Calculation of Sensitivity Derivatives in an MDAO Framework

Analytical derivatives in these components can be used to improve the speed and accuracy of the derivative calculation over a purely numerical calculation, however a multidisciplinary system may include both components for which derivatives are available and components for which they are not. Three methods to calculate the sensitivity of a mixed multidisciplinary system are presented: the nite dierence method, where the derivatives are calculated numerically, the chain rule method, where the derivatives are successively cascaded along the system’s network graph, and the analytic method, where the derivatives come from the solution of a linear system of equations. Some improvements to these methods to accommodate mixed multidisciplinary systems are presented; in particular, a new method is introduced to allow existing derivatives to be used inside of nite dierence. All three methods are implemented and demonstrated in the open-source MDAO framework OpenMDAO. It was found that there are advantages to each of them depending on the system being solved.

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