Abstract Summary
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. A resolution of the fast (micro) scale over this period can easily require more than a billion time steps, each corresponding to the solution of a computationally expensive FSI problem. To tackle this problem, we combine a temporal homogenization approach with parallel time-stepping. First, a temporal homogenization approach is developed, which separates the problem in an FSI problem on the micro scale and a reaction-diffusion problem on the macro scale. The approach is analyzed in detail for a simplified flow problem and estimates for the homogenization error and the discretization errors on both time scales are given. Second, a parallel time-stepping approach based on the parareal algorithm is applied on the macro scale of the homogenized system. We investigate modifications in the coarse propagator of the parareal algorithm to further reduce the number of expensive micro problems to be solved and test the numerical algorithms in detailed numerical studies.
