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

YILMAZ F. N., KARASÖZEN B.

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, vol.259, pp.771-779, 2014 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 259
  • Publication Date: 2014
  • Doi Number: 10.1016/j.cam.2013.06.036
  • Journal Name: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.771-779
  • Keywords: Optimal control, Burgers equation, All-at-once approach, Control constraints, Semi-implicit discretization, CONSTRAINED OPTIMAL-CONTROL, OPTIMIZATION, STRATEGY
  • Gazi University Affiliated: Yes

Abstract

We apply an all-at-once method for the optimal control of the unsteady Burgers equation. The nonlinear Burgers equation is discretized in time using the semi-implicit discretization and the resulting first order optimality conditions are solved iteratively by Newton's method. The discretize then optimize approach is used, because it leads to a symmetric indefinite saddle point problem. Numerical results for the distributed unconstrained and control constrained problems illustrate the performance of the all-at-once approach with semi-implicit time discretization. (C) 2013 Elsevier B.V. All rights reserved.