Results 11 to 20 of about 65,683 (285)
The role of numerical integration in numerical homogenization* [PDF]
ESAIM: Proceedings and Surveys, 2015 Finite elements methods (FEMs) with numerical integration play a central role in numerical homogenization methods for partial differential equations with multiple scales, as the effective data in a homogenization problem can only be ...
Abdulle Assyr
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Numerical Homogenization of Heterogeneous Fractional Laplacians [PDF]
Multiscale Modeling & Simulation, 2017 In this paper, we develop a numerical multiscale method to solve the fractional Laplacian with a heterogeneous diffusion coefficient. When the coefficient is heterogeneous, this adds to the computational costs.
Brown, Donald L. +2 more
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Numerical homogenization of H(curl)-problems [PDF]
SIAM Journal on Numerical Analysis, 2017 If an elliptic differential operator associated with an $\mathbf{H}(\mathrm{curl})$-problem involves rough (rapidly varying) coefficients, then solutions to the corresponding $\mathbf{H}(\mathrm{curl})$-problem admit typically very low regularity, which ...
Gallistl, Dietmar +2 more
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Reduced-order modelling numerical homogenization [PDF]
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2014 A general framework to combine numerical homogenization and reduced-order modelling techniques for partial differential equations (PDEs) with multiple scales is described. Numerical homogenization methods are usually efficient to approximate the effective solution of PDEs with multiple scales.
Abdulle Assyr, Bai Yun
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Homogeneous numerical semigroups [PDF]
Semigroup Forum, 2018 We introduce the concept of homogeneous numerical semigroups and show that all homogeneous numerical semigroups with Cohen-Macaulay tangent cones are of homogeneous type. In embedding dimension three, we classify all numerical semigroups of homogeneous type in to numerical semigroups with complete intersection tangent cones and the homogeneous ones ...
Jafari, Raheleh, Zarzuela, Santiago
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Numerical homogenization beyond scale separation [PDF]
Acta Numerica, 2021 Numerical homogenization is a methodology for the computational solution of multiscale partial differential equations. It aims at reducing complex large-scale problems to simplified numerical models valid on some target scale of interest, thereby accounting for the impact of features on smaller scales that are otherwise not resolved. While constructive
Altmann, Robert +2 more
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Numerical Computation of Homogeneous Slope Stability [PDF]
Computational Intelligence and Neuroscience, 2015 To simplify the computational process of homogeneous slope stability, improve computational accuracy, and find multiple potential slip surfaces of a complex geometric slope, this study utilized the limit equilibrium method to derive expression equations of overall and partial factors of safety.
Xiao, Shuangshuang +3 more
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Numerical homogenization of fractal interface problems
ESAIM: Mathematical Modelling and Numerical Analysis, 2022 We consider the numerical homogenization of a class of fractal elliptic interface problems inspired by related mechanical contact problems from the geosciences. A particular feature is that the solution space depends on the actual fractal geometry.
Kornhuber, Ralf +2 more
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Numerical Homogenization of Monotone Elliptic Operators [PDF]
Multiscale Modeling & Simulation, 2003 The authors present a numerical homogenization technique for nonlinear elliptic equations. The convergence of the numerical procedure is presented for the general case using \(G\)-convergence theory. To calculate the fine scale oscillations of the solutions, the authors propose a stochastic two-scale corrector, where one is a numerical scale and the ...
Efendiev, Yalchin, Pankov, Alexander
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Large enhancement of the effective second-order nonlinearity in graphene metasurfaces [PDF]
, 2019 Using a powerful homogenization technique, one- and two-dimensional graphene metasurfaces are homogenized both at the fundamental frequency (FF) and second harmonic (SH).
Panoiu, N. C., Ren, Qun, You, J. W.
core +2 more sources