of the ROM strongly depends on the relevancy of the selected RB [15,19,20].…”

Section: Introductionmentioning

confidence: 99%

Efficient hyper‐reduced‐order model (HROM) for thermal analysis in the moving frame

Zhang

Combescure

Gravouil

2017

Numerical Meth Engineering

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International audienceThe hyper-reduced-order model (HROM) is proposed for the thermal calculation with a constant moving thermal load. Firstly, the constant velocity transient process is simplified to a steady-state process in the moving frame. Secondly, the control volume is determined by the temperature rate, and the thermal equilibrium equation in the moving frame is derived by introducing an advective term containing the loading velocity. Thirdly, the HROM is performed on the control volume with a moving frame formulation. This HROM has been applied to the thermal loading on brick and ring disk specimens with a CPU gain of the order of 7 (107). In addition, two strategies are proposed for the HROM to improve its precision. Moreover, the high efficiency and high accuracy are kept for the parametric studies on thermal conductivity and amplitude of heat flux based on the developed HRO

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Efficient hyper reduced-order model (HROM) for parametric studies of the 3D thermo-elasto-plastic calculation

Cited by 18 publications

References 24 publications

Adaptive sparse grid based HOPGD: Toward a nonintrusive strategy for constructing space‐time welding computational vademecum

Adaptive sparse grid based HOPGD: Toward a nonintrusive strategy for constructing space‐time welding computational vademecum

Coupled domain decomposition–proper orthogonal decomposition methods for the simulation of quasi-brittle fracture processes

Efficient hyper‐reduced‐order model (HROM) for thermal analysis in the moving frame

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