Results 1  10
of
18
Xumerical solution of a flow control problem: vorticity reduction by dynamic boundary action
 Siam Journal in Control and Optimization
, 1998
"... Abstract. In order to laminarize an unsteady, internal flow, the vorticity field is minimized, in a leastsquares sense, using an optimalcontrol approach. The flow model is the Navier–Stokes equation for a viscous incompressible fluid, and the flow is controlled by suction and blowing on a part of ..."
Abstract

Cited by 28 (0 self)
 Add to MetaCart
(Show Context)
Abstract. In order to laminarize an unsteady, internal flow, the vorticity field is minimized, in a leastsquares sense, using an optimalcontrol approach. The flow model is the Navier–Stokes equation for a viscous incompressible fluid, and the flow is controlled by suction and blowing on a part of the boundary. A quasiNewton method is used for the minimization of a quadratic objective function involving a measure of the vorticity and a regularization term. The Navier–Stokes equations are approximated using a finitedifference scheme in time and finiteelement approximations in space. Accurate expressions for the gradient of the discrete objective function are needed to obtain a satisfactory convergence rate of the minimization algorithm. Therefore, firstorder necessary conditions for a minimizer of the objective function are derived in the fully discrete case. A memorysaving device is discussed without which problems of any realistic size, especially in three space dimensions, would remain computationally intractable. The feasibility of the optimalcontrol approach for flowcontrol problems is demonstrated by numerical experiments for a twodimensional flow in a rectangular cavity at a Reynolds number high enough for nonlinear effects to be important.
Second Order Methods For Optimal Control Of TimeDependent Fluid Flow
, 1999
"... Second order methods for open loop optimal control problems governed by the twodimensional instationary NavierStokes equations are investigated. Optimality systems based on a Lagrangian formulation and adjoint equations are derived. The Newton and quasiNewton methods as well as various variants o ..."
Abstract

Cited by 22 (5 self)
 Add to MetaCart
Second order methods for open loop optimal control problems governed by the twodimensional instationary NavierStokes equations are investigated. Optimality systems based on a Lagrangian formulation and adjoint equations are derived. The Newton and quasiNewton methods as well as various variants of SQPmethods are developed for applications to optimal ow control and their complexity in terms of system solves is discussed. Local convergence and rate of convergence are proved. A numerical example illustrates the feasibility of solving optimal control problems for twodimensional instationary NavierStokes equations by second order numerical methods in a standard workstation environment. Previously such problems were solved by gradient type methods.
The effect of stabilization in finite element methods for the optimal boundary control of the Oseen equations”, Finite Elements in Analysis and Design
"... We study the effect of the Galerkin/LeastSquares (GLS) stabilizationon the finite element discretization of optimal control problems governed by the linear Oseen equations. Control is applied in the form of suction or blowing on part of the boundary. Two ways of including the GLS stabilization into ..."
Abstract

Cited by 17 (7 self)
 Add to MetaCart
We study the effect of the Galerkin/LeastSquares (GLS) stabilizationon the finite element discretization of optimal control problems governed by the linear Oseen equations. Control is applied in the form of suction or blowing on part of the boundary. Two ways of including the GLS stabilization into the discretization of the optimal control problem are discussed. In one case the optimal control problem is first discretized and the resulting finite dimensional problem is then solved. In the other case, the optimality conditions are first formulated on the differential equation level and are then discretized. Both approaches lead to different discrete adjoint equations and, depending on the choice of the stabilization parameters and grid size, may significantly affect the computed control. The effect of the order in which the discretization is applied and the choice of the stabilization parameters are illustrated using two test problems. The cause of the differences in the computed controls are explored numerically. Diagnostics are introduced that may guide the selection of sensible stabilization parameters.
Second Order Methods for Boundary Control of the Instationary NavierStokes System
, 2002
"... Second order methods for open loop optimal boundary control problems governed by the instationary NavierStokes system are investigated. A general analytic framework is developed which allows an elegant representation of rst and second order derivatives of the objective functional and of the state e ..."
Abstract

Cited by 15 (2 self)
 Add to MetaCart
Second order methods for open loop optimal boundary control problems governed by the instationary NavierStokes system are investigated. A general analytic framework is developed which allows an elegant representation of rst and second order derivatives of the objective functional and of the state equations. Moreover a second order sucient optimality condition is proved which guarantees local quadratic convergence of Newton's method. 1
Constrained Optimal Control of NavierStokes Flow by Semismooth Newton Methods
 SYSTEMS & CONTROL LETTERS
, 2002
"... We propose and analyze a semismooth Newtontype method for the solution of a pointwise constrained optimal control problem governed by the timedependent incompressible NavierStokes equations. The method is based on a reformulation of the optimality system as an equivalent nonsmooth operator equati ..."
Abstract

Cited by 9 (2 self)
 Add to MetaCart
We propose and analyze a semismooth Newtontype method for the solution of a pointwise constrained optimal control problem governed by the timedependent incompressible NavierStokes equations. The method is based on a reformulation of the optimality system as an equivalent nonsmooth operator equation. We analyze the flow control problem and establish qsuperlinear convergence of the method. In the numerical implementation, adjoint techniques are combined with a truncated conjugate gradient method. Numerical results are presented that support our theoretical results and confirm the viability of the approach.
Fast Iterative Solution of Saddle Point Problems in Optimal Control Based on Wavelets
 COMPUT. OPTIM. APPL
, 2000
"... For the numerical solution of an elliptic boundary value problem with boundary control, the problem is formulated as minimizing a quadratic functional involving natural norms of the state and the control. Firstly the constraint, the elliptic boundary value problem, is formulated in an appropriate we ..."
Abstract

Cited by 8 (5 self)
 Add to MetaCart
For the numerical solution of an elliptic boundary value problem with boundary control, the problem is formulated as minimizing a quadratic functional involving natural norms of the state and the control. Firstly the constraint, the elliptic boundary value problem, is formulated in an appropriate weak form that allows to handle varying boundary conditions explicitly. Namely, the boundary conditions are appended by Lagrange multipliers, leading to a saddle point problem. This is combined with a fictitious domain approach in order to cover also more complicated boundaries. From the optimality conditions for the minimization problem, a second saddle point problem is derived. It is shown by standard techniques that the resulting weakly coupled system of the two saddle point problems admits a unique solution. For its discretization, (biorthogonal) wavelets are used which allows to formulate the matrix of the coupled system as an ` 2operator, initially in an infinitedimensional space. Using...
Trust Region SQP Methods With Inexact Linear System Solves For LargeScale Optimization
, 2006
"... by ..."
(Show Context)
Parallel NewtonKrylov Methods For PDEConstrained Optimization
 In Proceedings of Supercomputing ’99
, 1999
"... . Large scale optimization of systems governed by partial differential equations (PDEs) is a frontier problem in scientific computation. The stateoftheart for solving such problems is reducedspace quasiNewton sequential quadratic programming (SQP) methods. These take full advantage of existing ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
. Large scale optimization of systems governed by partial differential equations (PDEs) is a frontier problem in scientific computation. The stateoftheart for solving such problems is reducedspace quasiNewton sequential quadratic programming (SQP) methods. These take full advantage of existing PDE solver technology and parallelize well. However, their algorithmic scalability is questionable; for certain problem classes they can be very slow to converge. In this paper we propose a fullspace NewtonKrylov SQP method that uses the reducedspace quasiNewton method as a preconditioner. The new method is fully parallelizable; exploits the structure of and available parallel algorithms for the PDE forward problem; and is quadratically convergent close to a local minimum. We restrict our attention to boundary value problems and we solve a model optimal flow control problem, with both Stokes and NavierStokes equations as constraints. Algorithmic comparisons, scalability results, and para...
Control and Cybernetics
"... Local quadratic convergence of SQP for elliptic optimal control problems with mixed controlstate constraints ∗ by ..."
Abstract
 Add to MetaCart
(Show Context)
Local quadratic convergence of SQP for elliptic optimal control problems with mixed controlstate constraints ∗ by