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Conclusions • The theory behind the application of the complexstep method to real-world numerical algorithms was introduced. • The implementation of the complex-step method was successfully automated. • The sensitivity results given by this method have been further validated and shown to be very accurate. • Unlike finite-differencing, the complex-step method is relatively insensitive to the step size. • The complex-step method is now an attractive alternative to ADIFOR. – Joaquim Martins – January 12, 2000 – 19
Further Work • Continue to work on Complexify.py. Need feedback from users. • Apply the method to other solvers. • More detailed stability and convergence analysis. • Compare with CFD adjoint results. – Joaquim Martins – January 12, 2000 – 20
Page 1 and 2: AN AUTOMATED METHOD FOR SENSITIVITY
Page 3 and 4: Sensitivity Analysis Methods • Fi
Page 5 and 6: Cauchy-Riemann Equations • Extens
Page 7 and 8: Simple Numerical Example • Estima
Page 9 and 10: Complex Functions and Operators in
Page 11 and 12: Automatic Implementation • Cookbo
Page 13 and 14: Sensitivity Estimates vs. Step Size
Page 15 and 16: Aerodynamic Sensitivities: FLO82 RA
Page 17 and 18: Residual Convergence of Sensitivity
Page 19: Drag Coefficient Sensitivity 11 10

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