  We propose a two-scale finite element method designed for heterogeneous
microstructures. Our approach exploits domain diffeomorphisms between the
microscopic structures to gain computational efficiency. By using a
conveniently constructed pullback operator, we are able to model the different
microscopic domains as macroscopically dependent deformations of a reference
domain. This allows for a relatively simple finite element framework to
approximate the underlying PDE system with a parallel computational structure.
We apply this technique to a model problem where we focus on transport in plant
tissues. We illustrate the accuracy of the implementation with convergence
benchmarks and show satisfactory parallelization speed-ups. We further
highlight the effect of the heterogeneous microscopic structure on the output
of the two-scale systems. Our implementation (publicly available on GitHub)
builds on the deal.II FEM library. Application of this technique allows for an
increased capacity of microscopic detail in multiscale modeling, while keeping
running costs manageable.
