An automated method for sensitivity analysis using complex variables

Abstract

The complex-step method for calculating sensitivities and its use in numerical algorithms is presented. A general procedure for the implementation of this method is described in detail and a script is developed that automates its implementation. The numerical examples include the automatic conversion of a structural finite element and a two-dimensional computational fluid dynamics code. In both of these examples, the complex-step method is compared with other existing methods, namely finitedierencing, automatic dierentiation and an analytic method. The complex-step method is shown to have implementation advantages over automatic dierentiation and computational advantages over finite-dierencin g.