Department of Mathematics,
University of California San Diego
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Math 278C: Optimization and Data Science
Prof. Michele Benzi
Scuola Normale Superiore, Pisa
An augmented Lagrangian preconditioner for the control of the Navier--Stokes equations
Abstract:
After briefly recalling the history of the augmented Lagrangian approach to constrained optimization problems, the solution of the distributed control problem for the steady, incompressible Navier-Stokes equations is addressed via inexact Newton linearization of the optimality conditions. Upon discretization by a finite element scheme, a sequence of large symmetric linear systems of saddle-point type is obtained. An equivalent augmented Lagrangian formulation is solved by the flexible GMRES method used in combination with a block triangular preconditioner. The preconditioner is applied inexactly via a suitable multigrid solver. Numerical experiments indicate that the resulting solver appears to be fairly robust with respect to viscosity, mesh size, and the choice of regularization parameter when applied to 2D problems. This is joint work with Santolo Leveque (Houston) and Patrick Farrell (Oxford).
Host: Jiawang Nie
October 8, 2025
4:00 PM
APM 2402
Research Areas
Optimization****************************