Abstract
We consider the use of task pool teams in implementation of the master equation on random Sierpinski carpets. Though the basic idea of dynamic storage of the probability density reported earlier applies straightforward to random carpets, the randomized construction breaks up most of the simplifications possible for regular carpets. In addition, parallel implementations show highly irregular communication patterns. We compare four implementations on three different Beowulf-Cluster architectures, mainly differing in throughput and latency of their interconnection networks. It appears that task pool teams provide a powerful programming paradigm for handling the irregular communication patterns that arise in our application and show a promising approach to efficiently handle the problems that appear with such randomized structures. This will allow for highly improved modelling of anomalous diffusion in porous media, taking the random structure of real materials into account.
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Mandelbrot, B.B.: Fractals - Form, Chance and Dimension. W. H. Freeman, San Francisco (1977)
Franz, A., Schulzky, C., Seeger, S.: An efficient implementation of the exact enumeration method for random walks on Sierpinski carpets. Fractals 8(2), 155–161 (2000)
Anh, D.H.N., Hoffmann, K.H., Seeger, S., Tarafdar, S.: Diffusion in disordered fractals. Europhys. Lett. (accepted, 2005)
Chandra, S.: Superionic Solids: Principles and Applications. North-Holland, Amsterdam (1981)
Hippold, J., Rünger, G.: Task pool teams: A hybrid programming environment for irregular algorithms on smp clusters. Concurrency and Computation: Practice and Experience (to appear, 2006)
Reis, F.D.A.A.: Diffusion on regular random fractals. J. Phys. A: Math. Gen. 29(24), 7803–7810 (1996)
ben-Avraham, D., Havlin, S.: Diffusion and Reactions in Fractals and Disordered Systems. Cambridge University Press, Cambridge, UK (2000)
de Gennes, P.G.: La percolation: Un concept unificateur. La Recherche 7(72), 919–927 (1976)
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© 2006 Springer-Verlag Berlin Heidelberg
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Hoffmann, K.H., Hofmann, M., Rünger, G., Seeger, S. (2006). Task Pool Teams Implementation of the Master Equation Approach for Random Sierpinski Carpets. In: Nagel, W.E., Walter, W.V., Lehner, W. (eds) Euro-Par 2006 Parallel Processing. Euro-Par 2006. Lecture Notes in Computer Science, vol 4128. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11823285_110
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DOI: https://doi.org/10.1007/11823285_110
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-37783-2
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