In this work we report results from a new integrated method of automatically generating parallel code from Modelica models by combining parallelization at two levels of abstraction. Performing inline expansion of a Runge-Kutta solver combined with fine-grained automatic parallelization of the right-hand side of the resulting equation system opens up new possibilities for generating high performance code, which is becoming increasingly relevant when multi-core computers are becoming commonplace. An implementation, in the form of a backend module for the OpenModelica compiler, has been developed and used for measurements on two architectures: Intel Xeon and SGI Altix 3700 Bx2. This paper also contains some very recent results of a prototype implementation of this parallelization approach on the Cell BE processor architecture.

In this work we report results from a new integrated method of automatically generating parallel code from Modelica models by combining parallelization at two levels of abstraction. Performing inline expansion of a Runge-Kutta solver combined with fine-grained automatic parallelization of the right-hand side of the resulting equation system opens up new possibilities for generating high performance code, which is becoming increasingly relevant when multi-core computers are becoming commonplace. An implementation, in the form of a backend module for the OpenModelica compiler, has been developed and used for measurements on two architectures: Intel Xeon and SGI Altix 3700 Bx2. This paper also contains some very recent results of a prototype implementation of this parallelization approach on the Cell BE processor architecture.

During the most recent decades modern equation-based object-oriented modeling and simulation languages, such as Modelica, have become available. This has made it easier to build complex and more detailed models for use in simulation. To be able to simulate such large and complex systems it is sometimes not enough to rely on the ability of a compiler to optimize the simulation code and reduce the size of the underlying set of equations to speed up the simulation on a single processor. Instead we must look for ways to utilize the increasing number of processing units available in modern computers. However to gain any increased performance from a parallel computer the simulation program must be expressed in a way that exposes the potential parallelism to the computer. Doing this manually is not a simple task and most modelers are not experts in parallel computing. Therefore it is very appealing to let the compiler parallelize the simulation code automatically. This thesis investigates techniques of using automatic translation of models in typical equation based languages, such as Modelica, into parallel simulation code that enable high utilization of available processors in a parallel computer. The two main ideas investigated here are the following: first, to apply parallelization simultaneously to both the system equations and the numerical solver, and secondly. to use software pipelining to further reduce the time processors are kept waiting for the results of other processors. Prototype implementations of the investigated techniques have been developed as a part of the OpenModelica open source compiler for Modelica. The prototype has been used to evaluate the parallelization techniques by measuring the execution time of test models on a few parallel archtectures and to compare the results to sequential code as well as to the results achieved in earlier work. A measured speedup of 6.1 on eight processors on a shared memory machine has been reached. It still remains to evaluate the methods for a wider range of test models and parallel architectures.

This paper gives an introduction and overview of problems and solutions regarding simulating hybrid DAEs (systems of Differential Algebraic Equations) with event-handling, in the context of producing such equations from models in the Modelica language. Iimplementation and measurements are done in the OpenModelica environment. The basic hybrid DAE solution algorithm is presented, followed by a discussion of handling possibly varying structure of the active part of the hybrid DAE, and how to find consistent initial values at start or restart of simulation. The problem of detecting events during continuous-time simulation is dealt with using crossing functions and an algorithm for proper integration with a numerical solver, here DASRT. Event-related aspects of code generation from models are presented, followed by an example showing how the event mechanism works. Finally, preliminary results from translating and simulating two examples models, the bouncing ball and the full wave rectifier, are presented and compared with those from a commercial simulation tool (Dymola), giving identical results.

In this work we report preliminary results of automatically generating parallel code from equation-based models together at two levels: Performing inline expansion of a Runge-Kutta solver combined with fine-grained automatic parallelization of the resulting RHS opens up new possibilities for generating high performance code, which is becoming increasingly relevant when multi-core computers are becoming common-place.We have introduced a new way of scheduling the task graph generated from the simulation problem which utilizes knowledge about locality of the simulation problem. The scheduling is also done in a way that limits communication, to the greatest extent possible, to neighboring processors thus avoiding expensive global synchronization. Preliminary tests on a PC-cluster show speedup that is better than what was achieved in previous work where parallelization was done only at the equation system level.

Modelica is a modern, strongly typed, declarative, and object-oriented language for modeling and simulation of complex systems. This paper gives a quick overview of some aspects of the OpenModelica environment - an open-source environment for modeling, simulation, and development of Modelica applications. An introduction of the objectives of the environment is given, an overview of the architecture is outlined and a number of examples are illustrated.   

The paper gives an introduction to the problem simulating hybrid DAEs with event-handling using the Modelica language. An implementation in the OpenModelica compiler is presented, and some preliminary results are reported.