Robust optimal Robin boundary control for the transient heat equation with random input data. (2nd March 2016)

• Record Type: Journal Article
• Authors: Martínez‐Frutos, J.; Kessler, M.; Münch, A.; Periago, F.
• Is Part Of: International journal for numerical methods in engineering. Volume 108:Number 2(2016)
• Page Start: 116
• Page End: 135
• Publication Date: 2016-03-02
• Subjects: stochastic heat equation -- robust optimal control -- random fields -- stochastic collocation finite element method; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 620.001518
• DOI: 10.1002/nme.5210
• Languages: English
• ISSNs: 0029-5981

Abstract

Summary: The problem of robust optimal Robin boundary control for a parabolic partial differential equation with uncertain input data is considered. As a measure of robustness, the variance of the random system response is included in two different cost functionals. Uncertainties in both the underlying state equation and the control variable are quantified through random fields. The paper is mainly concerned with the numerical resolution of the problem. To this end, a gradient‐based method is proposed considering different functional costs to achieve the robustness of the system. An adaptive anisotropic sparse grid stochastic collocation method is used for the numerical resolution of the associated state and adjoint state equations. The different functional costs are analysed in terms of computational efficiency and its capability to provide robust solutions. Two numerical experiments illustrate the performance of the algorithm. Copyright © 2016 John Wiley & Sons, Ltd.