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On a multigrid solver for stationary Navier–Stokes velocity–pressure tracking-type control problems

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  • Butt, Muhammad Munir

Abstract

In this article, a multigrid solver for distributed optimal control problems governed by time-independent Navier–Stokes equations is presented. A mixed (velocity–pressure) tracking-type control problem is considered and first-order optimality conditions are discussed. We investigate a full multigrid method with coarsening by a factor-of-three strategy to stationary Navier–Stokes control problems. The potential advantage of multigrid with coarsening by a factor-of-three strategy is that it results in nested hierarchy of staggered grids and thus simplifies the inter-grid transfer operators, reduces the number of levels, and hence the CPU time. The construction of the multigrid algorithm for Stokes control problems of our earlier work gives us a natural extension but still significant challenges are rooted in the nonlinear part of the Navier–Stokes equations (constraints) and mixed (velocity–pressure) tracking-type control formulation. Numerical experiments are reported to show the behavior and efficiency of the proposed multigrid algorithm for small Reynolds numbers and moderate values of regularization parameter.

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  • Butt, Muhammad Munir, 2022. "On a multigrid solver for stationary Navier–Stokes velocity–pressure tracking-type control problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 192(C), pages 246-264.
    • Handle: RePEc:eee:matcom:v:192:y:2022:i:c:p:246-264
    DOI: 10.1016/j.matcom.2021.08.025
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    1. A. Borzì & E.-J. Park & M. Vallejos Lass, 2016. "Multigrid Optimization Methods for the Optimal Control of Convection–Diffusion Problems with Bilinear Control," Journal of Optimization Theory and Applications, Springer, vol. 168(2), pages 510-533, February.
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