Symbolically Derived Jacobians Using Automatic Differentiation - Enhancement of the OpenModelica Compiler

Abstract

Jacobian matrices are used in a wide range of applications -from solving the original DAEs to sensitivity analysis. Using Automatic Differentia-tion the necessary partial derivatives can be pro-vided efficiently within a Modelica-Tool. This pa-per describes the corresponding implementation work within the OpenModelica Compiler (OMC) to create a symbolic derivative module. This new OMC-feature generates symbolically partial derivatives in order to calculate Jacobian matrices with respect to different variables. Applications presented here, are the generation of linear mod-els of non-linear Modelica models and the usage of the Jacobian matrix in DASSL for simulating a model.