Table of Contents
ISRN Applied Mathematics
Volume 2014, Article ID 974305, 11 pages
http://dx.doi.org/10.1155/2014/974305
Research Article

Numerical Optimal Control for Problems with Random Forced SPDE Constraints

Department of Applied Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, P.O. Box 14115-134, Tehran, Iran

Received 22 September 2013; Accepted 10 December 2013; Published 20 February 2014

Academic Editors: H. Homeier and F. Zirilli

Copyright © 2014 R. Naseri and A. Malek. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A numerical algorithm for solving optimization problems with stochastic diffusion equation as a constraint is proposed. First, separation of random and deterministic variables is done via Karhunen-Loeve expansion. Then, the problem is discretized, in spatial part, using the finite element method and the polynomial chaos expansion in the stochastic part of the problem. This process leads to the optimal control problem with a large scale system in its constraint. To overcome these difficulties the adjoint technique for derivative computation to implementation of the optimal control issue in preconditioned Newton’s conjugate gradient method is used. By some numerical simulation, it is shown that this hybrid approach is efficient and simple to implement.