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An exact schur complement method for time-harmonic optimal control problems

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    0556767 - ÚGN 2023 RIV CH eng C - Conference Paper (international conference)
    Axelsson, Owe - Lukáš, D. - Neytcheva, M.
    An exact schur complement method for time-harmonic optimal control problems.
    Lecture Notes in Computer Science. Vol. 13127. Cham: Springer Nature Switzerland AG, 2022 - (Lirkov, I.; Margenov, S.), s. 91-100. ISBN 978-3-030-97548-7. ISSN 0302-9743. E-ISSN 1611-3349.
    [International Conference on Large-Scale Scientific Computing /13./. Sozopol (BG), 07.06.2021-11.06.2021]
    EU Projects: European Commission(XE) 847593 - EURAD
    Institutional support: RVO:68145535
    Keywords : PDE-constrained optimal control problems * distributed control * preconditioning * time-harmonic maxwell equations
    OECD category: Applied mathematics

    By use of Fourier time series expansions in an angular frequency variable, time-harmonic optimal control problems constrained by a linear differential equation decouples for the different frequencies. Hence, for the analysis of a solution method one can consider the frequency as a parameter. There are three variables to be determined, the state solution, the control variable, and the adjoint variable. The first order optimality conditions lead to a three-by-three block matrix system where the adjoint optimality variable can be eliminated. For the so arising two-by-two block system, in this paper we study a factorization method involving an exact Schur complement method and illustrate the performance of an inexact version of it
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