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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| Veröffentlicht in: | International journal for numerical methods in engineering Jg. 85; H. 8; S. 987 - 1016 |
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| Sprache: | Englisch |
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Chichester, UK
John Wiley & Sons, Ltd
25.02.2011
Wiley |
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| ISSN: | 0029-5981, 1097-0207, 1097-0207 |
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| Abstract | 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. |
|---|---|
| AbstractList | 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. 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. |
| Author | Küttler, U. Gee, M. W. Wall, W. A. |
| Author_xml | – sequence: 1 givenname: M. W. surname: Gee fullname: Gee, M. W. email: gee@lnm.mw.tum.de organization: Institute for Computational Mechanics, Technische Universität München, Boltzmannstrasse 15, D-85747 Garching b. München, Germany – sequence: 2 givenname: U. surname: Küttler fullname: Küttler, U. organization: Institute for Computational Mechanics, Technische Universität München, Boltzmannstrasse 15, D-85747 Garching b. München, Germany – sequence: 3 givenname: W. A. surname: Wall fullname: Wall, W. A. organization: Institute for Computational Mechanics, Technische Universität München, Boltzmannstrasse 15, D-85747 Garching b. München, Germany |
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| Keywords | 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 |
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| SubjectTerms | 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...) |
| Title | Truly monolithic algebraic multigrid for fluid-structure interaction |
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