| Summary: | 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.
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