Efficient numerical solution of parabolic optimization problems by finite element methods

Optimization Methods and Software

Volumn 22, Issue 5, 2007, Pages 813-833

  Becker, Roland ^a   Meidner, Dominik ^b   Vexler, Boris ^c  

^a UNIVERSITÉ DE PAU ET DES PAYS DE L'ADOUR   (France)

^b UNIVERSITY OF HEIDELBERG   (Germany)

^c JOHANN RADON INSTITUTE FOR COMPUTATIONAL AND APPLIED MATHEMATICS   (Austria)

Author keywords

Finite elements; Newton's method; Optimal control; Parabolic equations; Storage reduction

Indexed keywords

FINITE ELEMENT METHOD; NUMERICAL METHODS; OPTIMAL CONTROL SYSTEMS; PARTIAL DIFFERENTIAL EQUATIONS;

NEWTON'S METHOD; PARABOLIC EQUATIONS; STORAGE REDUCTION;

OPTIMIZATION;

EID: 34547949714     PISSN: 10556788     EISSN: 10294937     Source Type: Journal    
DOI: 10.1080/10556780701228532     Document Type: Article

References (21)

1. Griewank, A., 1992, Achieving logarithmic growth, of temporal and spatial complexity in reverse automatic differentiation. Optimization Methods and Software, 1, 35-54.
2. Griewank, A., 2000, Evaluating derivatives, principles and techniques of algorithmic differentiation. Frontiers in Applied Mathematics, Vol. 19, (Philadelphia: SIAM).
3. Berggren, M., Glowinski, R. and Lions, J.-L., 1996, A computational approach to controllability issues for flowrelated models. (I): Pointwise control of the viscous burgers equation. International Journal of Computational Fluid Dynamics, 7, 237-253.
4. Meidner, D. and Vexler, B., 2006, Adaptive space-time finite element methods for parabolic optimization problems. SIAM Journal on, Control and Optimization, to appear.
5. Eriksson, K., Johnson, C. and Thomée, V., 1985, Time discretization of parabolic problems by the discontinuous Galerkin method. RAIRO Modelisation Mathematical Analysis and Numerical Methods, 19, 611-643.
6. Dautray, R. and Lions, J.-L., 1992, Mathematical Analysis and Numerical Methods for Science and Technology: Evolution Problems I, Vol. 5 (Berlin: Springer-Verlag).
7. Lions, J.-L., 1971, Optimal control of systems governed by partial differential equations. Grundlehren der Mathematischen Wissenschaften, Vol. 170 (Berlin: Springer-Verlag).
8. Fursikov, A.V., 1999, Optimal control of distributed systems: theory and applications. Translations of Mathematical Monography, Vol. 187 (Providence: AMS).
9. Litvinov, W.G., 2000, Optimization in elliptic problems with applications to mechanics of deformable bodies and fluid mechanics. Operational Theory: Advances and Applications, Vol. 119 (Basel: Birkhäuser Verlag).
10. Tröltzsch, F., 2005, Optimale Steuerung partieller Differentialgleichungen (Wiesbaden: Friedr. Vieweg & Sohn Verlag).
11. Hinze, M. and Kunisch, K., 2001, Second order methods for optimal control of time-dependent fluid flow. SIAM Journal on Control and Optimization, 40, 925-946.
12. Tröltzsch, F., 1999, On the Lagrange-Newton-SQP method for the optimal control of semilinear parabolic equations. SIAM Journal on Control and Optimization, 38, 294-312.
13. Estep, D. and Larsson, S., 1993, The discontinuous Galerkin method for semilinear parabolic problems. RAIRO Modelisation Mathematical Analysis and Numerical Methods, 27, 35-54.
14. Ciariet, P.G., 2002. The finite element method for elliptic problems. Classics Applied Mathematics, Vol. 40 (Philadelphia: SIAM).
15. Schmich, M. and Vexler, B., 2006, Adaptivity with dynamic meshes for space-time finite element discretizations of parabolic equations. SIAM Journal of Scientific Computing, Submitted.
16. Walther, A. and Griewank, A., 2004, Advantages of binomial checkpointing for memory-reduced adjoint calculations. In: M. Feistauer, V. Dolejší, P. Knobloch and K. Najzar (Eds) Numerical Mathematics and Advanced Applications (Berlin: Springer), pp. 834-843. Proceeding of ENUMATH 2003.
17. Becker, R., 2001, Adaptive Finite Elements for Optimal Control Problems. Habilitationsschrift, Institut für Angewandte Mathematik, Universität Heidelberg.
18. Becker, R., Meidner, D. and Vexler, B., 2005, RoDoBo: A C++ library for optimization with stationary and nonstationary PDEs with interface to GASCOIGNE [19]. Available online at: http://www.rodobo.uni-hd.de.
19. Becker, R., Braack, M., Meidner, D., Richter, T., Schmich, M. and Vexler, B., 2005, The finite element toolkit GASCOIGNE. Available online at: http://www.gascoigne.uni-hd.de.
20. Becker, R., Dunne, T and Meidner, D., 2005, VISUSIMPLE: An interactive VTK-based visualization and graphics/mpeg-generation program. Available online at: http://www.visusimple.uni-hd.de.
21. Rannacher, R. and Vexler, B., 2005, A priori error estimates for the finite element discretization of elliptic parameter identification problems with pointwise measurements. SIAM Journal on Control and Optimization, 44, 1844-1863.