Numerical simulation of skin transport using Parareal

TL;DR

This paper explores the use of the Parareal time-parallel algorithm for simulating skin transport phenomena, demonstrating its effectiveness and analyzing factors affecting convergence and performance.

Contribution

It introduces a novel application of the Parareal algorithm to skin permeation modeling and evaluates its performance within a combined simulation framework.

Findings

Anisotropies and diffusion coefficient jumps minimally affect convergence.

Load imbalances influence parallel efficiency.

Spatio-temporal weak scaling is feasible with Parareal.

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.