The Tailored Finite Point Method

Han, Houde; Huang, Zhongyi

doi:10.1515/cmam-2014-0012

Cited by 16 publications

(8 citation statements)

References 52 publications

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“…Meshless methods include SPH, the mesh-free method [147], the finite point method [148,149], and the Galerkin meshless method [150]. The common feature of the meshless methods is that the local approximation of the function that is being searched for is based only on the values of this function at individual selected points in the area.…”

Section: Meshless 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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Section: Meshless Methodsmentioning

confidence: 99%

Multiphysics Modeling and Numerical Simulation in Computer-Aided Manufacturing Processes

Trzepieciński

Dell’Isola

Lemu

2021

Metals

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“…i,j and g n i,j = g +,n i,j + g −,n i,j , so ρ n i,j = f n i,j + g n i,j : adding equations in (26) gives,…”

Section: Consistency With Damped Diffusive Limits In 2dmentioning

confidence: 99%

“…Hereafter, both IMEX schemes (26) and (34) were set up on the same computational grid with ε = 10 ) .…”

Section: Diffusive Scalingmentioning

confidence: 99%

Diffusive limits of 2D well-balanced schemes for kinetic models of neutron transport

2021

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Two-dimensional dissipative and isotropic kinetic models, like the ones used in neutron transport theory, are considered. Especially, steady-states are expressed for constant opacity and damping, allowing to derive a scattering S-matrix and corresponding "truly 2D well-balanced" numerical schemes. A first scheme is obtained by directly implementing truncated Fourier–Bessel series, whereas another proceeds by applying an exponential modulation to a former, conservative, one. Consistency with the asymptotic damped parabolic approximation is checked for both algorithms. A striking property of some of these schemes is that they can be proved to be both 2D well-balanced and asymptotic-preserving in the parabolic limit, even when setting up IMEX time-integrators: see Corollaries 3.4 and A.1. These findings are further confirmed by means of practical benchmarks carried out on coarse Cartesian computational grids.

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“…Recently, a new kind of numerical methods, called "tailored finite point method (TFPM)" [6][7][8]11,12], has been developed. The method is tailored to some particular properties of the reduced problem, then we can get the well approximated solution on very coarse mesh.…”

Section: Introductionmentioning

confidence: 99%

Monotone finite point method for non-equilibrium radiation diffusion equations

Huang

2015

Bit Numer Math

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In this paper, we propose the monotone tailored-finite-point method for solving the non-equilibrium radiation diffusion equations. We first give two tailored finite point schemes for the nonlinear parabolic equation in one-dimensional case, then extend the idea to solve the radiation diffusion problem in 1D as well as 2D. By using variable substitute, our method satisfies the discrete maximum principle automatically, thus preserves the properties of monotonicity and positivity. Numerical results show that our method can capture the sharp front and can be accommodated to discontinues diffusion coefficient.

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The Tailored Finite Point Method

Cited by 16 publications

References 52 publications

Multiphysics Modeling and Numerical Simulation in Computer-Aided Manufacturing Processes

Multiphysics Modeling and Numerical Simulation in Computer-Aided Manufacturing Processes

Diffusive limits of 2D well-balanced schemes for kinetic models of neutron transport

Monotone finite point method for non-equilibrium radiation diffusion equations

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