Modelica is an object-oriented, equation-based modeling and simulation language being developed through an international effort by the Modelica Association. With Modelica it is possible to build computationally demanding models; however, simulating such models might take a considerable amount of time. Therefore techniques of utilizing parallel multi-core architectures for faster simulations are desirable. In this thesis the topic of simulation of Modelica on parallel architectures in general and on graphics processing units (GPUs) in particular is explored. GPUs support code that can be executed in a data-parallel fashion. It is also possible to connect and run several GPUs together which opens opportunities for even more parallelism. In this thesis several approaches regarding simulation of Modelica models on GPUs and multi-core architectures are explored. In this thesis the topic of expressing and solving partial differential equations (PDEs) in the context of Modelica is also explored, since such models usually give rise to equation systems with a regular structure, which can be suitable for efficient solution on GPUs. Constructs for PDE-based modeling are currently not part of the standard Modelica language specification. Several approaches on modeling and simulation with PDEs in the context of Modelica have been developed over the years. In this thesis we present selected earlier work, ongoing work and planned work on PDEs in the context of Modelica. Some approaches detailed in this thesis are: extending the language specification with PDE handling; using a software with support for PDEs and automatic discretization of PDEs; and connecting an external C++ PDE library via the functional mockup interface (FMI). Finally the topic of parallel skeletons in the context of Modelica is explored. A skeleton is a predefined, generic component that implements a common specific pattern of computation and data dependence. Skeletons provide a high degree of abstraction and portability and a skeleton can be customized with user code. Using skeletons with Modelica opens up the possibility of executing heavy Modelica-based matrix and vector computations on multi-core architectures. A working Modelica-SkePU library with some minor necessary compiler extensions is presented.
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