Simulating Partial Differential Equations using the Explicit Parallelism of ParModelica

Abstract: The Modelica language is a modelling and programming  language for modelling cyber-physical systems using equations and  algorithms. In this thesis two suggested extensions of the Modelica  language are covered. Those are Partial Differential Equations (PDE)  and explicit parallelism in algorithmic code.  While PDEs are not  yet supported by the Modelica language, this thesis presents a  framework for solving PDEs using the algorithmic part of the  Modelica language, including parallel extensions. Different  numerical solvers have been implemented using the explicit parallel  constructs suggested for Modelica by the ParModelica language  extensions, and implemented as part of OpenModelica. The solvers  have been evaluated using different models, and it can be seen how  bigger models are suitable for a parallel solver. The intention has  been to write a framework suitable for modelling and parallel  simulation of PDEs. This work can, however, also be seen as a case  study of how to write a custom solver using parallel algorithmic  Modelica and how to evaluate the performance of a parallel solver.