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Numerical simulation of skin transport using Parareal. (English) Zbl 1360.65337

Summary: 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.

MSC:

65Y05 Parallel numerical computation
65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs
92-08 Computational methods for problems pertaining to biology
92C05 Biophysics
92C50 Medical applications (general)
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