Analysis of the block Gauss–Seidel solution procedure for a strongly coupled model problem with reference to fluid–structure interaction

Joosten, M. M.; Dettmer, Wulf G.; Perić, D.

doi:10.1002/nme.2503

Cited by 69 publications

(76 citation statements)

References 32 publications

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“…The overlapping interface equations are combined with the interior fluid equations in (29). This means that the structural contributions to the interface equations are also contained within the fluid block, see (33), and the linear system (22) …”

Section: Newton Schemes On Fully Coupled Systemmentioning

confidence: 99%

Truly monolithic algebraic multigrid for fluid–structure interaction

Gee

Küttler

Wall

2010

Numerical Meth Engineering

187

264

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SUMMARYThe 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.

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Section: Newton Schemes On Fully Coupled Systemmentioning

confidence: 99%

Truly monolithic algebraic multigrid for fluid–structure interaction

Gee

Küttler

Wall

2010

Numerical Meth Engineering

187

264

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“…Moreover, the impact of the sequence of integration on the stability condition of decoupled solutions is demonstrated. The SSI problem [8].…”

Section: Resultsmentioning

confidence: 99%

“…3 is adopted to study the surface-coupled problem of solid-solid interaction (SSI). To scrutinise the importance of the sequence of integration, a forward and a reverse staggered solution scheme as described in [8] are considered. Executing the stability analysis, one finds the following distinguishable stability conditions: …”

Section: Applicationsmentioning

confidence: 99%

Stability Analysis of Decoupled Solution Strategies for Coupled Multi‐field Problems – A General Framework

Zinatbakhsh

Markert

Ehlers

2012

Proc Appl Math and Mech

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A coupled partial differential equation (PDE) system, stemming from the mathematical modelling of a coupled phenomenon, is usually solved numerically following a monolithic or a decoupled solution method. In spite of the potential unconditional stability offered by monolithic solvers, their usage for solving complex problems sometimes proves cumbersome. This has motivated the development of various partitioned and staggered solution strategies, generally known as decoupled solution schemes. To this end, the problem is broken down into several isolated yet communicating sub-problems that are independently advanced in time, possibly by different integrators. Nevertheless, using a decoupled solver introduces additional errors to the system and, therefore, may jeopardise the stability of the solution [1]. Consequently, to scrutinise the stability of the solution scheme becomes a pertinent step in proposing decoupled solution strategies. Here, we endeavour to present a practical stability analysis algorithm, which can readily be used to reveal the stability condition of numerical solvers. To illustrate its capabilities, the algorithm is then utilised for the stability analysis of solution schemes applied to multi variate coupled PDE systems resulting from the mathematical modelling of surface-and volume-coupled multi-field problems.

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“…After substitution of Equations (8), (10), (14) and (15) into Equation (18), and combining this with Equations (11), (12), (16), (19) and (20), the total set of equations to describe …”

Section: Stability and Accuracymentioning

confidence: 99%

“…The publications [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] and references therein describe different computational strategies for fluid-structure interaction and involve either one or more time integration schemes. It is noted that the information provided on the integration of time and the temporal matching of kinematic quantities at the interface is often missing or simply not given in an explicit way.…”

Section: Introductionmentioning

confidence: 99%

On the temporal stability and accuracy of coupled problems with reference to fluid–structure interaction

Joosten¹,

Dettmer²,

Perić³

2010

Numerical Methods in Fluids

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SUMMARYThis work investigates the effect of employing different time integration schemes in the sub-domains of a coupled problem, such as fluid-structure interaction. On the basis of a one-dimensional model problem and the two versions of the generalized-method developed for first-and second-order systems, it is shown that the overall problem is likely to be less stable and less accurate than the individual sub-problems unless special measures are taken. The benchmark problem of the oscillating flexible beam is used to demonstrate that these findings also apply to full computational fluid-structure interaction.

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Analysis of the block Gauss–Seidel solution procedure for a strongly coupled model problem with reference to fluid–structure interaction

Cited by 69 publications

References 32 publications

Truly monolithic algebraic multigrid for fluid–structure interaction

Truly monolithic algebraic multigrid for fluid–structure interaction

Stability Analysis of Decoupled Solution Strategies for Coupled Multi‐field Problems – A General Framework

On the temporal stability and accuracy of coupled problems with reference to fluid–structure interaction

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