Adjoint gradients compared to gradients from algorithmic differentiation in instantaneous control of the Navier-Stokes equations

Optimization Methods and Software

Volumn 18, Issue 3, 2003, Pages 299-315

  Hinze, Michael ^a   Slawig, Thomas ^b  

^a DRESDEN UNIVERSITY OF TECHNOLOGY   (Germany)

^b TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

Author keywords

Adjoint equation; Algorithmic differentiation; Instantaneous control; Navier Stokes equations

Indexed keywords

COMPUTER AIDED SOFTWARE ENGINEERING; DIFFERENTIATION (CALCULUS); ERROR ANALYSIS; FUNCTIONS; NAVIER STOKES EQUATIONS; PROBLEM SOLVING;

ADJOINT GRADIENTS; ALGORITHMIC DIFFERENTIATION; INSTANTANEOUS CONTROL;

ALGORITHMS;

EID: 0041344302     PISSN: 10556788     EISSN: None     Source Type: Journal    
DOI: 10.1080/1055678031000115331     Document Type: Article

References (21)

1. P. Constantin and C. Foias (1988). Navier-Stokes Equations. The University of Chicago Press.
2. R. Temam (1979). Navier-Stokes Equations. North-Holland.
3. M. Hinze (1999) Optimal and instantaneous control of the instationary Navier-Stokes equations. Habilitationsschrift, Fachbereich Mathematik, Technische Universität Berlin, [www http://www.math.tudresden.de/~hinze/publications.html].
4. C.E. García, D.M. Prett and M. Morari (1989). Model predictive control: Theory and practice - a survey. Automatica, 25(3), 335-348.
5. J. B. Rawlings and K.R. Muske (1993). The stability of constrained receding horizon control. IEEE Transactions on Automatic Control, 38(10), 1512-1516.
6. T. Bewley, H. Choi, R. Temam and P. Moin (1993). Optimal feedback control of turbulent channel flow. Center for Turbulence Research Annual Research Briefs.
7. H. Choi, M. Hinze and K. Kunisch (1999). Instantaneous control of backward-facing-step flows. Applied Numerical Mathematics, 31, 133-158.
8. S. Kang and H. Choi (2000). Suboptimal feedback control of turbulent flow over a backward-facing step. J. Fluid Mech. (Submitted).
9. F. Tröltzsch and A. Unger (2001). Fast solution of optimal control problems in selective cooling of steel. ZAMM, 81, 447-456.
10. M. Hinze (2002). Instantaneous closed loop control of the Navier-Stokes system. Preprint MATH-NM-09-2002. Institut für Numerische Mathematik, Technische Universität Dresden, Germany.
11. M. Hinze and S. Volkwein (2002). Instantaneous control for the Burgers equation: Convergence analysis and numerical implementation. Nonlinear Analysis, T.M.A., 50 (1), 1-26.
12. P. Hood and C. Taylor (1973). A numerical solution of the Navier-Stokes equations using the finite element technique. Comp. and Fluids, 1, 73-100.
13. R. Giering and T. Kaminski (1998). Recipes for Adjoint Code Construction. ACM Transactions on Math. Software, 24 (4), 437-474.
14. A. Griewank (2000). Evaluating Derivatives, SIAM Frontiers in Appl. Math., Philadelphia.
15. Homepage of the AutoDiff project. Argonne Nat. Lab., Argonne IL, USA. [www http://www.unix.mcs.anl.gov/autodiff/AD_Tools/index.html].
16. TAMC homepage. MIT, Boston MS, USA. [www http://www.autodiff.com/tamc].
17. TAF homepage. FastOpt GbR Hamburg. [www http://www.fastopt.com].
18. ODYSSEE homepage. INRIA, France. [www http://www.sop.inria.fr.safir/SAM/Odyssee].
19. Tapenade homepage. INRIA, France. [www http://www.sop.inria.fr/tropics].
20. Adifor homepage, Argonne National Laboratory, Argonne IL, USA, [www http://www.unix.mcs.anl.gov/autodiff/ADIFOR].
21. T. Slawig (2001). Domain Optimization of a multi-element airfoil using automatic differentiation. Advances in Engineering Software, 32, 225-237.