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Multigrid Method for Optimal Control Problem Constrained by Stochastic Stokes Equations with Noise

Author

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  • Muhammad Munir Butt

    (Department of Mathematics and Statistics, College of Sciences, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia)

Abstract

Optimal control problems governed by stochastic partial differential equations have become an important field in applied mathematics. In this article, we investigate one such important optimization problem, that is, the stochastic Stokes control problem with forcing term perturbed by noise. A multigrid scheme with three-factor coarsening to solve the corresponding discretized control problem is presented. On staggered grids, a three-factor coarsening strategy helps in simplifying the inter-grid transfer operators and reduction in computation (CPU time). For smoothing, a distributive Gauss–Seidel scheme with a line search strategy is employed. To validate the proposed multigrid staggered grid framework, numerical results are presented with white noise at the end.

Suggested Citation

  • Muhammad Munir Butt, 2021. "Multigrid Method for Optimal Control Problem Constrained by Stochastic Stokes Equations with Noise," Mathematics, MDPI, vol. 9(7), pages 1-13, March.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:7:p:738-:d:526029
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