Article | The 48th Scandinavian Conference on Simulation and Modeling (SIMS 2007); 30-31 October; 2007; Göteborg (Särö) | Automatic Parallelization of Mathematical Models Solved with Inlined Runge-Kutta Solvers

Title:
Automatic Parallelization of Mathematical Models Solved with Inlined Runge-Kutta Solvers
Author:
Håkan Lundvall: PELAB ‚Äď Programming Environment Lab, Dept. Computer Science, Link√∂ping University, Sweden Peter Fritzson: PELAB ‚Äď Programming Environment Lab, Dept. Computer Science, Link√∂ping University, Sweden
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Year:
2007
Conference:
The 48th Scandinavian Conference on Simulation and Modeling (SIMS 2007); 30-31 October; 2007; Göteborg (Särö)
Issue:
027
Article no.:
001
Pages:
1-7
No. of pages:
7
Publication type:
Abstract and Fulltext
Published:
2007-12-21
Series:
Linköping Electronic Conference Proceedings
ISSN (print):
1650-3686
ISSN (online):
1650-3740
Publisher:
Linköping University Electronic Press; Linköpings universitet


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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 finegrained 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.

Keywords: Modelica; automatic parallelization

The 48th Scandinavian Conference on Simulation and Modeling (SIMS 2007); 30-31 October; 2007; Göteborg (Särö)

Author:
Håkan Lundvall, Peter Fritzson
Title:
Automatic Parallelization of Mathematical Models Solved with Inlined Runge-Kutta Solvers
References:

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[4] Peter Fritzson. Principles of Object-Oriented Modeling and Simulation with Modelica 2.1; 940 pp.; ISBN 0- 471-471631; Wiley-IEEE Press; 2004. See also book web page: www.mathcore.com/drModelica


[5] The Modelica Association. The Modelica Language Specification Version 2.2; March 2005. http://www.modelica.org.


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[7] Joar Sohl. A Scalable Run-time System for NestStep on Cluster Supercomputers. Master thesis LITH-IDA-EX- 06/011-SE; IDA; Linköpings universitet; 58183 Linköping; Sweden; March 2006.


[8] Kaj Nystr√∂m and Peter Fritzson. Parallel Simulation with Transmission Lines in Modelica. In Proceedings ofthe 5th International Modelica Conference (Modelica’ 2006); Vienna; Austria; Sept. 4-5; 2006.


[9] Alexander Siemers; Dag Fritzson; and Peter Fritzson. Meta-Modeling for Multi-Physics Co-Simulations applied for OpenModelica. In Proceedings of International Congress on Methodologies for Emerging Technologies in Automation (ANIPLA2006); Rome; Italy; November 13- 15; 2006.


[10] Matthias Korch and Thomas Rauber. Optimizing Locality and Scalability of Embedded Runge-Kutta Solvers Using Block-Based Pipelining. Journal of Parallel and Distributed Computing; Volume 66 ; Issue 3 (March 2006); Pages: 444 ‚Äď 468.


[11] Peter Aronsson and Peter Fritzson. Automatic Parallelization in OpenModelica. In Proceedings of 5th EUROSIM Congress on Modeling and Simulation; Paris; France. ISBN (CD-ROM) 3-901608-28-1; Sept 2004.


[12] Christoph Kessler; Peter Fritzson and Mattias Eriksson. NestStepModelica: Mathematical Modeling and Bulk-Synchronous Parallel Simulation. PARA-06 Workshop on state-of-the-art in scientific and parallel computing; Umeå; Sweden; June 18-21; 2006.


[13] Thomas Rauber and Gudula Runger; Iterated Runge- Kutta Methods on Distributed Memory Multiprocessors. In Proceedings of the 3rd Euromicro Workshop on Parallel and Distributed Processing; pages 12--19; 1995


[14] Robert E. Tarjan; Depth First Search and Linear Graph Algorithms; SIAM Journal of Computing; 1; pages 146-160; 1972

The 48th Scandinavian Conference on Simulation and Modeling (SIMS 2007); 30-31 October; 2007; Göteborg (Särö)

Author:
Håkan Lundvall, Peter Fritzson
Title:
Automatic Parallelization of Mathematical Models Solved with Inlined Runge-Kutta Solvers
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