An object-oriented framework for the implementation of adjoint techniques in the design and control of complex continuum systems

International Journal for Numerical Methods in Engineering

Volumn 48, Issue 2, 2001, Pages 239-266

  Sampath, Rajiv ^a   Zabaras, Nicholas ^a  

^a Cornell University   (United States)

Author keywords

Adjoint method; Convection diffusion problems; Finite element method; Functional optimization; Inverse natural convection; Object oriented programming

Indexed keywords

COMPUTER SIMULATION; FINITE ELEMENT METHOD; INVERSE PROBLEMS; NATURAL CONVECTION; OBJECT ORIENTED PROGRAMMING; OPTIMIZATION;

ADJOINT METHODS; FUNCTIONAL OPTIMIZATION;

CONTINUUM MECHANICS;

EID: 0034187084     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0207(20000520)48:2<239::AID-NME877>3.0.CO;2-F     Document Type: Article

References (43)

1. Anderson E, Bai Z, Bischof C, Demmel J, Dongarra J, Du Croz J, Greenbaum A, Hammarling S, McKenney A, Ostrouchov S, Sorensen D. LAPACK Users' Guide (2nd edn). SIAM: Philadelphia, 1995.
2. Barton JJ, Nackman LR. Scientific and Engineering C++. Addison-Wesley: New York, 1994.
3. OON-SKI'93. Proceedings of the First Annual Object-Oriented Numerics Conference, Sunriver, Oregon, 1993.
4. Rüde U. Mathematical and computational techniques for multilevel adaptive methods. Frontiers in Applied Mathematics SIAM 1993; 13.
5. OON-SKI'94. Proceedings of the Second Annual Object-Oriented Numerics Conference, Sunriver, Oregon, 1994.
6. Daehlen M, Tveito A (eds). Numerical Methods and Software Tools in Industrial Mathematics. Birkhäuser: Boston, 1997.
7. Arge E, Bruaset AM, Langtangen H-P (eds). Modern Software Tools for Scientific Computing. Birkhäuser: Boston, 1997.
8. Langtangen HP. Computational Partial Differential Equations: Numerical Methods and Diffpack Programming. Springer: New York, 1999.
9. Mackie RI. Object oriented programming of the finite element method. International Journal for Numerical Methods in Engineering 1992; 35:425-436.
10. Zimmermann T, Dubois-Pèlerin Y, Bomme P. Object-oriented finite element programming: I Governing principles. Computer Methods in Applied Mechanics and Engineering 1992; 98:291-303.
11. Zeglinski GW, Han RPS. Object oriented matrix classes for use in a finite element code using C++. International Journal for Numerical Methods in Engineering 1994; 37:3921-3937.
12. Sampath R, Zabaras N. An object oriented implementation of a front tracking finite element method for directional solidification processes. International Journal for Numerical Methods in Engineering 1999; 44:1227-1265.
13. Luenberger DG. Optimization by Vector Space Methods. Wiley: New York, 1990.
14. Lions J-L. Optimal Control of Systems Governed by Partial Differential Equations. Springer: Berlin, 1971.
15. Cuvelier P. Optimal control of a system governed by the Navier-Stokes equations coupled with the heat equations. In New Developments in Differential Equations, Eckhaus W (ed.). North-Holland: Amsterdam, 1976; 81-98.
16. Dean EJ, Gubernatis P. Pointwise control of Burger's equation - a numerical approach. Computers and Mathematics with Applications 1994; 22:93-100.
17. Gunzburger MD, Hou L, Svobodny T. Heating and cooling control of temperature distributions along boundaries of flow domains. Journal of Mathematical Systems and Estimation Control 1993; 3(2):147-172.
18. Gunzburger MD, Lee HC. Analysis, approximation, and computation of a coupled solid/fluid temperature control problem. Computer Methods in Applied Mechanics and Engineering 1994; 118:133-152.
19. Berggren M, Glowinski R, Lions JL. A computational approach to controllability issue for flow related models. (1): pointwise control of the viscous Burger's equation. International Journal of Computational Fluid Dynamics 1996; 7:237-252.
20. Zabaras N, Yang G. A functional optimization formulation and FEM implementation of an inverse natural convection problem. Computer Methods in Applied Mechanics and Engineering 1997; 144(3-4): 245-274.
21. Berggren M. Numerical solution of a flow-control problem: vorticity reduction by dynamic boundary action. SIAM Journal of Scientific Computing 1998; 19(3):829-860.
22. Yang G, Zabaras N. The adjoint method for an inverse design problem in the directional solidification of binary alloys. Journal of Computational Physics 1998; 140(2):432-452.
23. Gladwell GML. Inverse Problems in Vibration. Martinus Nijhoff Publishers: Dordrecht, 1986.
24. Bennett AF. Inverse Methods in Physical Oceanography. Cambridge University Press: Cambridge, 1992.
25. Sun N-Z. Inverse Problems in Groundwater Modeling. Kluwer Academic Publishers: Boston, 1994.
26. Chavent G, Papanicolaou G, Sacks P, Symes WW (eds). Inverse Problems in Wave Propagation. Springer: New York, 1995.
27. Marchuk GI. Adjoint Equations and Analysis of Complex Systems. Kluwer Academic Publishers: Boston, 1995.
28. Rambaugh J, Lorensen W. Object-Oriented Modeling and Design. Prentice-Hall: Englewood Cliffs, NJ, 1991.
29. Wirfs-Brock R, Wilkerson B, Wiener L. Designing Object-Oriented Software. Prentice-Hall: Englewood Cliffs, NJ, 1990.
30. Stefik M, Brobow D. Object-oriented programming: themes and variations. Artificial Intelligence Magazine 1993; 6(4):40-62.
31. Thomas D. Object-oriented programming: what's an object. Byte Magazine 1989; 14(3):231-240.
32. Diffpack Basic Tools, Diffpack Reference Manual, vol. I, World Wide Web Document, SINTEF and University of Oslo, 1996 (URL: http://www.nobjects.com/prodserv/diffpack).
33. Diffpack Linear Algebra Tools, Diffpack Reference Manual, vol. II, World Wide Web Document, SINTEF and University of Oslo, 1996 (URL: http://www.nobjects.com/prodserv/diffpack).
34. Diffpack DpKernel and DpUtil, Diffpack Reference Manual, vol. III, World Wide Web Document, SINTEF and University of Oslo, 1996 (URL: http://www.nobjects.com/prodserv/diffpack).
35. Fletcher R. Practical Methods of Optimization (2nd edn). Wiley-Interscience: New York, 1987.
36. Brooks AN, Hughes TJR. Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Computer Methods in Applied Mechanics and Engineering 1982; 32:199-259.
37. Johnson C. Numerical Solution of Partial Differential Equations by the Finite Element Method. Cambridge University Press: Cambridge, 1987.
38. Tezduyar TE, Mittal S, Ray SE, Shih R. Incompressible flow computations with stabilized bilinear and linear equal-order-interpolation velocity-pressure elements. Computer Methods in Applied Mechanics and Engineering 1992; 95:221-242.
39. Franca LP, Frey SL. Stabilized finite element methods: II. The incompressible Navier-Stokes equations. Computer Methods in Applied Mechanics and Engineering 1992; 99:209-233.
40. Tezduyar TE, Behr M, Liou J. A new strategy for finite element computations involving moving boundaries and interfaces - The defortning-spatial-domain/space-time procedure: I. The concept and the preliminary numerical tests. Computer Methods in Applied Mechanics and Engineering 1992; 94:339-351.
41. Tezduyar, TE, Behr, M, Mittal S, Liou J. A new strategy for finite element computations involving moving boundaries and interfaces - The deforming-spatial-domain/space-time procedure: II. Computation of free-surface flows, two-liquid flows and flows with drifting cylinders. Computer Methods in Applied Mechanics and Engineering 1992; 94:353-371.
42. Tezduyar TE, Liou J, Glowinski R. Petrov-Galerkin methods on multiply connected domains for vorticity-stream function and velocity pressure formulations. Computers and Structures 1990; 35:445-472.
43. Bristeau MO, Glowinski R, Periaux J. Numerical methods for the Navier-Stokes equations: applications to the simulation of compressible and incompressible viscous flows. Computer Physics Report 1998; 6:73-187.