Aspects of computational homogenization at finite deformations: a unifying review from Reuss' to Voigt's bound
The objective of this contribution is to present a unifying review on strain-driven
computational homogenization at finite strains, thereby elaborating on computational …
computational homogenization at finite strains, thereby elaborating on computational …
[HTML][HTML] Deep CNNs as universal predictors of elasticity tensors in homogenization
B Eidel - Computer Methods in Applied Mechanics and …, 2023 - Elsevier
In the present work, 3D convolutional neural networks (CNNs) are trained to link random
heterogeneous, multiphase materials to their elastic macroscale stiffness thus replacing …
heterogeneous, multiphase materials to their elastic macroscale stiffness thus replacing …
Quantification of ergodicity in stochastic homogenization: optimal bounds via spectral gap on Glauber dynamics
We study quantitatively the effective large-scale behavior of discrete elliptic equations on the
lattice\mathbb Z^ d Z d with random coefficients. The theory of stochastic homogenization …
lattice\mathbb Z^ d Z d with random coefficients. The theory of stochastic homogenization …
An optimal variance estimate in stochastic homogenization of discrete elliptic equations
A Gloria, F Otto - 2011 - projecteuclid.org
We consider a discrete elliptic equation on the d-dimensional lattice ℤ d with random
coefficients A of the simplest type: they are identically distributed and independent from …
coefficients A of the simplest type: they are identically distributed and independent from …
Optimal local approximation spaces for generalized finite element methods with application to multiscale problems
The paper addresses a numerical method for solving second order elliptic partial differential
equations that describe fields inside heterogeneous media. The scope is general and treats …
equations that describe fields inside heterogeneous media. The scope is general and treats …
[HTML][HTML] Representative volume elements for matrix-inclusion composites-a computational study on the effects of an improper treatment of particles intersecting the …
We investigate volume-element sampling strategies for the stochastic homogenization of
particle-reinforced composites and show, via computational experiments, that an improper …
particle-reinforced composites and show, via computational experiments, that an improper …
Domain decomposition for multiscale PDEs
We consider additive Schwarz domain decomposition preconditioners for piecewise linear
finite element approximations of elliptic PDEs with highly variable coefficients. In contrast to …
finite element approximations of elliptic PDEs with highly variable coefficients. In contrast to …
Solving multiscale elliptic problems by sparse radial basis function neural networks
Z Wang, M Chen, J Chen - Journal of Computational Physics, 2023 - Elsevier
Abstract Machine learning has been successfully applied to various fields of scientific
computing in recent years. For problems with multiscale features such as flows in porous …
computing in recent years. For problems with multiscale features such as flows in porous …
Subspace decomposition based DNN algorithm for elliptic type multi-scale PDEs
While deep learning algorithms demonstrate a great potential in scientific computing, its
application to multi-scale problems remains to be a big challenge. This is manifested by the …
application to multi-scale problems remains to be a big challenge. This is manifested by the …
Multiscale-spectral GFEM and optimal oversampling
In this work we address the Multiscale Spectral Generalized Finite Element Method (MS-
GFEM) developed in Babuška and Lipton (2011). We outline the numerical implementation …
GFEM) developed in Babuška and Lipton (2011). We outline the numerical implementation …