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Robust optimal Robin boundary control for the transient heat equation with random input data
Author(s) -
MartínezFrutos J.,
Kessler M.,
Münch A.,
Periago F.
Publication year - 2016
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.5210
Subject(s) - robustness (evolution) , mathematics , sparse grid , heat equation , adjoint equation , collocation (remote sensing) , partial differential equation , mathematical optimization , optimal control , boundary (topology) , boundary value problem , computer science , mathematical analysis , biochemistry , chemistry , machine learning , gene
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.