UN CO RR EC TE D PR O O F 1 Robust Parameter - Free Multilevel Methods 2 for Neumann Boundary Control Problems 3
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چکیده
We consider a linear-quadratic elliptic control problem (LQECP). For the problem 8 we consider here, the control variable corresponds to the Neumann data on the boundary of 9 a convex polygonal domain. The optimal control unknown is the one for which the harmonic 10 extension approximates best a specified target in the interior of the domain. We propose a 11 multilevel preconditioner for the reduced Hessian resulting from the application of the Schur 12 complement method to the discrete LQECP. In order to derive robust stabilization parameters13 free preconditioners, we first show that the Schur complement matrix is associated to a linear 14 combination of negative Sobolev norms and then propose preconditioner based on multilevel 15 methods. We also present numerical experiments which agree with the theoretical results. 16
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تاریخ انتشار 2013