Acceleration of the spectral stochastic FEM using POD and element based discrete empirical approximation for a micromechanical model of heterogeneous materials with random geometry
From MaRDI portal
Publication:2175253
DOI10.1016/j.cma.2019.112689zbMath1441.74270OpenAlexW2987730291MaRDI QIDQ2175253
Paul Steinmann, Dmytro Pivovarov, Kai Willner
Publication date: 29 April 2020
Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.cma.2019.112689
Finite element methods applied to problems in solid mechanics (74S05) Micromechanics of solids (74M25) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Random materials and composite materials (74A40)
Related Items
A micromechanical mean‐field homogenization surrogate for the stochastic multiscale analysis of composite materials failure ⋮ Stochastic local FEM for computational homogenization of heterogeneous materials exhibiting large plastic deformations
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Modified SFEM for computational homogenization of heterogeneous materials with microstructural geometric uncertainties
- Reduced basis techniques for stochastic problems
- Homogenization-based constitutive models for magnetorheological elastomers at finite strain
- The GNAT method for nonlinear model reduction: effective implementation and application to computational fluid dynamics and turbulent flows
- Acceleration of uncertainty updating in the description of transport processes in heterogeneous materials
- Partitioned treatment of uncertainty in coupled domain problems: a separated representation approach
- Improving the \( k\)-\textit{compressibility} of hyper reduced order models with moving sources: applications to welding and phase change problems
- Model reduction in elastoplasticity: proper orthogonal decomposition combined with adaptive sub-structuring
- Homogenization of random heterogeneous media with inclusions of arbitrary shape modeled by XFEM
- Nonlinear model-order reduction for compressible flow solvers using the discrete empirical interpolation method
- Adaptive sparse polynomial chaos expansion based on least angle regression
- The LATIN multiscale computational method and the proper generalized decomposition
- A reduced spectral function approach for the stochastic finite element analysis
- A priori model reduction through proper generalized decomposition for solving time-dependent partial differential equations
- A priori hyperreduction method: an adaptive approach
- Solving elliptic boundary value problems with uncertain coefficients by the finite element method: the stochastic formulation
- Results and questions on a nonlinear approximation approach for solving high-dimensional partial differential equations
- On the size of RVE in finite elasticity of random composites
- The reduced model multiscale method (R3M) for the nonlinear homogenization of hyperelastic media at finite strains
- Heaviside enriched extended stochastic FEM for problems with uncertain material interfaces
- Simple estimation on effective transport properties of a random composite material with cylindrical fibres
- An adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations
- A multiscale stochastic finite element method on elliptic problems involving uncertainties
- A generalized spectral decomposition technique to solve a class of linear stochastic partial differential equations
- Galerkin v. least-squares Petrov-Galerkin projection in nonlinear model reduction
- On stochastic FEM based computational homogenization of magneto-active heterogeneous materials with random microstructure
- A numerical study of different projection-based model reduction techniques applied to computational homogenisation
- Examples of computational approaches for elliptic, possibly multiscale PDEs with random inputs
- An `empirical interpolation' method: Application to efficient reduced-basis discretization of partial differential equations
- A new approach for the stochastic analysis of finite element modelled structures with uncertain parameters.
- On solving elliptic stochastic partial differential equations
- An inverse micro-mechanical analysis toward the stochastic homogenization of nonlinear random composites
- On periodic boundary conditions and ergodicity in computational homogenization of heterogeneous materials with random microstructure
- Fuzzy uncertainty propagation in composites using Gram-Schmidt polynomial chaos expansion
- POD-DEIM model order reduction for strain-softening viscoplasticity
- Two reduction methods for stochastic FEM based homogenization using global basis functions
- Stochastic multiscale homogenization analysis of heterogeneous materials under finite deformations with full uncertainty in the microstructure
- Efficient model reduction of parametrized systems by matrix discrete empirical interpolation
- Comparative study of projection schemes for stochastic finite element analysis
- Determination of RVE size for random composites with local volume fraction variation
- An adaptive multi-element generalized polynomial chaos method for stochastic differential equations
- On the a priori model reduction: overview and recent developments
- A stochastic computational multiscale approach; application to MEMS resonators
- Multi-element stochastic reduced basis methods
- An extended stochastic finite element method for solving stochastic partial differential equations on random domains
- Generalized spectral decomposition method for solving stochastic finite element equations: invariant subspace problem and dedicated algorithms
- A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems
- Unified magnetomechanical homogenization framework with application to magnetorheological elastomers
- PHYSICAL INTERPRETATION OF THE PROPER ORTHOGONAL MODES USING THE SINGULAR VALUE DECOMPOSITION
- On micro-to-macro transitions for multi-scale analysis of non-linear heterogeneous materials: unified variational basis and finite element implementation
- Uncertainty quantification in homogenization of heterogeneous microstructures modeled by XFEM
- Discrete Empirical Interpolation in POD Model Order Reduction of Drift-Diffusion Equations in Electrical Networks
- Efficient Iterative Solvers for Stochastic Galerkin Discretizations of Log-Transformed Random Diffusion Problems
- An adaptive and efficient greedy procedure for the optimal training of parametric reduced-order models
- POD-based model reduction with empirical interpolation applied to nonlinear elasticity
- Nonlinear Model Reduction via Discrete Empirical Interpolation
- eXtended Stochastic Finite Element Method for the numerical simulation of heterogeneous materials with random material interfaces
- Recent advances on the use of separated representations
- Domain decomposition of stochastic PDEs: Theoretical formulations
- Reduced‐order modelling for linear heat conduction with parametrised moving heat sources
- Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations
- The Stochastic Perturbation Method for Computational Mechanics
- Localized Discrete Empirical Interpolation Method
- A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data
- Solution of stochastic partial differential equations using Galerkin finite element techniques