Towards parallel time-stepping for the numerical simulation of atherosclerotic plaque growth

TL;DR

This paper introduces a novel parallel time-stepping approach for simulating atherosclerotic plaque growth by combining macro-scale reaction-diffusion modeling with micro-scale fluid-structure interaction, improving computational efficiency.

Contribution

It proposes a hybrid parallel time-stepping method using a macro-scale parareal algorithm with modified coarse propagators to reduce micro-scale computations in plaque growth simulations.

Findings

Parallel time-stepping improves simulation efficiency.

Modified coarse propagators reduce micro problem computations.

Numerical tests validate the approach's effectiveness.

Abstract

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.