Results 241 to 250 of about 65,683 (285)
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Wavelet-Based Numerical Homogenization
SIAM Journal on Numerical Analysis, 1998Let \(L_\varepsilon\) be a family of operators indexed by a small parameter \(\varepsilon\) and let \(u_\varepsilon\) solve the equation \(L_\varepsilon u_\varepsilon= f\). If \(u_\varepsilon\to\overline u\), the homogenization problem can be roughly stated as to find an operator \(\overline L\) such that \(\overline L\overline u= f\).
Dorobantu, Mihai, Engquist, Björn
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Numerical = periodic homogenization
PAMM, 2018AbstractIn our work, we try to bridge the existing theory of classical homogenization and the practical methods in numerical homogenization. We suggest an effective coefficient, which stems from the LOD method and which is based on a triangulation of the underlying domain.
Daniel Peterseim, Dora Varga
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On Wavelet-Based Numerical Homogenization
Multiscale Modeling & Simulation, 2005This paper is devoted to subgrid scale models in the numerical solution of partial differential equations that involve information on different scales. To derive this model a wavelet-based method is used. The authors discuss different compact representations of the homogenized operator and show how to improve the efficiency of certain wavelet-based ...
Chertock, Alina, Levy, Doron
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Asymptotic and numerical homogenization
Acta Numerica, 2008Homogenization is an important mathematical framework for developing effective models of differential equations with oscillations. We include in the presentation techniques for deriving effective equations, a brief discussion on analysis of related limit processes and numerical methods that are based on homogenization principles.
Engquist, B., Souganidis, P. E.
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Numerical study of homogeneous nanodroplet growth
Journal of Colloid and Interface Science, 2015We investigate the axisymmetric homogeneous growth of 10-100 nm water nanodroplets on a substrate surface. The main mechanism of droplet growth is attributed to the accumulation of laterally diffusing water monomers, formed by the absorption of water vapour in the environment onto the substrate.
Quang Tran Si Bui +2 more
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Multilevel Monte Carlo Approaches for Numerical Homogenization [PDF]
Multiscale Modeling and Simulation, 2015 In this article, we study the application of Multi-Level Monte Carlo (MLMC) approaches to numerical random homogenization. Our objective is to compute the expectation of some functionals of the homogenized coefficients, or of the homogenized solutions. This is accomplished within MLMC by considering different levels of representative volumes (RVE), and,
Efendiev, Yalchin +2 more
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HOMOGENIZATION OF HAMILTON–JACOBI EQUATIONS: NUMERICAL METHODS
Mathematical Models and Methods in Applied Sciences, 2008We study approximation strategies for the limit problem arising in the homogenization of Hamilton–Jacobi equations. They involve first an approximation of the effective Hamiltonian then a discretization of the Hamilton–Jacobi equation with the approximate effective Hamiltonian.
CAMILLI, FABIO +2 more
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Wang Tilings in Numerical Homogenization
Applied Mechanics and Materials, 2016Stochastic Wang tiling has been shown to bring unexpected insights to microstructure representation efforts as it generalizes the conventional unit-cell approach. It allows to reconstruct stochastic realizations of the compressed medium without prior periodic assumptions on microstructural patterns.
Martin Doškář, Jan Novák
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The Black Box Multigrid Numerical Homogenization Algorithm
Journal of Computational Physics, 1998We propose a numerical approach for the homogenization of the permeability in models of single-phase saturated flow. Our approach is motivated by the observation that multiple length scales are captured automatically by robust multilevel iterative solvers, such as black box multigrid.
Moulton, J. David +2 more
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