A preconditioner for optimal control problems, constrained by Stokes equation with a time-harmonic control
نویسندگان
چکیده
In an earlier paper preconditioning of stationary Stokes-constrained optimal control problems has been considered. In this article we construct an efficient preconditioner for solving the algebraic systems arising from discretized optimal control problems with time-periodic Stokes equations. A simplified analysis of the derivation of the preconditioner and its properties is presented. The preconditioner is fully parameter independent and the condition number of the corresponding preconditioned matrix is bounded by 2. The so-constructed preconditioner is favourably compared with another preconditioner for the same problem.
منابع مشابه
Optimization with the time-dependent Navier-Stokes equations as constraints
In this paper, optimal distributed control of the time-dependent Navier-Stokes equations is considered. The control problem involves the minimization of a measure of the distance between the velocity field and a given target velocity field. A mixed numerical method involving a quasi-Newton algorithm, a novel calculation of the gradients and an inhomogeneous Navier-Stokes solver, to find the opt...
متن کاملPreconditioning Iterative Methods for the Optimal Control of the Stokes Equations
Solving problems regarding the optimal control of partial differential equations (PDEs) – also known as PDE-constrained optimization – is a frontier area of numerical analysis. Of particular interest is the problem of flow control, where one would like to effect some desired flow by exerting, for example, an external force. The bottleneck in many current algorithms is the solution of the optima...
متن کاملEfficient Preconditioning for an Optimal Control Problem with the Time-Periodic Stokes Equations
For the optimal control problem with time-periodic Stokes equations a practical robust preconditioner is presented. The discretization of the corresponding optimality system leads to a linear system with a large, sparse and complex 4-by-4 block matrix in saddle point form. We present a decoupling strategy, which reduces the system to two linear systems with a real 4-by-4 block matrix. Based on ...
متن کاملComparison of preconditioned Krylov subspace iteration methods for PDE-constrained optimization problems. Stokes control
The governing dynamics of fluid flow is stated as a system of partial differential equations referred to as the Navier-Stokes system. In industrial and scientific applications, fluid flow control becomes an optimization problem where the governing partial differential equations of the fluid flow are stated as constraints. When discretized, the optimal control of the Navier-Stokes equations lead...
متن کاملRobust Iterative Solution of a Class of Time-Dependent Optimal Control Problems
The fast iterative solution of optimal control problems, and in particular PDE-constrained optimization problems, has become an active area of research in applied mathematics and numerical analysis. In this paper, we consider the solution of a class of time-dependent PDE-constrained optimization problems, specifically the distributed control of the heat equation. We develop a strategy to approx...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- J. Computational Applied Mathematics
دوره 310 شماره
صفحات -
تاریخ انتشار 2017