Time-periodic steady-state solution of fluid-structure interaction and cardiac flow problems through multigrid-reduction-in-time

TL;DR

This paper introduces a time-periodic MGRIT algorithm that efficiently computes steady-state solutions for fluid-structure interaction and cardiac flow problems by exploiting inherent time periodicity, significantly reducing computational time.

Contribution

The paper presents a novel parallel-in-time MGRIT algorithm tailored for periodic-in-time problems, demonstrating its effectiveness across various linear and nonlinear multiphysics applications.

Findings

Achieves the same steady-state solutions as sequential methods

Reduces time-to-solution significantly across different models

Enables greater parallelism for complex simulations

Abstract

In this paper, a time-periodic MGRIT algorithm is proposed as a means to reduce the time-to-solution of numerical algorithms by exploiting the time periodicity inherent to many applications in science and engineering. The time-periodic MGRIT algorithm is applied to a variety of linear and nonlinear single- and multiphysics problems that are periodic-in-time. It is demonstrated that the proposed parallel-in-time algorithm can obtain the same time-periodic steady-state solution as sequential time-stepping. It is shown that the required number of MGRIT iterations can be estimated a priori and that the new MGRIT variant can significantly and consistently reduce the time-to-solution compared to sequential time-stepping, irrespective of the number of dimensions, linear or nonlinear PDE models, single-physics or coupled problems and the employed computing resources. The numerical experiments demonstrate that the time-periodic MGRIT algorithm enables a greater level of parallelism yielding faster turnaround, and thus, facilitating more complex and more realistic problems to be solved.