Multi-element flow-driven spectral chaos (ME-FSC) method for uncertainty quantification of dynamical systems

DOI10.1016/j.jcp.2022.111425OpenAlexW4284880647MaRDI QIDQ2162015

Hugo Esquivel, Arun Prakash, Guang Lin

Publication date: 5 August 2022

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

Full work available at URL: https://arxiv.org/abs/2207.10281

zbMATH Keywords

uncertainty quantificationstochastic dynamical systemslong-time integrationstochastic flow mapmulti-element flow-driven spectral chaos (ME-FSC)stochastic discontinuities

Mathematics Subject Classification ID

Stochastic analysis (60Hxx) Numerical methods for partial differential equations, boundary value problems (65Nxx) Probabilistic methods, stochastic differential equations (65Cxx)

Uses Software

• Xcode

Cites Work

• Unnamed Item
• Minimal multi-element stochastic collocation for uncertainty quantification of discontinuous functions
• An adaptive stochastic finite elements approach based on Newton-Cotes quadrature in simplex elements
• Uncertainty propagation using Wiener-Haar expansions
• Multi-resolution analysis of Wiener-type uncertainty propagation schemes
• Time-dependent generalized polynomial chaos
• Long-time uncertainty propagation using generalized polynomial chaos and flow map composition
• A domain adaptive stochastic collocation approach for analysis of MEMS under uncertainties
• Multi-element probabilistic collocation method in high dimensions
• A stochastic variational multiscale method for diffusion in heterogeneous random media
• Stochastic spectral methods for efficient Bayesian solution of inverse problems
• The multi-element probabilistic collocation method (ME-PCM): Error analysis and applications
• Long-term behavior of polynomial chaos in stochastic flow simulations
• An adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations
• A non-intrusive B-splines Bézier elements-based method for uncertainty propagation
• Flow-driven spectral chaos (FSC) method for long-time integration of second-order stochastic dynamical systems
• Flow-driven spectral chaos (FSC) method for simulating long-time dynamics of arbitrary-order non-linear stochastic dynamical systems
• Sparse grid collocation schemes for stochastic natural convection problems
• A unified framework for mesh refinement in random and physical space
• Stochastic collocation approach with adaptive mesh refinement for parametric uncertainty analysis
• Adaptive wavelet methods for elliptic partial differential equations with random operators
• An adaptive multi-element generalized polynomial chaos method for stochastic differential equations
• Beyond Wiener-Askey expansions: handling arbitrary PDFs
• Adaptive multi-element polynomial chaos with discrete measure: algorithms and application to SPDEs
• Multi-element stochastic reduced basis methods
• An adaptive stochastic Galerkin method for random elliptic operators
• Adaptive Discontinuous Galerkin Method for Response-Excitation PDF Equations
• eXtended Stochastic Finite Element Method for the numerical simulation of heterogeneous materials with random material interfaces
• Local Polynomial Chaos Expansion for Linear Differential Equations with High Dimensional Random Inputs
• The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
• A HYBRID GENERALIZED POLYNOMIAL CHAOS METHOD FOR STOCHASTIC DYNAMICAL SYSTEMS
• Dynamical Properties of Truncated Wiener-Hermite Expansions
• Dynamical Polynomial Chaos Expansions and Long Time Evolution of Differential Equations with Random Forcing

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