A Stochastic Collocation Algorithm for Uncertainty Analysis

By Lionel Mathelin, M. Yousuff Hussaini. 2003

199 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/a4537d114fe39d91becd0c94db4e8dfdae43b6e5

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Citations in the corpus

Least squares polynomial chaos expansion: A review of sampling strategies (2017, methodology): “A widely used sampling-based approach to compute the PC coefﬁcients is the stochastic collocation (SC) method [74, 126, 5, 20, 21, 61].”
Fast Numerical Methods for Stochastic Computations: A Review (2009, methodology): “Earlier work of stochastic collocation methods includes [52,77] and uses tensor products of one-dimensional quadrature points as “sampling pints”.”
High-Order Collocation Methods for Differential Equations with Random Inputs (2005, background): “For such a cases, point sets based on tensor products of one-dimensional quadrature points [37, 53] are not suitable, as the number of points grows too fast with increasing dimensions.”
Non-intrusive low-rank separated approximation of high-dimensional stochastic models (2012, methodology): “To address the low convergence rate of these methods, stochastic basis expansions, for instance, in chaos polynomials [32, 31, 76] and multivariate numerical integration/interpolation, such as those based on the sparse grid collocation [69, 52, 75], have been recently proposed.”
Modeling Multibody Systems with Uncertainties. Part I: Theoretical and Computational Aspects (2006, background): “In [35,36, 59 ] basis functions given by Eq. (24) of multi-dimensional order up to P are considered.”
Stochastic approaches to uncertainty quantification in CFD simulations (2005, methodology): “Stochastic collocation method The stochastic collocation method was developed by Mathelin and Hussaini [13] to enable application of stochastic methods to spectral discontinuous Galerkin methods (cf.”
A least-squares approximation of partial differential equations with high-dimensional random inputs (2009, background): “More recently, there has been a great amount of attention to collocation-based techniques that take advantage of existing deterministic solvers for moderate Oð10Þ number of uncertain variables [24,18,27,1,20,19].”
Coherence motivated sampling and convergence analysis of least squares polynomial Chaos regression (2014, background): “Collocation Method [7, 8, 9, 10], where points are often chosen with (6) in mind.”
A non-adapted sparse approximation of PDEs with stochastic inputs (2010, background): “Stochastic collocation schemes [58,45,66,1,51] belong to a different class of methods that rely upon (isotropic) sparse grid integration/ interpolation in the stochastic space of the problem to reduce the curse-of-dimensionality associated with the conventional”
Efficient Collocational Approach for Parametric Uncertainty Analysis (2007, methodology): “Key words: Collocation methods; pseudo-spectral methods; stochastic inputs; random differential equations; uncertainty quantification.”