Computing homogenized coefficientsviamultiscale representation and hierarchical hybrid grids
DOI10.1051/m2an/2020024zbMath1481.65255arXiv1905.06751OpenAlexW3015621600MaRDI QIDQ4958833
Antti Hannukainen, Jean-Christophe Mourrat, Harmen T. Stoppels
Publication date: 15 September 2021
Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1905.06751
Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27)
Related Items (1)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Special quasirandom structures: a selection approach for stochastic homogenization
- Analyticity of homogenized coefficients under Bernoulli perturbations and the Clausius-Mossotti formulas
- Mesoscopic higher regularity and subadditivity in elliptic homogenization
- First-order expansion of homogenized coefficients under Bernoulli perturbations
- An optimal variance estimate in stochastic homogenization of discrete elliptic equations
- Variance decay for functionals of the environment viewed by the particle
- A regularity theory for random elliptic operators
- The local microscale problem in the multiscale modeling of strongly heterogeneous media: Effects of boundary conditions and cell size
- Annealed estimates on the Green function
- A multiscale finite element method for elliptic problems in composite materials and porous media
- Quantitative results on the corrector equation in stochastic homogenization
- Examples of computational approaches for elliptic, possibly multiscale PDEs with random inputs
- Efficient methods for the estimation of homogenized coefficients
- Tetrahedral grid refinement
- Spectral measure and approximation of homogenized coefficients
- Improving on computation of homogenized coefficients in the periodic and quasi-periodic settings
- Averaging of dilute random media: a rigorous proof of the Clausius-Mossotti formula
- Quantification of ergodicity in stochastic homogenization: optimal bounds via spectral gap on Glauber dynamics
- Exponential decay of the resonance error in numerical homogenization via parabolic and elliptic cell problems
- The choice of representative volumes in the approximation of effective properties of random materials
- The additive structure of elliptic homogenization
- On homogenization and scaling limit of some gradient perturbations of a massless free field
- An optimal error estimate in stochastic homogenization of discrete elliptic equations
- Quantitative
- FFT, FMM, or Multigrid? A comparative Study of State-Of-the-Art Poisson Solvers for Uniform and Nonuniform Grids in the Unit Cube
- Numerical approximation of effective coefficients in stochastic homogenization of discrete elliptic equations
- Some variance reduction methods for numerical stochastic homogenization
- A Numerical Approach Related to Defect-Type Theories for Some Weakly Random Problems in Homogenization
- Numerical study in stochastic homogenization for elliptic partial differential equations: Convergence rate in the size of representative volume elements
- Hierarchical hybrid grids: data structures and core algorithms for multigrid
- Geometric aspects of averaging
- Multiscale Finite Element Methods
- Ergodic theorems for superadditive processes.
- Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients
- Elliptic Regularity and Quantitative Homogenization on Percolation Clusters
- Elements of Mathematical Foundations for Numerical Approaches for Weakly Random Homogenization Problems
- The Clausius--Mossotti Formula for Dilute Random Media of Perfectly Conducting Inclusions
- An Embedded Corrector Problem for Homogenization. Part I: Theory
- Random walk in random environment, corrector equation and homogenized coefficients: from theory to numerics, back and forth
- The Clausius--Mossotti Formula in a Dilute Random Medium with Fixed Volume Fraction
- Quantitative Stochastic Homogenization and Large-Scale Regularity
- An informal introduction to quantitative stochastic homogenization
- The Mathematical Theory of Finite Element Methods
- Generalized Clausius-Mossotti formula for random composite with circular fibers.
- Lipschitz regularity for elliptic equations with random coefficients
- Reduction in the resonance error in numerical homogenization. II: Correctors and extrapolation
This page was built for publication: Computing homogenized coefficientsviamultiscale representation and hierarchical hybrid grids