Contributions to Parallel Simulation of Equation-Based Models on Graphics Processing Units

In this thesis we investigate techniques and methods for parallel simulation of equation-based, object-oriented (EOO) Modelica models on graphics processing units (GPUs). Modelica is being developed through an international effort via the Modelica Association. With Modelica it is possible to build computationally heavy models; simulating such models however might take a considerable amount of time. Therefor techniques of utilizing parallel multi-core architectures for simulation are desirable. The goal in this work is mainly automatic parallelization of equation-based models, that is, it is up to the compiler and not the end-user modeler to make sure that code is generated that can efficiently utilize parallel multi-core architectures. Not only the code generation process has to be altered but the accompanying run-time system has to be modified as well. Adding explicit parallel language constructs to Modelica is also discussed to some extent. GPUs can be used to do general purpose scientific and engineering computing. The theoretical processing power of GPUs has surpassed that of CPUs due to the highly parallel structure of GPUs. GPUs are, however, only good at solving certain problems of data-parallel nature. In this thesis we relate several contributions, by the author and co-workers, to each other. We conclude that the massively parallel GPU architectures are currently only suitable for a limited set of Modelica models. This might change with future GPU generations. CUDA for instance, the main software platform used in the thesis for general purpose computing on graphics processing units (GPGPU), is changing rapidly and more features are being added such as recursion, function pointers, C++ templates, etc.; however the underlying hardware architecture is still optimized for data-parallelism

Parallel Simulation of Equation-Based Models on CUDA-Enabled GPUs

Our contributions with this work are methods and a prototype implementation for compiling and executing a limited set of equation-based mathematical models (written in the object-oriented equation-based modeling language Modelica) on CUDA-enabled GPUs. We look at methods of finding parallelism in Modelica models, that can be used on the massively parallel CUDA architecture. The methods have been implemented in a new back-end module of the OpenModelica compiler (an open-source Modelica compiler). This paper shows that it is possible to automatically generate simulation code for pure continuous-time models that can be reduced to an ordinary differential equation system without algebraic loops and where the initial values of all variables and parameters are known at compile time. It is possible to get some speedup compared with simulation on a single CPU core, a (approximated) relative speedup of 4.6 was for instance obtained for one model

Parallel Simulation of Equation-based Object-Oriented Models with Quantized State Systems on a GPU

This work focuses on the use of parallel hardware to improve the simulation speed of equation-based object-oriented Modelica models. With this intention,a method has been developed that allows for the translation of a restricted class of Modelica models to parallel simulation code, targeted for the Nvidia Tesla architecture and based on the Quantized State Systems(QSS) simulation algorithm. The OpenModelica Compiler (OMC) has been extended with a new back-end module for automatic generation of the simulation code that uses the CUDA extensions to the C language to be executable with a General Purpose Graphic Processing Unit (GPGPU). Preliminary performance measurments of a small example model havebeen done on the Tesla architecture

PDE MODELING WITH MODELICA VIA FMI IMPORT OF HIFLOW3 C++ COMPONENTS WITH PARALLEL MULTI-CORE SIMULATIONS

ABSTRACT The Modelica modeling and simulation language is widely used in academia and industry to model complex, coupled dynamic systems which can be described by systems of ordinary differential equations (ODE) or differential algebraic equations (DAE). Recent work by the authors showed a way to enable partial differential equation (PDE) modeling with Modelica via functional mock-up interface (FMI) import of C++ components based on the multi-purpose finite element library HiFlow3. The finite element method (FEM) is largely used in both research and industry as a reliable technique for solving PDE problems. In contrast to methods based on language extensions or automatic semi-discretizations in space, the approach with FMI import of HiFlow3 components into Modelica requires no change to the Modelica language, enables the use of specialized PDE solvers, and it allows for full flexibility in the choice of geometry, model parameters, and space discretization between simulation runs without recompilation. However, the computationally intensive PDE solving part in this approach can form a bottleneck in the simulations. In this work, we enhance the PDE solver by using a distributed memory parallelization based on a domain decomposition. As an example application, we consider a mechanical linear elasticity problem consisting of physical forces applied on a beam. Beams, plates and shells are common elements of solid structures with a sizable quantity of application in engineering design, appearing in fuselage, ship hulls, concrete roof structure, etc. The derivation of elastic stress strain relations is a crucial point for mechanical analysis and validation, as the bending properties of the structure effects greatly the stability properties. In this work the actual beam is modeled and solved in parallel using a C++ HiFlow3 component whereas the physical force acting on the beam is modeled using Modelica. We use the OpenModelica development environment but the same approach can be adapted to other Modelica environments