MULTIGRID PRECONDITIONERS FOR THE NEWTON-KRYLOV METHOD IN THE OPTIMAL CONTROL OF THE STATIONARY NAVIER-STOKES EQUATIONS

被引:2
作者
Soane, Ana Maria [1 ]
Draganescu, Andrei [2 ]
机构
[1] US Naval Acad, Dept Math, Annapolis, MD 21402 USA
[2] Univ Maryland, Dept Math & Stat, Baltimore, MD 21250 USA
基金
美国国家科学基金会;
关键词
multigrid methods; PDE-constrained optimization; Navier-Stokes equations; finite elements; CONSTRAINED OPTIMAL-CONTROL; VELOCITY TRACKING PROBLEM; LINEAR-SYSTEMS; APPROXIMATION; OPTIMIZATION; FLOWS;
D O I
10.1137/18M1175264
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The focus of this work is on the construction and analysis of optimal-order multigrid preconditioners to be used in the Newton-Krylov method for a distributed optimal control problem constrained by the stationary Navier-Stokes equations. As in our earlier work [Appl. Math. Comput., 219 (2013), pp. 5622-5634] on the optimal control of the stationary Stokes equations, the strategy is to eliminate the state and adjoint variables from the optimality system and solve the reduced nonlinear system in the control variables. While the construction of the preconditioners extends naturally the work in the aforementioned, the analysis shown in this paper presents a set of significant challenges that are rooted in the nonlinearity of the constraints. We also include numerical results that showcase the behavior of the proposed preconditioners and show that for low to moderate Reynolds numbers they can lead to significant drops in the number of iterations and wall-clock savings.
引用
收藏
页码:1494 / 1523
页数:30
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