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

Research output: Contribution to journalArticlepeer-review

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

Original languageEnglish
Article number114368
JournalCOMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
Volume389
DOIs
Published1 Feb 2022

Bibliographical note

Funding Information: O.R. and A.H. were funded by Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy - EXC 2075 - 390740016 . We acknowledge the support by the Stuttgart Center for Simulation Science (SimTech). Funding Information: This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344 , LLNL-JRNL-820515 . Funding Information: D.N. would like to acknowledge funding from Engineering and Physical Sciences Research Council ( EP/N011554/1 and EP/R003866/1 ). Publisher Copyright: © 2021 Elsevier B.V.

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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.

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