Parallelizing Equation-Based Models for Simulation on Multi-Core Platforms by Utilizing Model Structure

In today’s world of high tech manufacturing and computer-aided design simulations of models is at the heart of the whole manufacturing process. Trying to represent and study the variables of real world models using simulation computer programs can turn out to be a very expensive and time consuming task. On the other hand advancements in modern multi-core CPUs promise remarkable computational power. Modern modeling environments provide different optimization and parallelization options to take advantage of the available computational power. Some of these parallelization approaches are based on automatically extracting parallelism with the help of the model compiler or translator. Another approach is to provide the model programmers with the necessary language constructs to express any potential parallelism in their models. In this paper we present an automatic parallelization approach for Modelica models using Transmission Line Modeling (TLM). TLM is suitable for parallel simulations because larger models can be partitioned into smaller independent sub-models. TLM introduces parallelism into the system by decoupling subsystems using delays greater than the step size of the numerical solver. A prototype has been implemented in the OpenModelica Compiler (OMC) framework. Our approach re-uses the dependency analysis from the sequential translation step of OMC. With the help of the dependency analysis information the set of equations for a model is partitioned into a number of sub-systems. The resulting independent sub-systems are scheduled and executed in parallel. The run-time system for OMC has been improved to provide thread safety and handle parallelism while keeping the introduced overhead to minimum for normal sequential operation and maintaining portability