Abstract
We develop a high performance computing (HPC) framework for efficient simulations of a class of fractional-order partial differential equations (FPDE), using high-order in time and space parallel algorithms. HPC systems provide a large number of processing cores with limitations on the amount of memory available per core. Such limitations impose severe constraints for resolving fine spatial structures that require large degrees of freedom (DoF). In this article, using several message passing interface (MPI) communicators, we develop and demonstrate an efficient hybrid framework that combines parallel in time and space tasks that facilitate careful balance between parallel performance within the memory constraint to simulate the FPDE model. We demonstrate the approach for a 3D fractional PDE using several million spatial DoF.
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Acknowledgements
The research of the first author was supported by Aramco and the second author was supported, in part, by grant DMS-1216889 from the NSF. Support of the Colorado Golden Energy Computing Organization is gratefully acknowledged.
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Alyoubi, A., Ganesh, M. (2015). A Parallel-in-Time-and-Space HPC Framework for a Class of Fractional Evolution Equations. In: Kirby, R., Berzins, M., Hesthaven, J. (eds) Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014. Lecture Notes in Computational Science and Engineering, vol 106. Springer, Cham. https://doi.org/10.1007/978-3-319-19800-2_9
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DOI: https://doi.org/10.1007/978-3-319-19800-2_9
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-19799-9
Online ISBN: 978-3-319-19800-2
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