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.

翻译：动脉粥样硬化斑块生长的数值模拟在计算上代价极高，因为该问题既涉及特征时间尺度为毫秒至秒的复杂心血管流固耦合（FSI）问题，又包含由反应-扩散方程描述、历时数月的斑块生长过程。本研究将时间均匀化方法（用于分离微观尺度上计算昂贵的FSI问题与宏观尺度上的反应-扩散问题）与并行时间推进算法相结合。文献表明，直接对FSI问题应用并行时间推进算法效果不佳。为规避此问题，本文对宏观尺度的反应-扩散问题（而非微观尺度的FSI问题）采用parareal算法。我们研究了parareal算法中粗传播子的改进方法，以期进一步减少需要求解的昂贵微观问题数量。基于串行模拟的详细数值实验对所提方法进行了验证。