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Numerical simulation of skin transport using Parareal

  • Published:
Computing and Visualization in Science

Abstract

In silico investigation of skin permeation is an important but also computationally demanding problem. To resolve all scales involved in full detail will not only require exascale computing capacities but also suitable parallel algorithms. This article investigates the applicability of the time-parallel Parareal algorithm to a brick and mortar setup, a precursory problem to skin permeation. The C++ library Lib4PrM implementing Parareal is combined with the UG4 simulation framework, which provides the spatial discretization and parallelization. The combination’s performance is studied with respect to convergence and speedup. It is confirmed that anisotropies in the domain and jumps in diffusion coefficients only have a minor impact on Parareal’s convergence. The influence of load imbalances in time due to differences in number of iterations required by the spatial solver as well as spatio-temporal weak scaling is discussed.

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Notes

  1. The coarse method is often represented by \(\mathcal {G}\), probably because of the French word “gros” for coarse.

  2. http://user.cscs.ch/computing_systems/piz_dora/.

  3. http://www.top500.org/list/2014/11.

  4. https://gcc.gnu.org.

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Authors and Affiliations

  1. Institute of Computational Science, Faculty of Informatics, Università della Svizzera italiana, Via Giuseppe Buffi 13, 6904, Lugano, Switzerland

    Andreas Kreienbuehl, Daniel Ruprecht & Rolf Krause

  2. Goethe-Center for Scientific Computing, Goethe-University Frankfurt, Kettenhofweg 139, 60325, Frankfurt a.M, Germany

    Arne Naegel & Gabriel Wittum

  3. Jülich Supercomputing Centre, Institute for Advanced Simulation, Forschungszentrum Jülich GmbH, Wilhelm-Johnen-Strasse, 52425, Jülich, Germany

    Robert Speck

Authors
  1. Andreas Kreienbuehl
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  2. Arne Naegel
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  3. Daniel Ruprecht
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  4. Robert Speck
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  5. Gabriel Wittum
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Corresponding author

Correspondence to Andreas Kreienbuehl.

Additional information

Communicated by Volker Schulz.

This research is funded by the Deutsche Forschungsgemeinschaft (DFG) as part of the “Exasolvers” project in the Priority Programme 1648 ”Software for Exascale Computing” (SPPEXA) and by the Swiss National Science Foundation (SNSF) under the lead agency agreement as grant SNF-145271. The research of A.K., D.R., and R.K. is also funded through the FUtuRe SwIss Electrical InfraStructure (FURIES) project of the Swiss Competence Centers for Energy Research (SCCER).

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Kreienbuehl, A., Naegel, A., Ruprecht, D. et al. Numerical simulation of skin transport using Parareal. Comput. Visual Sci. 17, 99–108 (2015). https://doi.org/10.1007/s00791-015-0246-y

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