论文标题
迈向平行时间步长以进行动脉粥样硬化斑块生长的数值模拟
Towards parallel time-stepping for the numerical simulation of atherosclerotic plaque growth
论文作者
论文摘要
动脉粥样硬化斑块生长的数值模拟在计算上是过度的，因为它涉及复杂的心血管流体结构相互作用（FSI）问题，其特征性的时间尺度是毫秒至几秒钟的特征时间，以及一个由反应扩散方程控制的斑块生长过程，发生在几个月内。在这项工作中，我们结合了一种时间同质化方法，该方法将微观量表上的计算昂贵的FSI问题和宏观尺度上的反应扩散问题与平行时间稳定算法分开。在文献中已经发现，直接应用于FSI问题时，平行时间步变算法的性能不佳。为了解决这个问题，对宏观尺度反应扩散问题而不是微尺度FSI问题应用了瘫痪算法。我们研究了瘫痪算法的粗糙传播器中的修改，以进一步减少要解决的昂贵的微问题的数量。基于串行模拟的详细数值研究对这些方法进行了测试。
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.
