A three-dimensional enriched finite element method for nonlinear transient heat transfer in functionally graded materials

Malek, Mustapha; Izem, Nouh; Mohamed, M. Shadi; Seaı̈d, Mohammed

doi:10.1016/j.ijheatmasstransfer.2020.119804

Cited by 25 publications

(13 citation statements)

References 27 publications

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“…It has also been proven that the enrichment significantly reduce the error achieved using an order of magnitude less degrees of freedom. At the same time comparisons to the standard finite element method show a corresponding reduction in the computational time [15,16].…”

Section: Introductionmentioning

confidence: 89%

A Partition of unity finite element method for valuation American option under Black-Scholes model

kharrazi

Izem

Malek

et al. 2021

Moroccan Journal of Pure and Applied Analysis

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In this paper, we present an intelligent combination of partition of unity (PU) and finite element (FE) methods for valuing American option pricing problems governed by the Black-Scholes (BS) model. The model is based on a partial differential equation (PDE) from which one can deduce the Black-Scholes formula, which gives a theoretical estimated value of options using current stock prices, expected dividends, the option’s strike price, expected interest rates, time to expiration and expected volatility. Although the finite element method (FEM) seems to be an alternative tool for pricing options with a few applications reported in the literature, this combination called the Partition of Unity Finite Element Method (PUFEM) appears to offer many of the desired properties. The main advantage of the proposed approach is its ability to locally refine the solution by adapting an incorporated specific class of enrichment in the finite element space instead of generating a new fine mesh for the problem under study. Numerical computations are carried out to show a huge reduction in the number of degrees of freedom required to achieve a fixed accuracy which confirms that the PUFE method used is very efficient and gives better accuracy than the conventional FE method.

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Section: Introductionmentioning

confidence: 89%

A Partition of unity finite element method for valuation American option under Black-Scholes model

kharrazi

Izem

Malek

et al. 2021

Moroccan Journal of Pure and Applied Analysis

Self Cite

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“…By comparing V y profiles for both cases, it is shown, on the one hand, that as Ra decreases the velocity magnitude undergoes a significant diminution from V y,max ≃ 0:048 for Ra = 10 6 to V y,max ≃ 0 for Ra = 10 3 near the left and right walls. On the second hand, in the cold chip case, this magnitude decreases with respect to the hot case, V y,max ≃ 0:031 for Ra = 10 6 . This effect of fast and slow vertical circulation in the hot and cold chip cases, respectively, induced by the temperature gradient vanishes far from the walls ð0:2 ≲ X ≲ 0:8Þ.…”

Section: Flow Property Discussionmentioning

confidence: 84%

“…In the hybrid schemes, besides the classical LBM used to describe the hydrodynamic flow properties, the finite difference method (FDM) can be used to calculate the flow temperature distribution [5]. In addition, recent works are focused on the finite element method (FEM) based solvers to simulate transient heat transfer in composite materials where the thermal conductivity is also dependent on the temperature [6], diffusion [7], and time-dependent value problems [8].…”

Section: Introductionmentioning

confidence: 99%

Heat Transfer of Gas Flow within a Partially Heated or Cooled Square Cavity

Hssikou

Elguennouni

Baliti

et al. 2020

Modelling and Simulation in Engineering

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Natural convection of gas flow (air) confined within an enclosed square-section cavity is investigated numerically using the lattice Boltzmann method (LBM). The right (left) side of the enclosure is partially heated (cooled) by a hot (cold) chip, while the left (right) one is completely kept at cold (hot) temperature. However, the horizontal walls and vertical parts near the chip are kept adiabatic. The buoyancy effect induced by the gravity acceleration, related to the convection force, is evaluated through the Rayleigh number in the range of 1 0 3 − 1 0 6 (laminar regime). The wall heating-ratio effect on the flow properties such as temperature and velocity profiles was examined. The heat transfer is analyzed through the Nusselt number for different chip lengths. Results show that the wall heat ratio has an interesting effect on the flow behavior. Results show good agreement with those of full natural convection in the literature, experimental, and simulation data.

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“…FEM has been widely used in most areas of engineering, most frequently in the aviation, automotive, and machine industries for strength calculations and optimization of the forming processes. FEM makes it possible to simulate the flow of fluids [17] and heat transfer problems [18,19]. The correctness of the numerical model is primarily determined by the boundary conditions and the adopted constitutive model of the material [20].…”

Section: Finite Element Methodsmentioning

confidence: 99%

Multiphysics Modeling and Numerical Simulation in Computer-Aided Manufacturing Processes

Trzepieciński

Dell’Isola

Lemu

2021

Metals

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The concept of Industry 4.0 is defined as a common term for technology and the concept of new digital tools to optimize the manufacturing process. Within this framework of modular smart factories, cyber-physical systems monitor physical processes creating a virtual copy of the physical world and making decentralized decisions. This article presents a review of the literature on virtual methods of computer-aided manufacturing processes. Numerical modeling is used to predict stress and temperature distribution, springback, material flow, and prediction of phase transformations, as well as for determining forming forces and the locations of potential wrinkling and cracking. The scope of the review has been limited to the last ten years, with an emphasis on the current state of knowledge. Intelligent production driven by the concept of Industry 4.0 and the demand for high-quality equipment in the aerospace and automotive industries forces the development of manufacturing techniques to progress towards intelligent manufacturing and ecological production. Multi-scale approaches that tend to move from macro- to micro- parameters become very important in numerical optimization programs. The software requirements for optimizing a fully coupled thermo-mechanical microstructure then increase rapidly. The highly advanced simulation programs based on our knowledge of physical and mechanical phenomena occurring in non-homogeneous materials allow a significant acceleration of the introduction of new products and the optimization of existing processes.

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A three-dimensional enriched finite element method for nonlinear transient heat transfer in functionally graded materials

Cited by 25 publications

References 27 publications

A Partition of unity finite element method for valuation American option under Black-Scholes model

A Partition of unity finite element method for valuation American option under Black-Scholes model

Heat Transfer of Gas Flow within a Partially Heated or Cooled Square Cavity

Multiphysics Modeling and Numerical Simulation in Computer-Aided Manufacturing Processes

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