In today’s world of high tech manufacturing and computer-aided design simulations of models is at theheart of the whole manufacturing process. Trying to represent and study the variables of real worldmodels using simulation computer programs can turn out to be a very expensive and time consumingtask. On the other hand advancements in modern multi-core CPUs and general purpose GPUs promiseremarkable computational power. Properly utilizing this computational power can provide reduced simulation time. To this end modernmodeling environments provide different optimization and parallelization options to take advantage ofthe available computational power. Some of these parallelization approaches are based onautomatically extracting parallelism with the help of a compiler. Another approach is to provide themodel programmers with the necessary language constructs to express any potential parallelism intheir models. This second approach is taken in this thesis work. The OpenModelica modeling and simulation environment for the Modelica language has beenextended with new language constructs for explicitly stating parallelism in algorithms. This slightlyextended algorithmic subset of Modelica is called ParModelica. The new extensions allow modelswritten in ParModelica to be translated to optimized OpenCL code which can take advantage of thecomputational power of available Multi-core CPUs and general purpose GPUs.

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.

The move from single core and processor systems to multi-core and many-processors systemscomes with the requirement of implementing computations in a way that can utilizethese multiple units eciently. This task of writing ecient multi-threaded algorithmswill not be possible with out improving programming languages and compilers to providethe mechanisms to do so. Computer aided mathematical modeling and simulationis one of the most computationally intensive areas of computer science. Even simpli-ed models of physical systems can impose a considerable amount of computational loadon the processors at hand. Being able to take advantage of the potential computationpower provided by multi-core systems is vital in this area of application. This thesis triesto address how we can take advantage of the potential computation power provided bythese modern processors to improve the performance of simulations. The work presentsimprovements for the Modelica modeling language and the OpenModelica compiler. Two approaches of utilizing the computational power provided by modern multi-corearchitectures are presented in this thesis: Automatic and Explicit parallelization. Therst approach presents the process of extracting and utilizing potential parallelism fromequation systems in an automatic way with out any need for extra eort from the modelers/programmers side. The thesis explains improvements made to the OpenModelicacompiler and presents the accompanying task systems library for ecient representation,clustering, scheduling proling and executing complex equation/task systems with heavydependencies. The Explicit parallelization approach explains the process of utilizing parallelismwith the help of the modeler or programmer. New programming constructs havebeen introduced to the Modelica language in order to enable modelers write parallelizedcode. the OpenModelica compiler has been improved accordingly to recognize and utilizethe information from this new algorithmic constructs and generate parallel code toimprove the performance of computations. / <p>The series name <em>Linköping Studies in Science and Technology Licentiate Thesis</em> is incorrect. The correct series name is <em>Linköping Studies in Science and Technology Thesis.</em></p>