  Heterogeneous multiscale methods (HMM) combine molecular accuracy of
particle-based simulations with the computational efficiency of continuum
descriptions to model flow in soft matter liquids. In these schemes, molecular
simulations typically pose a computational bottleneck, which we investigate in
detail in this study. We find that it is preferable to simulate many small
systems as opposed to a few large systems, and that a choice of a simple
isokinetic thermostat is typically sufficient while thermostats such as
Lowe-Andersen allow for simulations at elevated viscosity. We discuss suitable
choices for time steps and finite-size effects which arise in the limit of very
small simulation boxes. We also argue that if colloidal systems are considered
as opposed to atomistic systems, the gap between microscopic and macroscopic
simulations regarding time and length scales is significantly smaller. We also
propose a novel reduced-order technique for the coupling to the macroscopic
solver, which allows us to approximate a non-linear stress-strain relation
efficiently and thus further reduce computational effort of microscopic
simulations.
