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Articles written by Sachdeva, S.K.

  1. Sachdeva, S.K., Nair, P.B., and Keane, A.J.. "Comparative study of projection schemes for stochastic finite element analysis" Computer Methods in Applied Mechanics and Engineering. 195 (19-22). 2006. pp. 2371--2392.

    We present a comparison of subspace projection schemes for stochastic finite element analysis in terms of accuracy and computational efficiency. More specifically, we compare the polynomial chaos projection scheme with reduced basis projection schemes based on the preconditioned stochastic Krylov subspace. Numerical studies are presented for two problems: (1) static analysis of a plate with random Young's modulus and (2) settlement of a foundation supported on a randomly heterogeneous soil. Monte Carlo simulation results based on exact structural analysis are used to generate benchmark results against which the projection schemes are compared. We show that stochastic reduced basis methods require significantly less computer memory and execution time compared to the polynomial chaos approach, particularly for large-scale problems with many random variables. For the class of problems considered, we find that stochastic reduced basis methods can be up to orders of magnitude faster, while providing results of comparable or better accuracy.


  2. Sachdeva, S.K., Nair, P.B., and Keane, A.J.. "Hybridization of stochastic reduced basis methods with polynomial chaos expansions" Probabilitic Engineering Mechanics. 21 (2). APR 2006. pp. 182--192.

    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. (C) 2005 Elsevier Ltd. All rights reserved.