  The numerical simulation of atherosclerotic plaque growth is computationally
prohibitive, since it involves a complex cardiovascular fluid-structure
interaction (FSI) problem with a characteristic time scale of milliseconds to
seconds, as well as a plaque growth process governed by reaction-diffusion
equations, which takes place over several months. In this work we combine a
temporal homogenization approach, which separates the problem in
computationally expensive FSI problems on a micro scale and a
reaction-diffusion problem on the macro scale, with parallel time-stepping
algorithms. It has been found in the literature that parallel time-stepping
algorithms do not perform well when applied directly to the FSI problem. To
circumvent this problem, a parareal algorithm is applied on the macro-scale
reaction-diffusion problem instead of the micro-scale FSI problem. We
investigate modifications in the coarse propagator of the parareal algorithm,
in order to further reduce the number of costly micro problems to be solved.
The approaches are tested in detailed numerical investigations based on serial
simulations.
