Truly monolithic algebraic multigrid for fluid-structure interaction

The coupling of flexible structures to incompressible fluids draws a lot of attention during the last decade. Many different solution schemes have been proposed. In this contribution, we concentrate on the strong coupling fluid–structure interaction by means of monolithic solution schemes. Therein,...

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Bibliographic Details
Published in:International journal for numerical methods in engineering Vol. 85; no. 8; pp. 987 - 1016
Main Authors: Gee, M. W., Küttler, U., Wall, W. A.
Format: Journal Article
Language:English
Published: Chichester, UK John Wiley & Sons, Ltd 25.02.2011
Wiley
Subjects:
Algebra
algebraic multigrid
Approximation
Blocking
Coarsening
Exact sciences and technology
Fluid-structure interaction
Fundamental areas of phenomenology (including applications)
Joining
Mathematical analysis
Mathematical models
Mathematics
Methods of scientific computing (including symbolic computation, algebraic computation)
monolithic solution schemes
Numerical analysis
Numerical analysis. Scientific computation
Numerical approximation
Physics
Sciences and techniques of general use
Solid mechanics
Structural and continuum mechanics
Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...)
Performance evaluation
Algebraic structure
Vibration
monolithic solution schemes
Krylov subspace method
Fluid structure interaction
Modeling
fluid-structure interaction
Multigrid
Algebraic method
algebraic multigrid
Coupling
Incompressible fluid
Non linear effect
Gauss Seidel method
Newton method
Preconditioning
ISSN:0029-5981, 1097-0207, 1097-0207
Online Access:Get full text
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Summary:The coupling of flexible structures to incompressible fluids draws a lot of attention during the last decade. Many different solution schemes have been proposed. In this contribution, we concentrate on the strong coupling fluid–structure interaction by means of monolithic solution schemes. Therein, a Newton–Krylov method is applied to the monolithic set of nonlinear equations. Such schemes require good preconditioning to be efficient. We propose two preconditioners that apply algebraic multigrid techniques to the entire fluid–structure interaction system of equations. The first is based on a standard block Gauss–Seidel approach, where approximate inverses of the individual field blocks are based on a algebraic multigrid hierarchy tailored for the type of the underlying physical problem. The second is based on a monolithic coarsening scheme for the coupled system that makes use of prolongation and restriction projections constructed for the individual fields. The resulting nonsymmetric monolithic algebraic multigrid method therefore involves coupling of the fields on coarse approximations to the problem yielding significantly enhanced performance. Copyright © 2010 John Wiley & Sons, Ltd.
Bibliography:ark:/67375/WNG-Q2LFH9RX-Q
istex:AB3537332DF857BC7A47F100B8263C682CFC6EF6
ArticleID:NME3001
ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0029-5981
1097-0207
1097-0207
DOI:10.1002/nme.3001