Adaptive Finite Element Refinement

Zienkiewicz, O.C.; Taylor, Robert L.; Zhu, J.Z.

doi:10.1016/b978-1-85617-633-0.00016-2

Cited by 467 publications

(687 citation statements)

References 35 publications

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“…For µ > 0 the solution of (2) can be obtained using numerical solution techniques such as the finite element method (e.g. (Zienkiewicz and Taylor, 1991)). In order to account for variable (but deterministic) population sizes we set N (t) = N ρ(t) and the coefficients a and b in equation (1) …”

Section: Summary and Discussionmentioning

confidence: 99%

A non-equilibrium neutral model for analysing cultural change

Kandler

Shennan

2013

Journal of Theoretical Biology

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This is the accepted version of the paper.This version of the publication may differ from the final published version. Abstract. Neutral evolution is a frequently used model to analyse changes in frequencies of cultural variants over time. Variants are chosen to be copied according to their relative frequency and new variants are introduced by a process of random mutation. Here we present a non-equilibrium neutral model which accounts for temporally varying population sizes and mutation rates and makes it possible to analyse the cultural system under consideration at any point in time. This framework gives an indication whether observed changes in the frequency distributions of a set of cultural variants between two time points are consistent with the random copying hypothesis. We find that the likelihood of the existence of the observed assemblage at the end of the considered time period (expressed by the probability of the observed number of cultural variants present in the population during the whole period under neutral evolution) is a powerful indicator of departures from neutrality. Further, we study the effects of frequency-dependent selection on the evolutionary trajectories and present a case study of change in the decoration of pottery in early Neolithic Central Europe. Based on the framework developed we show that neutral evolution is not an adequate description of the observed changes in frequency. Permanent repository link

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Section: Summary and Discussionmentioning

confidence: 99%

A non-equilibrium neutral model for analysing cultural change

Kandler

Shennan

2013

Journal of Theoretical Biology

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“…[30]) are described in [20] in detail and will not be repeated here. The elements are isoparametric hexahedral, and given the particular geometry of the TEs the mesh is structured.…”

Section: Finite Element Formulationmentioning

confidence: 99%

“…These partial differential equations can be discretized following the Galerkin method (viz. [30] for details), to give a specially developed FE algorithm. Five degrees-of-freedom (dof) are required to study elastothermoelectric couplings in three-dimensions (3D): three displacements, temperature and voltage.…”

Section: Finite Element Formulationmentioning

confidence: 99%

Elasto-thermoelectric non-linear, fully coupled, and dynamic finite element analysis of pulsed thermoelectrics

Pérez-Aparicio

Palma

Moreno-Navarro

2016

Applied Thermal Engineering

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This paper presents a numerical study on the influence of pulsed electric signals applied to the overcooling of thermoelectric devices. To this end, an experimental setup taken from the literature and a commercial cell are simulated using a complete, specially developed research finite element code. The electro-thermal coupling is extended to include the elastic field, demonstrating that the increment of cooling can produce mechanical failure. Numerical results are developed and the variation of overcooling versus pulse gain and versus duration is validated towards a new analytical expression and the experimental data. The issue of optimal intensity at steady-state is also newly developed. Thermal and mechanical trends are presented using constant and variable (with temperature) material properties for a single thermoelement. While some of the first trends are similar to those of published works, others are different or directly new, all closer to those of the experiments. The mechanical results have not been thoroughly studied until recently. The three-dimensional finite element mesh includes non-thermoelectric materials that are fundamental for the current study. Distribution of stresses during steady and transient states are shown inside the thermoelement, for five components and for the combined Tresca stress. Concentrations at corners of the lower side appear close to the cold face. Due to these concentrations, 27-node isoparametric, quadratic brick elements are used. It is shown that the mechanical field is an important factor in the design of pulsed thermoelectrics, since for practical applications the stress levels are close or slightly above the admissible limits.

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“…Numerical techniques such as Ab-Initio [8], Discrete Element Method [9,10], Discrete Dislocation Dynamics [11], Finite Element Method [12,13] and Molecular Dynamics [14][15][16] have been used to study contact/friction problems. Two of the most classical techniques are the Finite Element Method [17,18] and the Molecular Dynamics [19]. A large literature has had recourse to the Finite Element Method, which is a computationally efficient strategy, to model contact at the asperity level [12,[20][21][22].…”

Section: Modeling Techniques Of Contact At Nanoscalementioning

confidence: 99%

MD/FE Multiscale Modeling of Contact

Ramisetti

Anciaux

Molinari

2014

Fundamentals of Friction and Wear on the Nanoscale

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Limitations of single scale approaches to study the complex physics involved in friction have motivated the development of multiscale models. We review the state-of-the-art multiscale models that have been developed up to date. These have been successfully applied to a variety of physical problems, but that were limited, in most cases, to zero Kelvin studies. We illustrate some of the technical challenges involved with simulating a frictional sliding problem, which by nature generates a large amount of heat. These challenges can be overcome by a proper usage of spatial filters, which we combine to a direct finite-temperature multiscale approach coupling molecular dynamics with finite elements. The basic building block relies on the proper definition of a scale transfer operator using the least square minimization and spatial filtering. Then, the restitution force from the generalized Langevin equation is modified to perform a two-way thermal coupling between the two models. Numerical examples are shown to illustrate the proposed coupling formulation.

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Adaptive Finite Element Refinement

Cited by 467 publications

References 35 publications

A non-equilibrium neutral model for analysing cultural change

A non-equilibrium neutral model for analysing cultural change

Elasto-thermoelectric non-linear, fully coupled, and dynamic finite element analysis of pulsed thermoelectrics

MD/FE Multiscale Modeling of Contact

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