Multiscale stochastic preconditioners in non-intrusive spectral projection

DOI10.1007/s10915-011-9486-2zbMath1242.65009OpenAlexW1997011833MaRDI QIDQ421341

Omar M. Knio, Mohamed Iskandarani, Olivier P. Le Maître, Alen Alexanderian, Habib N. Najm

Publication date: 23 May 2012

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-011-9486-2

zbMATH Keywords

numerical examplespreconditioningpolynomial chaosuncertain dynamical systemnon-intrusive spectral projectionstochastic preconditionerstretched measure

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Ordinary differential equations and systems with randomness (34F05) Generation, random and stochastic difference and differential equations (37H10) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30) Numerical chaos (65P20)

Related Items

Surrogate-based parameter inference in debris flow model, Enforcing positivity in intrusive PC-UQ methods for reactive ODE systems, Polynomial Chaos Expansions for Stiff Random ODEs, Bayesian inference of earthquake parameters from buoy data using a polynomial chaos-based surrogate, Surrogate combining harmonic decomposition and polynomial chaos for seismic shear waves in uncertain media, Preconditioned Bayesian regression for stochastic chemical kinetics, Polynomial chaos level points method for one-dimensional uncertain steep problems, On the construction of uncertain time series surrogates using polynomial chaos and Gaussian processes, Probabilistic modeling and global sensitivity analysis for CO\(_2\) storage in geological formations: a spectral approach, Uncertainty quantification of geochemical and mechanical compaction in layered sedimentary basins, Surrogate Models for Oscillatory Systems Using Sparse Polynomial Chaos Expansions and Stochastic Time Warping

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Uncertainty quantification in a chemical system using error estimate-based mesh adaption
• Uncertainty propagation using Wiener-Haar expansions
• Multi-resolution analysis of Wiener-type uncertainty propagation schemes
• Asynchronous time integration for polynomial chaos expansion of uncertain periodic dynamics
• An adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations
• Linear operator theory in engineering and science. Repr. of the 1971 orig., publ. by Holt, Rinehart \& Winston, Inc.
• Numerical integration using sparse grids
• On the Smolyak cubature error for analytic functions
• Sparse grid collocation schemes for stochastic natural convection problems
• An adaptive multi-element generalized polynomial chaos method for stochastic differential equations
• Higher order corrections in the approximation of low-dimensional manifolds and the construction of simplified problems with the CSP method
• The orthogonal development of non-linear functionals in series of Fourier-Hermite functionals
• Parallel Solution of Stochastic PDEs
• Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures
• Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
• Stochastic finite element: a non intrusive approach by regression
• Stochastic convergence acceleration through basis enrichment of polynomial chaos expansions
• Spectral Methods for Uncertainty Quantification
• An Anisotropic Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data
• Uncertainty quantification in chemical systems
• Gaussian Hilbert Spaces
• A Compressed Sensing Approach for Partial Differential Equations with Random Input Data
• Natural Convection in a Closed Cavity under Stochastic Non-Boussinesq Conditions
• Uncertainty Quantification in CFD Simulations: A Stochastic Spectral Approach
• The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
• Multi‐Resolution‐Analysis Scheme for Uncertainty Quantification in Chemical 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
• Compressed sensing
• Fast calculation of coefficients in the Smolyak algorithm
• A posteriori error estimation for the semidiscrete finite element method of parabolic differential equations