Multi-resolution analysis of wiener-type uncertainty propagation schemes

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

370 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/148c365894d0b4793c5ad8b006a56f3e9fca49ab

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In Civil and Structural Engineering

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Citations in the corpus

Analysis and implementation issues for the numerical approximation of parabolic equations with random coefficients (2009, methodology): “For instance one may use piecewise polynomial functions [7, 1, 29, 30, 28], wavelets [17, 18 , 19], etc.”
Efficient characterization of the random eigenvalue problem in a polynomial chaos decomposition (2007, background): “Extensions to other representations besides Hermite polynomials have recently been introduced in the literature [14, 15].”
High-Order Collocation Methods for Differential Equations with Random Inputs (2005, methodology): “The generalizations, also called generalized polynomial chaos, employ non-Hermite polynomials to improve efficiency for a wider class of problems and include global polynomial expansions based on hypergeometrical polynomials [53, 52, 54], piecewise polynomial expansions [2, 12], and wavelet basis ex”
An adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations (2009, methodology): “The same problem also exists for the Stochastic Galerkin [13] and Wiener-Haar expansion [16] methods.”
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].”
Recent Developments in Spectral Stochastic Methods for the Numerical Solution of Stochastic Partial Differential Equations (2009, methodology): “This kind of approach then makes sense in the context of adaptive approximation procedures [62,128,72,129,81].”
Nonlinear Propagation of Orbit Uncertainty Using Non-Intrusive Polynomial Chaos (2013, methodology): “This work examines the application of PCEs [13,18,20,27–35] to the solution of Eq.”
Proper Generalized Decompositions and Separated Representations for the Numerical Solution of High Dimensional Stochastic Problems (2010, background): “where the Hα(ξ ) form a basis of classical stochastic approximation spaces, such as polynomial or piecewise polynomial spaces [10, 31 , 43, 47, 52].”
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.”
An adaptive multi-element generalized polynomial chaos method for stochastic differential equations (2005, methodology): “To this end, a new method, termed the Wiener-Haar method, was developed in [6,7] based on wavelets; its primary aim was to address problems related to the aforementioned discontinuities in random space.”