Sensitivity analysis of differential-algebraic equations and partial differential equations

Computers and Chemical Engineering

Volumn 30, Issue 10-12, 2006, Pages 1553-1559

  Petzold, Linda ^a   Li, Shengtai ^b   Cao, Yang ^c   Serban, Radu ^d  

^a University of California   (United States)

^b LOS ALAMOS NATIONAL LABORATORY   (United States)

^c State University   (United States)

^d LAWRENCE LIVERMORE NATIONAL LABORATORY   (United States)

Author keywords

Adjoint method; Differential algebraic equations; Sensitivity analysis

Indexed keywords

ALGEBRA; ALGORITHMS; COMPUTER SOFTWARE; OPTIMAL CONTROL SYSTEMS; PARTIAL DIFFERENTIAL EQUATIONS; SENSITIVITY ANALYSIS;

DIFFERENTIAL-ALGEBRAIC EQUATIONS (DAE); EXPERIMENTAL DESIGN; MODEL REDUCTION; TIME-DEPENDENT PARTIAL DIFFERENTIAL EQUATION;

PROCESS ENGINEERING;

ALGEBRA; ALGORITHMS; COMPUTER SOFTWARE; OPTIMAL CONTROL SYSTEMS; PARTIAL DIFFERENTIAL EQUATIONS; PROCESS ENGINEERING; SENSITIVITY ANALYSIS;

EID: 33747889036     PISSN: 00981354     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compchemeng.2006.05.015     Document Type: Article

References (31)

1. Anderson W.K., and Venkatakrishnan V. Aerodynamic design optimization on unstructured grid with a continuous adjoint formulation. AIAA 97-0643, 35th aerospace science meeting & exhibit (1997)
2. Arian E., and Salas M. Admitting the inadmissible: Adjoint formulation for incomplete cost functionals in aerodynamic optimization. AIAA Journal 37 1 (1999) 37-44
3. Ascher U.M., and Petzold L.R. Computer methods for ordinary differential equations and differential-algebraic equations (1998), SIAM
4. Barton P., and Tolsma J. DAEPACK: An open modeling environment for legacy models. Industrial and Engineering Chemistry Research 39 6 (2000) 1826-1839
5. Berger M.J., and Oliger J. Adaptive mesh refinement for hyperbolic partial differential equations. Journal of Computational Physics 53 (1984) 484-512
6. Bischof C., Carle A., Corliss G., Griewank A., and Hovland P. ADIFOR-generating derivative codes from Fortran programs. Scientific Programming 1 (1992) 11-29
7. Bischof, C., Roh, L., & Mauer, A. (1996). ADIC-an extensible automatic differentiation tool for ANSI-C. Technical Report ANL/MCS-P626-1196. Mathematics and Computer Science Division, Argonne National Laboratory.
8. Borggaard J., and Burns J. A PDE sensitivity equation method for optimal aerodynamic design. Journal of Computational Physics 136 (1997) 366-384
9. Brenan K.E., Campbell S.L., and Petzold L.R. Numerical solution of initial-value problems in differential-algebraic equations. 2nd ed. (1996), SIAM
10. Brown P.N., Hindmarsh A.C., and Petzold L.R. Using Krylov methods in the solution of large-scale differential-algebraic systems. SIAM Journal of Scientific Computing (1994) 1467-1488
11. Cao Y., Li S., and Petzold L. Adjoint sensitivity analysis for differential-algebraic equations: Algorithms and software. Journal of Computational and Applied Mathematics 149 (2002) 171-192
12. Cao Y., Li S., Petzold L., and Serban R. Adjoint sensitivity analysis for differential-algebraic equations: The adjoint DAE system and its numerical solution. SIAM Journal of Scientific Computing 24 3 (2003) 1076-1089
13. Errico R.M. What is an adjoint model?. Bulletin of the American Meteorological Society 78 (1997) 2577-2591
14. Feehery W.F., Tolsma J.E., and Barton P.I. Efficient sensitivity analysis of large-scale differential-algebraic systems. Applied Numerical Mathematics 25 (1997) 41-54
15. Ghattas O., and Bark J.-H. Optimal control of two and three-dimensional incompressible Navier-Stokes Flows. Journal of Computational Physics 136 (1997) 231-244
16. Giering R., and Kaminski T. Recipes for adjoint code construction. ACM Transactions on Mathematical Software 24 (1998) 437-474
17. Giles, M. B., & Pierce, N. A. (1997). Adjoint equations in CFD: Duality, boundary conditions and solution behaviour. AIAA Paper 97-1850.
18. Hindmarsh A.C., Brown P.N., Grant K.E., Lee S.L., Serban R., Shumaker D.E., and Woodward C.S. SUNDIALS, suite of nonlinear and differential/algebraic equation solvers. ACM Transactions on Mathematical Software 31 3 (2005) 363-396
19. Jameson A. Aerodynamic design via control theory. Journal of Scientific Computing 3 (1988) 233-260
20. Jarny Y., Ozisik M.N., and Barton J.P. A general optimization method using adjoint equation for solving multidimensional inverse heat conduction. International Journal of Heat Mass Transfer 34 (1991) 2911-2919
21. Knapp D., Barocas V., Yoo K., Petzold L., and Tranquillo R. Rheology of reconstituted type I collagen gel in confined compression. Journal of Rheology 41 (1997) 971-993
22. Li, S., & Petzold, L. (1999). Design of new DASPK for sensitivity analysis, technical report. Department of Computer Science, Technical Report UCSB.
23. Li S., and Petzold L. Software and algorithms for sensitivity analysis of large-scale differential-algebraic systems. Journal of Computational and Applied Mathematics 125 (2000) 131-145
24. Li, S., & Petzold, L. (2002). Description of DASPKADJOINT: An adjoint sensitivity solver for differential-algebraic equations. UCSB Technical Report 2002, www.engineering.ucsb.edu/cse.
25. Li S., and Petzold L. Adjoint sensitivity analysis for time-dependent partial differential equations with adaptive mesh refinement. Journal of Computational Physics 198 1 (2004) 310-325
26. Li S., Petzold L., and Hyman J. Solution adapted mesh refinement and sensitivity analysis for parabolic partial differential equations. In: Biegler L.T., Ghattas O., Heinkenschloss M., and van Bloeman Waanders B. (Eds). Lecture notes in computational science and engineering Vol. 30 (2003), Springer-Verlag, Heidelberg
27. Li S., Petzold L., and Zhu W. Sensitivity analysis of differential-algebraic equations: A comparison of methods on a special problem. Applied Numerical Mathematics 32 (2000) 161-174
28. Maly T., and Petzold L.R. Numerical methods and software for sensitivity analysis of differential-algebraic systems. Applied Numerical Mathematics 20 (1997) 57-79
29. Nadarajah, S. K., & Jameson, A. (2002). A comparison of the continuous and discrete adjoint approach to automatic aerodynamic optimisation. AIAA paper 00-0067.
30. Raja L.L., Kee R.J., Serban R., and Petzold L. Dynamic optimization of chemically reacting stagnation flows. Proceedings of Electrochemical Society (1998)
31. Serban R., and Hindmarsh A.C. CVODES, the sensitivity-enabled ODE solver in SUNDIALS. Proceedings of the ASME international design engineering technical conferences. Long Beach, CA, 24-28 September (2005)