Uncertainty propagation using Wiener-Haar expansions

By O. L. Le Maître, Omar M. Knio, Habib N. Najm, Roger G. Ghanem. 2004

483 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Environmental Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/6a8ace7d98c7b2f8d4e502458e433a9a82de4c8b

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In Civil and Structural Engineering

In Environmental Engineering

In Statistics and Probability

Citations in the corpus

A stochastic collocation approach to Bayesian inference in inverse problems (2009, unknown): “See, for example, [2,8,15,28,29].”
Analysis and implementation issues for the numerical approximation of parabolic equations with random coefficients (2009, methodology): “Clearly, other forms of approximation other than global polynomials are possible and have been explored in recent years, such as wavelet approximations [17, 19] or piecewise polynomials [1, 30].”
Recent Developments in Spectral Stochastic Methods for the Numerical Solution of Stochastic Partial Differential Equations (2009, methodology): “Classical choices rely on classical construction of polynomial basis (polynomial chaos [130,23,48], generalized polynomial chaos [132], Lagrange interpolation [8]) or piecewise polynomial functions ( nite elements [34,128], wavelets [71,72]).”
A generalized spectral decomposition technique to solve a class of linear stochastic partial differential equations (2007, unknown): “For the case of non-smooth solutions, other approximation techniques have been introduced (Wiener-Haar chaos [18], finite elements [6]).”
Efficient Collocational Approach for Parametric Uncertainty Analysis (2007, methodology): “Such a Galerkin procedure has been used extensively in the literature [2, 8, 11, 16, 27–29].”
Long-Term Behavior of Polynomial Chaos in Stochastic Flow Simulations (2006, methodology): “The former was studied in [11,12] with Wiener–Haar expansions and in [19,20] with ME-gPC.”
Fast Numerical Methods for Stochastic Computations: A Review (2009, background): “Such approaches include piecewise polynomial basis [5, 66], wavelet basis [42, 43], and multi-element gPC [80, 82].”
An Anisotropic Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data (2008, background): “) and polynomial approximation in the probability domain, either by full polynomial spaces [30, 22, 16], tensor product polynomial spaces [2, 12, 25], or piecewise polynomial spaces [8, 2, 19, 28, 21].”
Model order reduction based on proper generalized decomposition for the propagation of uncertainties in structural dynamics (2012, background): “Furthermore, the solution can be a highly nonlinear function of the random variables and it may require the use of very fine approximation spaces SP (such as finite element [31] or wavelets [32]).”
Uncertainty propagation in CFD using polynomial chaos decomposition (2006, background): “For zero-order multi-wavelets (MW), one obtains a Wiener-Haar expansion which is a piece-wise constant approximation of the uncertain flow [26], i.”
A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data (2008, unknown): “We mention, among others, the Spectral Galerkin method [3, 4, 16, 20, 22, 25, 27, 36], Stochastic Collocation [5, 24, 29, 35], perturbation methods or Neumann expansions [1, 17,30,34].”
The stochastic finite element method: Past, present and future (2009, background): “In these cases of non-smooth solutions, the choice of other basis functions such as wavelets or the use of an adaptive multi-element generalized PCE has been suggested as a remedy to the problem [101,185,131].”