×

Optimized extrapolation methods for parallel solution of IVPs on different computer architectures. (English) Zbl 0859.65070

Extrapolation methods are known to be well suited for parallelism, but parallel execution of codes optimized for sequential computation cannot be optimal on parallel machines. In this paper, the authors discuss parallel implementations on different architectures of the two most widely used extrapolation methods: the extrapolated mid-point rule for nonstiff systems and the extrapolated semi-implicit Euler method for stiff systems.
The architectures include shared memory, distributed and virtually shared systems and the number of processors can be fixed, unlimited or dynamically limited throughout runtime. The results are better for problems requiring a lot of computing time and on architectures with fast internodal communication.
Reviewer: T.C.Mohan (Madras)

MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
65Y05 Parallel numerical computation
34E13 Multiple scale methods for ordinary differential equations
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations

Software:

PVM
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Beguelin, A.; Dongarra, J.; Geist, A.; Manchek, R.; Sunderam, V., A Users’s Guide to PVM Parallel Virtual Machine, (Technical Report (1992), Oak Ridge National Laboratory), ORNL/TM-11826, Oak Ridge, Tennessee 37831 · Zbl 0825.68199
[2] MPI Forum, MPI: A Message Passing Interface, (Technical Report (March 1994), University of Tennessee: University of Tennessee Knoxville, Tennessee)
[3] Lenke, M.; Rathmayer, S.; Bode, A.; Michl, M.; Wagner, S., Parallelization with a Real-World CFD Application on Different Parallel Architectures (1994), Computational Mechanics Publications: Computational Mechanics Publications Southhampton, UK
[4] Frank, S.; Burkhardt, H.; Rothnie, J., The ksr1: Bridging the gap between shared memory and mpps, (Proceedings of Compcon (February 1993)), 285-294, San Francisco, CA
[5] International Commission on Radiological Protection, (Age Dependent Doses to Members of the Public from Intake of Radionuclides, Volume 2 (1993), Pergamon Press)
[6] Perzl, M., Implementierung eines numerischen Algorithmus zur Lösung steifer gewöhnlicher Differentialgleichungen—zur Anwendung auf komplexe Kompartiment-Modelle—für Multiprozessoren unter verschiedenen Programmiermodellen, (Master’s Thesis (August 1992), Technische Universität München—Institut für Informatik)
[7] Bruno, J.; Hoffman, E. G.; Sethi, R., Scheduling independent tasks to reduce mean finishing time, Communication of the ACM., 17, 7, 382-387 (July 1974)
[8] Hairer, E.; Nørsett, S. P.; Wanner, C., Solving Ordinary Differential Equations I (1987), Springer · Zbl 0638.65058
[9] Hairer, E.; Wanner, G., Solving Ordinary Differential Equations II (1991), Springer · Zbl 0729.65051
[10] Kappeller, M., Parallele Extrapolationsverfahren zur Lösung von gewöhnlichen Differentialgleichungen, (Master’s Thesis (1994), Technische Universität München—Mathematisches Institut)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.