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

Abstract: 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.