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Multigrid Methods for Elliptic Optimal Control Problems with Neumann Boundary Control

In: Numerical Mathematics and Advanced Applications 2009

Author

Listed:
  • Stefan Takacs

    (Johannes Kepler University Linz, Doctoral Program Computational Mathematics)

  • Walter Zulehner

    (Johannes Kepler University Linz, Institute of Computational Mathematics)

Abstract

In this article we discuss multigrid methods for solving discretized optimality systems for elliptic optimal control problems. We concentrate on a model problem of tracking type with Neumann boundary control, whose optimality system is a linear system for the state y, the control u and the adjoined state p. An Uzawa-type smoother is used for the multigrid method. Moreover, we will compare this approach with standard smoothers, like damped Jacobi iteration applied to the normal equation of the Karush–Kuhn–Tucker system. A rigorous multigrid convergence analysis is presented for both smoothers.

Suggested Citation

  • Stefan Takacs & Walter Zulehner, 2010. "Multigrid Methods for Elliptic Optimal Control Problems with Neumann Boundary Control," Springer Books, in: Gunilla Kreiss & Per Lötstedt & Axel Målqvist & Maya Neytcheva (ed.), Numerical Mathematics and Advanced Applications 2009, pages 855-863, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-11795-4_92
    DOI: 10.1007/978-3-642-11795-4_92
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