Paper Info
Title
MULTIGRID PRECONDITIONERS FOR THE NEWTON-KRYLOV METHOD IN THE OPTIMAL CONTROL OF THE STATIONARY NAVIER-STOKES EQUATIONS
Abstract
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.
Year
DOI
Venue
2019
10.1137/18M1175264
SIAM JOURNAL ON NUMERICAL ANALYSIS
Keywords
Field
DocType
multigrid methods,PDE-constrained optimization,Navier-Stokes equations,finite elements
Convergence (routing),Newton–Krylov method,Optimal control,Mathematical analysis,Mathematics,Multigrid method,Navier–Stokes equations
Journal
Volume
Issue
ISSN
57
3
0036-1429
Citations 
PageRank 
References 
0
0.34
0
Authors
2
Name
Order
Citations
PageRank
Ana Maria Soane100.34
Andrei Drăgănescu2667.90