article

Space/time multigrid for a fluid--structure-interaction problem

Authors:

E. H. van Brummelen,

K. G. van der Zee,

R. de BorstAuthors Info & Claims

Applied Numerical Mathematics, Volume 58, Issue 12

Pages 1951 - 1971

https://doi.org/10.1016/j.apnum.2007.11.012

Published: 01 December 2008 Publication History

Abstract

The basic iterative method for solving fluid-structure-interaction problems is a defect-correction process based on a partitioning of the underlying operator into a fluid part and a structural part. In the present work we establish for a prototypical model problem that this defect-correction process yields an excellent smoother for multigrid, on account of the relative compactness of the fluid part of the operator with respect to the structural part. We show that the defect-correction process in fact represents an asymptotically-perfect smoother, i.e., the effectiveness of the smoother increases as the mesh is refined. Consequently, on sufficiently fine meshes the fluid-structure-interaction problem can be solved to arbitrary accuracy by one iteration of the defect-correction process followed by a coarse-grid correction. Another important property of the defect-correction process is that it smoothens the error in space/time, so that the coarsening in the multigrid method can be applied in both space and time.

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Cited By

Failer LRichter T(2020)A Parallel Newton Multigrid Framework for Monolithic Fluid-Structure InteractionsJournal of Scientific Computing10.1007/s10915-019-01113-y82:2Online publication date: 21-Jan-2020
https://dl.acm.org/doi/10.1007/s10915-019-01113-y
Ma WLu ZYuan WHu X(2017)Parallelization of an Unsteady ALE Solver with Deforming Mesh Using OpenACCScientific Programming10.1155/2017/46101382017Online publication date: 1-Jan-2017
https://dl.acm.org/doi/10.1155/2017/4610138
Carraro TFriedmann EGerecht D(2016)Coupling vs decoupling approaches for PDE/ODE systems modeling intercellular signalingJournal of Computational Physics10.1016/j.jcp.2016.03.020314:C(522-537)Online publication date: 1-Jun-2016
https://dl.acm.org/doi/10.1016/j.jcp.2016.03.020
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Space/time multigrid for a fluid--structure-interaction problem

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Published In

cover image Applied Numerical Mathematics

Applied Numerical Mathematics Volume 58, Issue 12

December, 2008

236 pages

ISSN:0168-9274

Issue’s Table of Contents

Copyright © IMACS © 2007.

Publisher

Elsevier Science Publishers B. V.

Netherlands

Publication History

Published: 01 December 2008

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Cited By

Failer LRichter T(2020)A Parallel Newton Multigrid Framework for Monolithic Fluid-Structure InteractionsJournal of Scientific Computing10.1007/s10915-019-01113-y82:2Online publication date: 21-Jan-2020
https://dl.acm.org/doi/10.1007/s10915-019-01113-y
Ma WLu ZYuan WHu X(2017)Parallelization of an Unsteady ALE Solver with Deforming Mesh Using OpenACCScientific Programming10.1155/2017/46101382017Online publication date: 1-Jan-2017
https://dl.acm.org/doi/10.1155/2017/4610138
Carraro TFriedmann EGerecht D(2016)Coupling vs decoupling approaches for PDE/ODE systems modeling intercellular signalingJournal of Computational Physics10.1016/j.jcp.2016.03.020314:C(522-537)Online publication date: 1-Jun-2016
https://dl.acm.org/doi/10.1016/j.jcp.2016.03.020
(2016)Parallel coupling numerics for partitioned fluid-structure interaction simulationsComputers & Mathematics with Applications10.1016/j.camwa.2015.12.02571:4(869-891)Online publication date: 1-Feb-2016
https://dl.acm.org/doi/10.1016/j.camwa.2015.12.025
Michler CBrummelen HBorst R(2011)An investigation of Interface-GMRES(R) for fluid---structure interaction problems with flutter and divergenceComputational Mechanics10.1007/s00466-010-0519-847:1(17-29)Online publication date: 1-Jan-2011
https://dl.acm.org/doi/10.1007/s00466-010-0519-8

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