Multivariate Polynomial Chaos Expansions with Dependent Variables

DOI10.1137/15M1020447zbMath1379.60075MaRDI QIDQ4602895

Hans Petter Langtangen, Vinzenz Gregor Eck, Jonathan Feinberg

Publication date: 7 February 2018

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

zbMATH Keywords

wave propagationuncertainty quantificationblood flow simulationvariable transformationspolynomial chaos expansionsdependent stochastic variables

Mathematics Subject Classification ID

Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) (74F10) Applications of stochastic analysis (to PDEs, etc.) (60H30) Physiological flow (92C35)

Related Items

Surrogate modeling for high dimensional uncertainty propagation via deep kernel polynomial chaos expansion ⋮ Generating Nested Quadrature Rules with Positive Weights based on Arbitrary Sample Sets ⋮ Convergence Analysis and Adaptive Order Selection for the Polynomial Chaos Approach to Direct Optimal Control under Uncertainties

Uses Software

• OPQ
• Chaospy

Cites Work

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• On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals
• A method for numerical integration on an automatic computer
• Probabilistic arithmetic. I: Numerical methods for calculating convolutions and dependency bounds
• The Gibbs- Wilbraham phenomenon: An episode in Fourier analysis
• Bootstrap methods: another look at the jackknife
• Numerical integration using sparse grids
• One-dimensional modelling of a vascular network in space-time variables
• Modeling uncertainty in flow simulations via generalized polynomial chaos.
• Parametric uncertainty analysis of pulse wave propagation in a model of a human arterial network
• Generation and Use of Orthogonal Polynomials for Data-Fitting with a Digital Computer
• Spectral Methods for Time-Dependent Problems
• Robust generalized cross-validation for choosing the regularization parameter
• Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials
• On the Gibbs Phenomenon and Its Resolution
• The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
• Calculation of Gauss Quadrature Rules
• Construction of Gauss-Christoffel Quadrature Formulas
• The Homogeneous Chaos
• Remarks on a Multivariate Transformation