Stochastic collocation approach with adaptive mesh refinement for parametric uncertainty analysis

DOI10.1016/j.jcp.2018.06.003zbMath1415.65013arXiv1709.04584OpenAlexW2754162223MaRDI QIDQ2425303

Michael D. Shields, Anindya Bhaduri, L. L. Graham-Brady, Robert M. Kirby, Yanyan He

Publication date: 26 June 2019

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1709.04584

zbMATH Keywords

adaptive mesh refinementstochastic collocationgeneralized polynomial chaosinteraction check

Mathematics Subject Classification ID

Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) PDEs with randomness, stochastic partial differential equations (35R60) Numerical solutions to stochastic differential and integral equations (65C30) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50)

Related Items (6)

An adaptive high-order piecewise polynomial based sparse grid collocation method with applications ⋮ A fully adaptive multilevel stochastic collocation strategy for solving elliptic PDEs with random data ⋮ Uncertainty quantification for complex systems with very high dimensional response using Grassmann manifold variations ⋮ Multi-element flow-driven spectral chaos (ME-FSC) method for uncertainty quantification of dynamical systems ⋮ A deep learning model to predict the failure response of steel pipes under pitting corrosion ⋮ New algorithms for virtual reconstruction of heterogeneous microstructures

Uses Software

• Spinterp

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Minimal multi-element stochastic collocation for uncertainty quantification of discontinuous functions
• Uncertainty propagation using Wiener-Haar expansions
• A domain adaptive stochastic collocation approach for analysis of MEMS under uncertainties
• Multi-element probabilistic collocation method in high dimensions
• The multi-element probabilistic collocation method (ME-PCM): Error analysis and applications
• An adaptive high-dimensional stochastic model representation technique for the solution of stochastic partial differential equations
• Discontinuity detection in multivariate space for stochastic simulations
• An adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations
• General foundations of high-dimensional model representations
• Efficient input-output model representations
• Advances in multidimensional integration
• Modeling uncertainty in flow simulations via generalized polynomial chaos.
• An adaptive multi-element generalized polynomial chaos method for stochastic differential equations
• Beyond Wiener-Askey expansions: handling arbitrary PDFs
• An Efficient Method for Uncertainty Propagation using Fuzzy Sets
• Algorithm 847
• A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data
• Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials
• The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
• Efficient Localization of Discontinuities in Complex Computational Simulations
• Sparse grids
• High-Order Collocation Methods for Differential Equations with Random Inputs
• A generalized dimension‐reduction method for multidimensional integration in stochastic mechanics
• A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data
• High dimensional model representations generated from low dimensional data samples. I: mp-cut-HDMR

This page was built for publication: Stochastic collocation approach with adaptive mesh refinement for parametric uncertainty analysis