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
ABSTRACT
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