The Reference Point Method, a “hyperreduction” technique: Application to PGD-based nonlinear model reduction

Capaldo, Matteo; Guidault, Pierre‐Alain; Néron, David

doi:10.1016/j.cma.2017.04.033

Cited by 17 publications

(9 citation statements)

References 39 publications

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“…Unlike the one-dimensional problem introduced in Sect. 5.1, the calculation of the search direction operators is considerably expensive, so they are not calcu-lated at every iteration.The Reference Point Method, a hyper reduction technique, has been proposed in [6], and will be introduced in the future. In the current stage, search direction operators are only updated if the difference between two successive global solutions becomes lower than a certain tolerance.…”

Section: "L" Shaped Structurementioning

confidence: 99%

A LATIN-based model reduction approach for the simulation of cycling damage

et al. 2017

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The objective of this article is to introduce a new method including model order reduction for the life prediction of structures subjected to cycling damage. Contrary to classical incremental schemes for damage computation, a non-incremental technique, the LATIN method, is used herein as a solution framework. This approach allows to introduce a PGD model reduction technique which leads to a drastic reduction of the computational cost. The proposed framework is exemplified for structures subjected to cyclic loading, where damage is considered to be isotropic and micro-defect closure effects are taken into account. A difficulty herein for the use of the LATIN method comes from the state laws which can not be transformed into linear relations through an internal variable transformation. A specific treatment of this issue is introduced in this work.

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Section: "L" Shaped Structurementioning

confidence: 99%

A LATIN-based model reduction approach for the simulation of cycling damage

et al. 2017

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“…This is done offline with the PGD computation. Our answer is the so-called Reference Point Method (RPM) [4].…”

Section: Nonlinear Problems With Parametersmentioning

confidence: 99%

Extended-PGD Model Reduction for Nonlinear Solid Mechanics Problems Involving Many Parameters

Paillet

Néron

2017

Computational Methods in Applied Sciences

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Reduced models and especially those based on Proper Generalized Decomposition (PGD) are decision-making tools which are about to revolutionize many domains. Unfortunately, their calculation remains problematic for problems involving many parameters, for which one can invoke the "curse of dimensionality". The paper starts with the state-of-the-art for nonlinear problems involving stochastic parameters. Then, an answer to the challenge of many parameters is given in solid mechanics with the so-called "parameter-multiscale PGD", which is based on the Saint-Venant principle.

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“…As an alternative MOR technique, the PGD generates a reduced-order basis in an a priori manner through an iterative algorithm during the solution process. The POD and PGD methods have triggered a group of methods for reducing the dimensions of nonlinear models, including GNAT, 15,16 hyperreduction, 17,18 DEIM, 19,20 RPM, 21 POD-ECSW, 22 randomized SVD, 23,24 and MEM. 25 A POD-based method has been proposed to integrate the domain decomposition method to solve nonlinear structural problems under dynamic loads.…”

Section: Introductionmentioning

confidence: 99%

An adaptive model order reduction method for nonlinear seismic analysis of civil structures based on the elastic–plastic states

Fang

Wang

2021

Numerical Meth Engineering

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As an approach to evaluating the seismic performance of civil structures, nonlinear seismic analysis faces a challenge in terms of computational efficiency for high-fidelity simulations of large-scale finite element models. In this article, an adaptive model order reduction (AMOR) method is proposed for alleviating the computational burden of nonlinear seismic analysis based on elastic-plastic states. The elastic-plastic states are classified as the initial-elastic, plastic-deforming, and residual-elastic states. The finite element model of a civil structure is automatically partitioned into linear and nonlinear substructures according to the time-varying spatial distribution of the plastic deformation zone, and the Craig-Bampton method was employed to construct the reduced governing equations in each elastic-plastic state. An elastic-plastic-triggered reanalysis method was proposed to conduct a seamless transformation of the reduced governing equations between different elastic-plastic states. In the back-off step, the reduced response vectors are projected back to the physical coordinate space. In the reanalysis step, the response vectors are initialized, partitioned, and transformed onto the hybrid coordinate space spanned by reduced-order bases. Compared with a conventional time step integration method, the AMOR method yields comparative results with a higher computational efficiency.

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The Reference Point Method, a “hyperreduction” technique: Application to PGD-based nonlinear model reduction

Cited by 17 publications

References 39 publications

A LATIN-based model reduction approach for the simulation of cycling damage

A LATIN-based model reduction approach for the simulation of cycling damage

Extended-PGD Model Reduction for Nonlinear Solid Mechanics Problems Involving Many Parameters

An adaptive model order reduction method for nonlinear seismic analysis of civil structures based on the elastic–plastic states

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