An automated method for sensitivity analysis using complex variables

38th Aerospace Sciences Meeting and Exhibit

Volumn , Issue , 2000, Pages

  Martins, Joaquim R R A ^a   Kroo, Ilan M ^a   Alonso, Juan J ^a  

^a 496 Lomita Mall   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

AEROSPACE ENGINEERING; COMPUTATIONAL FLUID DYNAMICS; SENSITIVITY ANALYSIS;

AUTOMATIC CONVERSION; AUTOMATIC DIFFERENTIATIONS; COMPLEX-STEP METHOD; COMPUTATIONAL ADVANTAGES; COMPUTATIONAL FLUID DYNAMICS CODES; FINITE DIFFERENCING; NUMERICAL ALGORITHMS; STRUCTURAL FINITE ELEMENTS;

NUMERICAL METHODS;

EID: 85087602839     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.2514/6.2000-689     Document Type: Conference Paper

References (16)

1. 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.
2. Lyness, J. N., and C. B. Moler, "Numerical differentiation of analytic functions", SIAM J. Numer. Anal., Vol. 4, 1967, pp. 202-210.
3. Lyness, J. N., "Numerical algorithms based on the theory of complex variables", Proc. ACM 22nd Nat. Conf., Thompson Book Co., Washington DC, 1967, pp. 124134.
4. Squire, W., and G. Trapp, "Using Complex Variables to Estimate Derivatives of Real Functions", SIAM Review, Vol. 10, No. 1, March 1998, pp. 100-112.
5. 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.
6. Newman, J. C., W. K. Anderson, D. L. Whitfield, fultidisciplinary Sensitivity Derivatives Using Complex Variables", MSSU-COE-ERC-98-08, Jul. 1998.
7. Saff, E. B., A. D. Snider, Fundamentals of Complex Analysis, Prentice Hall, New Jersey, 1976.
8. Olver, F. W. J., "Error Analysis of Complex Arithmetic", Computational Aspects of Complex Analysis, pp. 279-292, 1983.
9. Lyness, J. N., and G. Sande, "ENTCAF and ENTCRE Evaluation of Normalized Taylor Coefficients of an Analytic Function", Corn. ACM, Vol. 14, No. 10, 1971, Washington DC, 1967, pp. 124-134.
10. Lutz, M., Programming Python, O'Reilly, New York, Cambridge, 1996.
11. http://www.python.org
12. http://aero-comlab.stanford.edu/jmartins
13. Holden, M. E., "Aeroelastic Optimization using the Collocation Method", PhD Thesis, Stanford, May 1999.
14. Adelman, H. M., R. T. Haftka, "S. e nsitivity Analysis of Discrete Structural Systems", AIAA Journal, Vol. 24, No. 5, May 1986.
15. Jameson, A., W. Schmidt and E. Turkel, "Numerical Solution of the Euler Equations by Finite Volume Methods Using Runge-Kutta Time Stepping Schemes", AIAA Paper No. 81-1259, June, 1981.
16. J. Reuther, J. J. Alonso and A. Jameson, "Constrained Multipoint Aerodynamic Shape Optimization Using an Adjoint Formulation and Parallel Computers: Part I", Journal of Aircraft, 36(1):51-60, 1999.