Adjoint sensitivity analysis for time-dependent partial differential equations with adaptive mesh refinement

Journal of Computational Physics

Volumn 198, Issue 1, 2004, Pages 310-325

  Li, Shengtai ^a   Petzold, Linda ^b  

^a LOS ALAMOS NATIONAL LABORATORY   (United States)

^b Santa Barbara   (United States)

Author keywords

Adaptive mesh method; Adjoint method; Adjoint PDE; Continuous approach; Discrete approach; Partial differential equations; Sensitivity analysis

Indexed keywords

BOUNDARY CONDITIONS; MESH GENERATION; PARTIAL DIFFERENTIAL EQUATIONS;

ADAPTIVE MESH METHOD; ADAPTIVE MESH REFINEMENT; ADJOINT METHODS; ADJOINT PDE; ADJOINT SENSITIVITY ANALYSIS; ADJOINTS; CONTINUOUS APPROACH; DISCRETE APPROACH; DISCRETIZATIONS; TIME-DEPENDENT PARTIAL DIFFERENTIAL EQUATIONS;

SENSITIVITY ANALYSIS;

EID: 3042734351     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jcp.2003.01.001     Document Type: Article

References (23)

1. W.K. Anderson, V. Venkatakrishnan, Aerodynamic design optimization on unstructured grid with a continuous adjoint formulation, in: 35'th Aerospace Science Meeting & Exhibit, 1997, AIAA 97-0643
2. E. Arian, M. Salas, Admitting the inadmissible: adjoint formulation for incomplete cost functionals in aerodynamic optimization, ICASE Report No. 97-69, 1997
3. Berger M.J. Oliger J. Adaptive mesh refinement for hyperbolic partial differential equations J. Comput. Phys. 53 1984 484-512
4. Bewley T.R. Flow control: new challenges for a new renaissance Prog. Aerospace Sci. 37 2001 21-58
5. Borggaard J. Burns J. A PDE sensitivity equation method for optimal aerodynamic design J. Comput. Phys. 136 1997 366-384
6. Bischof C. Carle A. Corliss G. Griewank A. Hovland P. ADIFOR - generating derivative codes from Fortran programs Sci. Program. 1 1992 11-29
7. Cao Y. Li S. Petzold L. Serban R. Adjoint sensitivity analysis for differential-algebraic equations: the adjoint DAE system and its numerical solution SIAM J. Sci. Comput. 24 2003 1076-1089
8. P. Colella, Dan Martin, and other staffs in applied numerical analysis group, Chombo1.2, released in 2002, Lawrence Berkley National Laboratory. Available from http://seesar.lbl.gov/anag/ chombo/index.html
9. P. Eberhard, C. Bischof, Automatic differentiation of numerical integration algorithms, Argonne National Lab., ANL/MCS-P621-1196, 1996 (preprint)
10. Fryxell B. Olson K. Ricker P. Timmes F.X. Zingale M. Lamb D.Q. MacNeice P. Rosner R. Truran J.W. Tufo H. Flash: an adaptive mesh hydrodynamics code fro modeling astrophysical thermonuclear flashes ApJS 131 2000 273
11. Jarny Y. Ozisik M.N. Bardon J.P. A general optimization method using adjoint equation for solving multidimensional inverse heat conduction Int. J. Heat Mass Transfer 34 1991 2911-2919
12. Giering R. Kaminski T. Recipes for adjoint code construction ACM Trans. Math. Software 24 1998 437-474
13. M.B. Giles, N.A. Pierce, Adjoint equations in CFD: duality, boundary conditions and solution behaviour, AIAA Paper 97-1850, 1997
14. Ghattas P. Bark J.-H. Optimal control of two and three-dimensional incompressible Navier-Stokes flows J. Comput. Phys. 136 1997 231-244
15. Jameson A. Aerodynamic design via control theory J. Sci. Computing 3 1988 233-260
16. S.K. Nadarajah, A. Jameson, A comparison of the continuous and discrete adjoint approach to automatic aerodynamic optimization, AIAA paper 00-0067, 2000
17. S. Li, L. Petzold, User's guide for the DASPK adjoint solver, Technical Report 01-39, University of California, Santa Barbara, 2001
18. Li S. Petzold L. Hyman J. Solution adapted nested grid refinement and sensitivity analysis for parabolic partial differential equations Lecture Notes in Computational Science and Engineering 2001 Springer Berlin
19. Martinson W.S. Barton P.I. A differentiation index for partial differential-algebraic equations SIAM J. Sci. Comput. 21 2000 2295-2315
20. Campbell S.L. Gear C.W. ODE/DAE integrators and MOL problems Z. Angew. Math. Mech. 76S 1996 251-254
21. Serban R. Li S. Petzold L. Adaptive algorithms for optimal control of time-dependent partial differential-algebraic equation systems Int. J. Numer. Meth. Eng. 57 2003 1457-1469
22. A. Sei, W.W. Symes, A note on consistency and adjointness for numerical schemes, Technical Report TR95-04, Department of Computational and Applied Mathematics, Rice University, 1995
23. P.A. Zegeling, Moving finite-element solution of time-dependent partial differential equations in two space dimensions, Department of Numerical Mathematics, CWI, Amsterdam, Report NM-R9206, 1992