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We propose a two-scale finite element method designed for heterogeneousmicrostructures. Our approach exploits domain diffeomorphisms between themicroscopic structures to gain computational efficiency. By using aconveniently constructed pullback operator, we are able to model the differentmicroscopic domains as macroscopically dependent deformations of a referencedomain. This allows for a relatively simple finite element framework toapproximate the underlying PDE system with a parallel computational structure.We apply this technique to a model problem where we focus on transport in planttissues. We illustrate the accuracy of the implementation with convergencebenchmarks and show satisfactory parallelization speed-ups. We furtherhighlight the effect of the heterogeneous microscopic structure on the outputof the two-scale systems. Our implementation (publicly available on GitHub)builds on the deal.II FEM library. Application of this technique allows for anincreased capacity of microscopic detail in multiscale modeling, while keepingrunning costs manageable.

Parallel two-scale finite element implementation of a system with varying microstructures