Stochastic Modeling of Flow-Structure Interactions Using Generalized Polynomial Chaos

By Dongbin Xiu, Didier Lucor, G. Em Karniadakis. 2002

313 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Environmental Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/505f703e02a3c503c09cf1a528319e1927c0b260

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In Biomedical Engineering

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Citations in the corpus

A Stochastic Collocation Algorithm for Uncertainty Analysis (2003, methodology): “Originating in the work of Wiener (1938) and mainly applied ill the field of structural mechanics, this technique is now making its way in the fluid mechanics community ([15, 16, 12, 14]).”
Stochastic approaches to uncertainty quantification in CFD simulations (2005, methodology): “Originating from the work of Wiener (1938) and mainly applied to date in the field of structural mechanics, this technique is now making its way in the fluid mechanics community [4,9,10,22,24-26].”
Fast Numerical Methods for Stochastic Computations: A Review (2009, background): “1), and the examples are for linear problems, the gPC framework can be readily applied to complex problems including the time-dependent and nonlinear ones, for example, Burgers’ equation [34, 94], fluid dynamics [40, 41, 44, 46, 92], flow-structure interactions [96], hyperbolic problems [11,31], mat”
Physical Systems with Random Uncertainties: Chaos Representations with Arbitrary Probability Measure (2005, background): “Chaos decomposition techniques have indeed been recently applied to a wide range of problems in scientific computing relating to uncertain systems [8, 9, 7, 18, 6, 5, 2, 16, 4, 23].”
A new stochastic approach to transient heat conduction modeling with uncertainty (2003, unknown): “It includes the classical Hermite polynomial chaos as a subset and has been applied to various problems [37,35,38].”
Numerical Methods and Smolyak Quadrature for Nonlinear Stochastic Partial Differential Equations (2003, background): “[55], but publications on Galerkin methods for nonlinear stochastic operators are scarce.”
Adaptive sparse polynomial chaos expansion based on least angle regression (2011, background): “It was later extended to other types of random variables together with basis functions from the Askey family of hypergeometric polynomials [24, 25, 26].”
Inverse Problems in Heat Transfer (2009, background): “Finally, in section 2.6, directions for further investigation in the use of spectral methods for stochastic inverse problems are suggested.”
A Polynomial Chaos-Based Kalman Filter Approach for Parameter Estimation of Mechanical Systems (2010, methodology): “Xiu extended the approach to general formulations based on Wiener-Askey polynomials family [43], and applied it to fluid mechanics [44-46].”
Modeling Uncertainty in Steady State Diffusion Problems via Generalized Polynomial Chaos (2002, methodology): “We have applied the generalized polynomial chaos to the solution of steady state random diffusion problems, as a natural extension of our earlier work [17,19,20].”