Hybridization of stochastic reduced basis methods with polynomial chaos expansions
Sachdeva, Sachin, Nair, Prasanth B. and Keane, Andy J (2006) Hybridization of stochastic reduced basis methods with polynomial chaos expansions. Probabilistic Engineering Mechanics, 21, (2), 182-192. (doi:10.1016/j.probengmech.2005.09.003).
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We propose a hybrid formulation combining stochastic reduced basis methods with polynomial chaos expansions for solving linear random algebraic equations arising from discretization of stochastic partial differential equations. Our objective is to generalize stochastic reduced basis projection schemes to non-Gaussian uncertainty models and simplify the implementation of higher-order approximations. We employ basis vectors spanning the preconditioned stochastic Krylov subspace to represent the solution process. In the present formulation, the polynomial chaos decomposition technique is used to represent the stochastic basis vectors in terms of multidimensional Hermite polynomials. The Galerkin projection scheme is then employed to compute the undetermined coefficients in the reduced basis approximation. We present numerical studies on a linear structural problem where the Youngs modulus is represented using Gaussian as well as lognormal models to illustrate the performance of the hybrid stochastic reduced basis projection scheme. Comparison studies with the spectral stochastic finite element method suggest that the proposed hybrid formulation gives results of comparable accuracy at a lower computational cost.
|Subjects:||T Technology > TK Electrical engineering. Electronics Nuclear engineering|
|Divisions:||University Structure - Pre August 2011 > School of Engineering Sciences
|Date Deposited:||11 May 2006|
|Last Modified:||28 Jun 2012 10:12|
|Contributors:||Sachdeva, Sachin (Author)
Nair, Prasanth B. (Author)
Keane, Andy J (Author)
|Contact Email Address:||P.B.Nair@soton.ac.uk|
|RDF:||RDF+N-Triples, RDF+N3, RDF+XML, Browse.|
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