Alleviating mesh constraints: Model reduction, parallel time integration and high resolution homogenization

Chinesta, Francisco; Ammar, Amine; Lemarchand, François; Beauchêne, Pierre; Boust, Fabrice

doi:10.1016/j.cma.2007.07.022

Cited by 65 publications

(71 citation statements)

References 18 publications

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“…For accounting for all the microstructural details very fine meshes must be preferably used, however, fine meshes imply important computation time and computer resources. In this case the use of separated representations could be an appealing choice [9]. However, in some applications, the primal field is not the field of interest, and then one must define a more appropriate error estimator as a stopping criterion for the enrichment of a separated representation.…”

Section: Solving a 3d Modelmentioning

confidence: 99%

An error estimator for separated representations of highly multidimensional models

Ammar

Chinesta

Dı́ez

et al. 2010

Computer Methods in Applied Mechanics and Engineering

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108

109

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Keywords: Separated representations, Finite sums decomposition, Error estimation, Curse of dimensionality High dimensional models Fine modeling of the structure and mechanics of materials from the nanometric to the micrometric scales uses descriptions ranging from quantum to statistical mechanics. Most of these models consist of a partial differential equation defined in a highly multidimensional domain (e.g. Schrodinger equation, FokkerPlanck equations among many others). The main challenge related to these models is their associated curse of dimensionality. We proposed in some of our former works a new strategy able to circumvent the curse of dimensionality based on the use of separated representations (also known as finite sums decomposition). This technique proceeds by computing at each iteration a new sum that consists of a product of functions each one defined in one of the model coordinates. The issue related to error estimation has never been addressed. This paper presents a first attempt on the accuracy evaluation of such a kind of discretization techniques.

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Section: Solving a 3d Modelmentioning

confidence: 99%

An error estimator for separated representations of highly multidimensional models

Ammar

Chinesta

Dı́ez

et al. 2010

Computer Methods in Applied Mechanics and Engineering

Self Cite

108

109

View full text Add to dashboard Cite

show abstract

“…In the extreme case of meshes that are too fine, advanced solvers based on the use of separated representations (at the heart of the Proper Generalized Decomposition (PGD)) could be a valuable alternative [29,30].…”

Section: Calculating the Equivalent Thermal Conductivitymentioning

confidence: 99%

Thermal Conductivity of Suspension of Aggregating Nanometric Rods

Ammar

Chinesta

Heyd

2016

Entropy

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Enhancing thermal conductivity of simple fluids is of major interest in numerous applicative systems. One possibility of enhancing thermal properties consists of dispersing small conductive particles inside. However, in general, aggregation effects occur and then one must address systems composed of dispersed clusters composed of particles as well as the ones related to percolated networks. This papers analyzes the conductivity enhancement of different microstructures scaling from clusters dispersed into a simple matrix to the ones related to percolated networks exhibiting a fractal morphology.

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“…From these solutions, the KarhunenLoève decomposition [3] can be performed, allowing to extract the most relevant functions describing the solution evolution.…”

Section: Reduced Modelingmentioning

confidence: 99%

“…In the first part of this paper, we present the use of boundary element method (BEM) and DRM applied to unsteady heat transfer of injection moulds. The BEM software, developed at the CROMeP laboratory [2], was combined with an adaptive reduced modelling [3]. This procedure permits to reduce considerably the computing time during the linear system resolution in unsteady prob-lem.…”

Section: Introductionmentioning

confidence: 99%

Optimization of BEM-based Cooling Channels Injection Moulding Using Model Reduction

et al. 2008

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Today, around 30% of manufactured plastic goods rely on injection moulding. The cooling time can represent more than 70% of the injection cycle. In this process, heat transfer during the cooling step has a great influence both on the quality of the final parts that are produced, and on the moulding cycle time. Models based on a full 3D finite element method renders unpractical the use of optimization of the design and placement of the cooling channel in injection moulds. We have extended the use of boundary element method (BEM) to this process. We introduce in this paper a practical methodology to optimize both the position and the shape of the cooling channels in injection moulding processes. We couple the direct computation with an optimization algorithm such as SQP (Sequential Quadratic Programming). First, we propose an implementation of the model reduction in the BEM solver. This technique permits to reduce considerably the computing time during the linear system resolution (unsteady case). Secondly, we couple it with an optimization algorithm to evaluate its potentiality. For example, we can minimize the maximal temperature on the cavity surface subject to a temperature uniformity constraint. Thirdly, we present encouraging computational results on plastic parts that show that our optimization methodology is viable.

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Alleviating mesh constraints: Model reduction, parallel time integration and high resolution homogenization

Cited by 65 publications

References 18 publications

An error estimator for separated representations of highly multidimensional models

An error estimator for separated representations of highly multidimensional models

Thermal Conductivity of Suspension of Aggregating Nanometric Rods

Optimization of BEM-based Cooling Channels Injection Moulding Using Model Reduction

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