Parallel-in-time simulation of biofluids

We extend Parareal, a parallel-in-time method that alternates between a serial sweep and a parallel sweep, to simulate the fluid flow around bio-inspired, dynamic structures over a period of time. Our main contributions include demonstrating the applicability of Parareal to the simulation of biofluids and developing novel solvers for the serial sweeps of Parareal. We propose to construct non-intrusive solvers by extrapolating a parametrized family of existing solvers. Compared to the existing solvers, they either allow the use of larger time steps, have a higher order of accuracy in time, or both. They are also straightforward to implement and parallelize. Numerical results show that when the number of biological structures is small or the number of computer cores employed is sufficiently large, the proposed variant of Parareal can achieve a significantly higher parallel speedup than the more commonly used spatial parallelization.