ExaSolvers

The Priority Programme “Software for Exascale Computing” (SPPEXA) of the Deutsche Forschungsgemeinschaft (DFG) addresses fundamental research on the various aspects of HPC software, which is particularly urgent against the background that we are currently entering the era of ubiquitous massive parallelism.

“ExaSolvers” is a project within SPPEXA, concerned with the development of solvers for coupled problems that can be used efficiently in extreme-scale simulations. The benchmark problem of the project is the numerical simulation of permeation of human skin, an application that is of great interest for example for the development of pharmaceuticals [1], [2]. Through the lead agency agreement between, SNSF is funding a subproject within ExaSolvers at ICS Lugano SNSF-145271, which, in the framework of the project, addresses the development of efficient time-parallel solvers and their application to heterogeneous diffusion problems on complex domains.

1. KreienbuehlEtAl2015

   A. Kreienbuehl, A. Naegel, D. Ruprecht, R. Speck, G. Wittum, and R. Krause, “Numerical simulation of skin transport using Parareal,” Computing and Visualization in Science, vol. 17, no. 2, pp. 99–108, 2015, doi: 10.1007/s00791-015-0246-y. [Online]. Available at: http://dx.doi.org/10.1007/s00791-015-0246-y

   BibTeX

   Abstract

   BibTeX entry KreienbuehlEtAl2015

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   @article{KreienbuehlEtAl2015,
     author = {Kreienbuehl, Andreas and Naegel, Arne and Ruprecht, Daniel and Speck, Robert and Wittum, Gabriel and Krause, Rolf},
     doi = {10.1007/s00791-015-0246-y},
     issue = {2},
     journal = {Computing and Visualization in Science},
     pages = {99--108},
     title = {{Numerical simulation of skin transport using Parareal}},
     url = {http://dx.doi.org/10.1007/s00791-015-0246-y},
     volume = {17},
     year = {2015}
   }
   

   Abstract for BibTeX entry KreienbuehlEtAl2015

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   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.
2. RuprechtEtAl2016

   D. Ruprecht, R. Speck, and R. Krause, “Parareal for Diffusion Problems with Space- and Time-Dependent Coefficients,” in Domain Decomposition Methods in Science and Engineering XXII, 2016, pp. 371–378, doi: 10.1007/978-3-319-18827-0_37 [Online]. Available at: http://dx.doi.org/10.1007/978-3-319-18827-0_37

   BibTeX

   Abstract

   BibTeX entry RuprechtEtAl2016

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   @inproceedings{RuprechtEtAl2016,
     author = {Ruprecht, Daniel and Speck, Robert and Krause, Rolf},
     booktitle = {Domain Decomposition Methods in Science and Engineering {XXII}},
     doi = {10.1007/978-3-319-18827-0_37},
     editor = {Dickopf, Thomas and Gander, J. Martin and Halpern, Laurence and Krause, Rolf and Pavarino, F. Luca},
     pages = {371--378},
     publisher = {Springer International Publishing},
     title = {Parareal for Diffusion Problems with Space- and Time-Dependent Coefficients},
     url = {http://dx.doi.org/10.1007/978-3-319-18827-0_37},
     year = {2016}
   }
   

   Abstract for BibTeX entry RuprechtEtAl2016

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   For the time-parallel Parareal method, there exists both numerical and analytical proof that it converges very well for diffusive problems like the heat equation. Many applications, however, do not lead to simple homogeneous diffusive problems but feature strongly inhomogeneous and possibly anisotropic coefficients. In the talk, we will present results from a numerical study of how non-constant coefficients in a diffusion problem influence the convergence behaviour of Parareal. Further, the effect of different parameters like e.g. temporal and spatial resolution and geometry is explored.