Electronic Journal of Differential Equations,
Conference 03 (1999), pp. 13-27.

Title: Use of discrete sensitivity analysis to transform explicit 
simulation codes into design optimization codes

Author:  Clarence O. E. Burg (Mississippi State Univ., MS, USA)

Abstract: 
Sensitivity analysis is often used in high fidelity numerical optimization 
to estimate design space derivatives efficiently. Typically, explicit 
codes are combined with the adjoint formulation of continuous sensitivity 
analysis, which requires the derivation and solution of the adjoint 
equations along with appropriate boundary conditions. However, 
for implicit codes, which already calculate the Jacobian matrix of the 
discretized governing equations, the discrete approach of sensitivity 
analysis is relatively easy to implement. Using the complex Taylor's 
series expansion method to generate derivatives, a highly accurate 
approximation to the Jacobian matrix can be generated for implicit or 
explicit codes, allowing uniform application of discrete sensitivity 
analysis to both implicit and explicit codes.

Published July 10, 2000.
Math Subject Classifications: 76N25, 49Q12.
Key Words: Design optimization; sensitivity analysis; adjoint methods; 
computational fluid dynamics.