Space and chaos‐expansion Galerkin proper orthogonal decomposition low‐order discretization of partial differential equations for uncertainty quantification

DOI10.1002/nme.7229arXiv2009.01055MaRDI QIDQ6082495

Peter Benner, Jan Heiland

Publication date: 29 November 2023

Published in: International Journal for Numerical Methods in Engineering (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2009.01055

zbMATH Keywords

proper orthogonal decompositionmodel reductiontensor spacesuncertainty quantification

Mathematics Subject Classification ID

Numerical analysis (65-XX)

Cites Work

• Unnamed Item
• Unnamed Item
• Proper generalized decompositions and separated representations for the numerical solution of high dimensional stochastic problems
• Multilevel Monte Carlo methods and applications to elliptic PDEs with random coefficients
• Efficient uncertainty quantification in stochastic finite element analysis based on functional principal components
• Galerkin methods for linear and nonlinear elliptic stochastic partial differential equations
• Propagation of probabilistic uncertainty in complex physical systems using a stochastic finite element approach
• Multi-index stochastic collocation for random PDEs
• Model Reduction Based on Proper Generalized Decomposition for the Stochastic Steady Incompressible Navier--Stokes Equations
• Low-Rank Solution of Unsteady Diffusion Equations with Stochastic Coefficients
• Discrete Input/Output Maps and their Relation to Proper Orthogonal Decomposition
• Galerkin reduced-order modeling scheme for time-dependent randomly parametrized linear partial differential equations
• Reduced chaos expansions with random coefficientsin reduced-dimensional stochastic modeling of coupled problems
• Constrained Optimization with Low-Rank Tensors and Applications to Parametric Problems with PDEs
• A Kronecker Product Preconditioner for Stochastic Galerkin Finite Element Discretizations
• Tensor-Structured Galerkin Approximation of Parametric and Stochastic Elliptic PDEs
• Hierarchical Tensor Approximation of Output Quantities of Parameter-Dependent PDEs
• A Multilinear Singular Value Decomposition
• Physical Systems with Random Uncertainties: Chaos Representations with Arbitrary Probability Measure
• Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations
• MODEL REDUCTION FOR FLUIDS, USING BALANCED PROPER ORTHOGONAL DECOMPOSITION
• A Weighted Reduced Basis Method for Elliptic Partial Differential Equations with Random Input Data
• Tensor numerical methods for multidimensional PDES: theoretical analysis and initial applications
• Space-Time Galerkin POD with Application in Optimal Control of Semilinear Partial Differential Equations

This page was built for publication: Space and chaos‐expansion Galerkin proper orthogonal decomposition low‐order discretization of partial differential equations for uncertainty quantification