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

Andreas Hessenthaler*, Robert D. Falgout, Jacob B. Schroder, Adelaide de Vecchi, David Nordsletten, Oliver Röhrle

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


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.

Original languageEnglish
Article number114368
Publication statusPublished - 1 Feb 2022


  • Analytic Solutions
  • Cardiac flow
  • Fluid-Structure Interaction
  • Multigrid-reduction-in-time (MGRIT)
  • Speedup
  • Time-periodic parallel-in-time solver


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