Print Email Facebook Twitter Preconditioning Optimal In-Domain Control of Navier-Stokes Equation Using Multilevel Sequentially Semiseparable Matrix Computations Title Preconditioning Optimal In-Domain Control of Navier-Stokes Equation Using Multilevel Sequentially Semiseparable Matrix Computations Author Qiu, Y. Van Gijzen, M.B. Van Wingerden, J.W. Verhaegen, M. Vuik, C. Faculty Electrical Engineering, Mathematics and Computer Science Department Delft Institute of Applied Mathematics Date 2015-06-30 Abstract In this manuscript, we study preconditioning techniques for optimal in-domain control of the Navier-Stokes equation, where the control only acts on a few parts of the domain. Optimization and linearization of the optimal in-domain control problem results in a generalized linear saddle-point system. The Schur complement for the generalized saddle-point system is very difficult or even impossible to approximate. This prohibits satisfactory performance of the standard block preconditioners. We apply the multilevel sequentially semiseparable (MSSS) preconditioner to the underlying system. Compared with standard block preconditioning techniques, the MSSS preconditioner computes an approximate factorization of the global generalized saddle-point matrix up to a prescribed accuracy in linear computational complexity. This in turn gives parameter independent convergence for MSSS preconditioned Krylov solvers. We use a simple wind farm control example to illustrate the performance of the MSSS preconditioner. We also ompare with the performance of the state-of-the-art preconditioning techniques. Our results show the superiority of the MSSS preconditioning techniques to standard block preconditioning techniques for optimal in-domain control of the Navier-Stokes equation. Subject in-domain flow controlMSSS preconditionersgeneralized saddle-point systemNavier-Stokes control To reference this document use: http://resolver.tudelft.nl/uuid:0705c999-d9d1-4c3c-92ae-45b958c883a7 Publisher Delft University of Technology, Faculty of Electrical Engineering, Mathematics and Computer Science, Delft Institute of Applied Mathematics ISSN 1389-6520 Source Reports of the Delft Institute of Applied Mathematics, 15-06 Part of collection Institutional Repository Document type report Rights (c)2015 Qiu, Y., Van Gijzen, M.B., Van Wingerden, J.W., Verhaegen, M., Vuik, C. Files PDF 15-06_NS_Control_Qiu__2_.pdf 922.38 KB Close viewer /islandora/object/uuid:0705c999-d9d1-4c3c-92ae-45b958c883a7/datastream/OBJ/view