The connection between the complex-step derivative approximation and algorithmic differentiation

39th Aerospace Sciences Meeting and Exhibit

Volumn , Issue , 2001, Pages

  Martins, Joaquim R R A ^a   Sturdza, Peter ^a   Alonso, Juan J ^a  

^a Department of Aeronautics and Astronautics Department of Mechanical Engineering and Industrial for Computational and Mathematical Engineering   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMIC DIFFERENTIATIONS; APPROXIMATION METHODS; AUTOMATIC IMPLEMENTATION; COMPLEX STEPS; MULTI DISCIPLINARY PROGRAMS;

AEROSPACE ENGINEERING;

EID: 84897585489     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (19)

1. Martins, J. R. R. A., I. M. Kroo, and J. J. Alonso An Automated Method for Sensitivity Analysis using Complex Variables Proceedings of the 38th Aerospace Sciences Meeting, Reno, NV, January 2000. AIAA Paper 2000-0689.
2. Anderson, W. K., J. C. Newman, D. L. Whitfield, E. J. Nielsen, Sensitivity Analysis for the Navier-Stokes Equations on Unstructured Meshes Using Complex Variables, AIAA Paper No. 99-3294, Proceedings of the 17th Applied Aerodynamics Conference, 28 Jun. 1999.
3. Newman, J. C., W. K. Anderson, D. L. Whitfield, Multidisciplinary Sensitivity Derivatives Using Complex Variables, MSSU-COE-ERC-98-08, Jul. 1998.
4. http://aero-comlab.Stanford.edu/jmartins
5. Griewank, A., Evaluating Derivatives, SIAM, Philadelphia, 2000.
6. Bischof, C, A. Carle, G. Corliss, A. Grienwank, P. Hoveland, ADIFOR: Generating Derivative Codes from Fortran Programs, Scientific Programming, Vol. 1, No. 1, 1992, pp. 11-29.
7. Bischof, C, G. Corliss, A. Grienwank, 'ADIFOR Exception Handling, Argonne Technical Memorandum, MCS-TM-159, 1991.
8. Beck, T. and H. Fischer, The if-problem in automatic differentiation, Journal of Computational and Applied Mathematics, Vol. 50, pp. 119-131, 1994.
9. Griewank, A., C. Bischof, Derivative Convergence for Iterative Equation Solvers Optimization Methods and Software, Vol. 2, pp. 321-355, 1993.
10. Beck, T., Automatic Differentiation of iterative processes Journal of Computational and Applied Mathematics, Vol. 50, pp. 109-118, 1994.
11. http://www.sc.rwth-aachen.de/Research/AD/subject.html
12. Bischof, C, L. Roh, A. Mauer, ADIC - An Extensible Automatic Differentiation Tool for ANSI-C, to appear in Software: Practice and Experience, also ANL/MCS-P626-1196 (http: //inf o.mcs. anl.gov/pub/techjreports /reports/P626.ps.Z)
13. Griewank, A., et al., ADOL-C: A Package for the Automatic Differentiation of Algorithms Written in C/C++, ACM TOMS, Vol. 22(2), June 199, pp. 131-167, Algorithm 755.
14. Reuther, J., J. J. Alonso, J. R. R. A. Martins, and S. C. Smith, A Coupled Aero-Structural Optimization Method for Complete Aircraft Configurations, Proceedings of the 31th Aerospace Sciences Meeting, AIAA Paper 1999-0187. Reno, NV, January 1999.
15. Reuther, J., J. J. Alonso and A. Jameson, Constrained Multipoint Aerodynamic Shape Optimization Using an Adjoint Formulation and Parallel Computers: Part I, Journal of Aircraft, 36(l):51-60, 1999.
16. Holden, M. E., Aeroelastic Optimization using the Collocation Method, PhD Thesis, Stanford, May 1999.
17. Olver, F. W. J., Error Analysis of Complex Arithmetic, Computational Aspects of Complex Analysis, pp. 279-292, 1983.
18. Sturdza, P., V. M. Manning, I. M. Kroo, and R. R. Tracy, Boundary Layer Calculations for Preliminary Design of Wings in Supersonic Flow, AIAA Paper 99-3104, Proceedings of the 17th Applied Aerodynamics Conference, 28 June 1999.
19. Krist, S. L., R. T. Biedron, and C. L. Rumsey, CFL3D User's Manual (Version 5.0) NASA/TM-1998-208444, June 1998.