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.