Third M.I.T. Conference on Computational Fluid and Solid Mechanics June 14–17, 2005  

A new projection scheme for linear stochastic problems

Sachin K. Sachdeva*, Prasanth B. Nair, Andy J. Keane
Computational Engineering and Design Group, School of Engineering Sciences, University of Southampton, Highfield, Southampton SO17 1BJ, UK

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In this paper we present a new projection scheme for solving linear stochastic partial differential equations. The solution process is approximated using a set of basis vectors spanning a preconditioned stochastic Krylov subspace. We propose a strong Galerkin condition which ensures that the stochastic residual error is orthogonal to the approximating subspace with probability one. We present numerical studies for a model problem in stochastic structural mechanics to demonstrate that the proposed strong Galerkin projection scheme gives better results than the weak Galerkin scheme.

Keywords:  Stochastic projection schemes; Polynomial chaos; Krylov subspace

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