Commun. Comput. Phys., 14 (2013), pp. 722-752.


A Distributed Control Approach for the Boundary Optimal Control of the Steady MHD Equations

G. Bornia 1, M. Gunzburger 2*, S. Manservisi 1

1 Laboratory of Nuclear Engineering of Montecuccolino, DIENCA, University of Bologna, Italy.
2 Department of Scientific Computing, Florida State University, USA.

Received 16 March 2012; Accepted (in revised version) 7 November 2012
Available online 28 February 2013
doi:10.4208/cicp.160312.071112a

Abstract

A new approach is presented for the boundary optimal control of the MHD equations in which the boundary control problem is transformed into an extended distributed control problem. This can be achieved by considering boundary controls in the form of lifting functions which extend from the boundary into the interior. The optimal solution is then sought by exploring all possible extended functions. This approach gives robustness to the boundary control algorithm which can be solved by standard distributed control techniques over the interior of the domain.

AMS subject classifications: 49J20, 93C20, 75W05, 65N30

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Key words: Boundary control, optimal control, magnetohydrodynamics, finite element methods.

*Corresponding author.
Email: giorgio.bornia@unibo.it (G. Bornia), gunzburg@fsu.edu (M. Gunzburger), sandro.manservisi@unibo.it (S. Manservisi)
 

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