Solving optimal control problems for the unsteady Burgers equation in COMSOL Multiphysics

Authors:
F. Yılmaz;B. Karasözen
Affiliations:
Department of Mathematics, Gazi University, 06500 Ankara, Turkey;Department of Mathematics and Institute of Applied Mathematics, Middle East Technical University, 06531 Ankara, Turkey
Venue:
Journal of Computational and Applied Mathematics
Year:
2011

Citing 5
Cited 2

Distributed Control Problems for the Burgers Equation

Computational Optimization and Applications
Optimal Control of the Viscous Burgers Equation Using an Equivalent Index Method

Journal of Global Optimization
Analysis of instantaneous control for the Burgers equation

Nonlinear Analysis: Theory, Methods & Applications
The Primal-Dual Active Set Strategy as a Semismooth Newton Method

SIAM Journal on Optimization
Adjoint concepts for the optimal control of Burgers equation

Computational Optimization and Applications

An all-at-once approach for the optimal control of the unsteady Burgers equation

Journal of Computational and Applied Mathematics
Distributed optimal control of time-dependent diffusion-convection-reaction equations using space-time discretization

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	7.29

Visualization

Abstract

The optimal control of unsteady Burgers equation without constraints and with control constraints are solved using the high-level modelling and simulation package COMSOL Multiphysics. Using the first-order optimality conditions, projection and semi-smooth Newton methods are applied for solving the optimality system. The optimality system is solved numerically using the classical iterative approach by integrating the state equation forward in time and the adjoint equation backward in time using the gradient method and considering the optimality system in the space-time cylinder as an elliptic equation and solving it adaptively. The equivalence of the optimality system to the elliptic partial differential equation (PDE) is shown by transforming the Burgers equation by the Cole-Hopf transformation to a linear diffusion type equation. Numerical results obtained with adaptive and nonadaptive elliptic solvers of COMSOL Multiphysics are presented both for the unconstrained and the control constrained case.