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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
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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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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