Theory for the Sensitivity Interface
About Sensitivity Analysis
The Sensitivity interface is special in the sense that it does not contain any physics of its own. Instead, it is a tool for evaluating the sensitivity of a model with respect to almost any variable. The Sensitivity interface is used together with a Sensitivity study step, which in turn controls the Sensitivity solver extension. Simple cases can be handled directly in the Sensitivity study step, while more advanced cases must be set up in a Sensitivity interface prior to solving.
Simulation is a powerful tool for predicting the behavior of physical systems, particularly those that are governed by partial differential equations. However, a single simulation is often not enough to provide sufficient understanding of a system. Hence, a more exploratory process might be needed, such as sensitivity analysis, where one is interested in the sensitivity of a specific quantity with respect to variations in certain parameters included in the model. Such an analysis can, for example, be used for estimating modeling errors caused by uncertainties in material properties or for predicting the effect of a geometrical change.
Many times it is possible to reformulate problems of the above type as the problem of calculating derivatives, so differentiation plays a central role in solving such problems. The Sensitivity study step and corresponding physics interface can calculate derivatives of a scalar objective function with respect to a specified set of control variables. The objective function is in general a function of the solution to a multiphysics problem, which is in turn parameterized by the control variables.