On the capabilities of the polynomial chaos expansion method within SFE analysis -- an overview
From MaRDI portal
Publication:2443839
DOI10.1007/s11831-011-9058-5zbMath1284.74129OpenAlexW1983874447WikidataQ113323897 ScholiaQ113323897MaRDI QIDQ2443839
H. M. Panayirci, Gerhard Iwo Schuëller
Publication date: 8 April 2014
Published in: Archives of Computational Methods in Engineering (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s11831-011-9058-5
Finite element methods applied to problems in solid mechanics (74S05) Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids (74-02) Stochastic and other probabilistic methods applied to problems in solid mechanics (74S60)
Related Items
Subspace inverse power method and polynomial chaos representation for the modal frequency responses of random mechanical systems ⋮ Stochastic analysis using the generalized perturbation stable node-based smoothed finite element method ⋮ An interval random perturbation method for structural-acoustic system with hybrid uncertain parameters ⋮ Stochastic analysis of structures under limited observations using kernel density estimation and arbitrary polynomial chaos expansion ⋮ Efficient uncertainty quantification in stochastic finite element analysis based on functional principal components ⋮ Unified polynomial expansion for interval and random response analysis of uncertain structure-acoustic system with arbitrary probability distribution ⋮ Condensed SFEs for nonlinear mechanical problems ⋮ Hybrid uncertainty propagation in structural-acoustic systems based on the polynomial chaos expansion and dimension-wise analysis ⋮ A copula-based perturbation stochastic method for fiber-reinforced composite structures with correlations
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Reduced chaos decomposition with random coefficients of vector-valued random variables and random fields
- Robust model updating with insufficient data
- Geometrically nonlinear behavior of structural systems with random material property: an asymptotic spectral stochastic approach
- Identification of high-dimension polynomial chaos expansions with random coefficients for non-Gaussian tensor-valued random fields using partial and limited experimental data
- Sparse polynomial chaos expansions and adaptive stochastic finite elements using a regression approach
- The use of kernel densities and confidence intervals to cope with insufficient data in validation experiments
- Identification of Bayesian posteriors for coefficients of chaos expansions
- Probabilistic equivalence and stochastic model reduction in multiscale analysis
- Identification of chaos representations of elastic properties of random media using experimental vibration tests
- A least-squares approximation of partial differential equations with high-dimensional random inputs
- Stochastic model reduction for chaos representations
- A comparative study of sparse approximate inverse preconditioners
- A multigrid solver for two-dimensional stochastic diffusion equations.
- Iterative solution of linear systems in the 20th century
- Stochastic approaches to uncertainty quantification in CFD simulations
- Iterative solution of systems of linear equations arising in the context of stochastic finite elements
- Efficient and reliable iterative methods for linear systems
- Krylov subspace techniques for reduced-order modeling of large-scale dynamical systems
- Mid-frequency structural dynamics with parameter uncertainty.
- Modeling uncertainty in flow simulations via generalized polynomial chaos.
- Efficient uncertainty quantification with the polynomial chaos method for stiff systems
- Comparative study of projection schemes for stochastic finite element analysis
- Efficient iterative algorithms for the stochastic finite element method with application to acoustic scattering
- On the construction and analysis of stochastic models: characterization and propagation of the errors associated with limited data
- Numerical solution of spectral stochastic finite element systems
- Multi-element stochastic reduced basis methods
- Generalized spectral decomposition method for solving stochastic finite element equations: invariant subspace problem and dedicated algorithms
- Spectral stochastic finite element analysis for laminated composite plates
- Three‐dimensional stochastic finite element method for elasto‐plastic bodies
- Identification of random shapes from images through polynomial chaos expansion of random level set functions
- Efficient numerical strategies for spectral stochastic finite element models
- Maximum likelihood estimation of stochastic chaos representations from experimental data
- Generalized probabilistic approach of uncertainties in computational dynamics using random matrices and polynomial chaos decompositions
- Protein labeling reactions in electrochemical microchannel flow: Numerical simulation and uncertainty propagation
- Performance Evaluation of Generalized Polynomial Chaos
- A multi-scale spectral stochastic method for homogenization of multi-phase periodic composites with random material properties
- Efficient characterization of the random eigenvalue problem in a polynomial chaos decomposition
- Algebraic multigrid for stationary and time‐dependent partial differential equations with stochastic coefficients
- Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics
- Stochastic finite element: a non intrusive approach by regression
- Strain and stress computations in stochastic finite element methods
- A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data
- An Anisotropic Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data
- Sensitivity analysis and stochastic simulations of non‐equilibrium plasma flow
- A FETI‐preconditioned conjugate gradient method for large‐scale stochastic finite element problems
- Probability Theory in Geophysics
- An improved incomplete Cholesky factorization
- Physical Systems with Random Uncertainties: Chaos Representations with Arbitrary Probability Measure
- Numerical Challenges in the Use of Polynomial Chaos Representations for Stochastic Processes
- Incomplete Cholesky Factorizations with Limited Memory
- The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
- Iterative solution of the random eigenvalue problem with application to spectral stochastic finite element systems
- High-Order Collocation Methods for Differential Equations with Random Inputs
- The Homogeneous Chaos
- A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data