A Newton method using exact jacobians for solving fluid–structure coupling

Fernández, Miguel Ángel; Moubachir, Marwan

doi:10.1016/j.compstruc.2004.04.021

Cited by 264 publications

(283 citation statements)

References 30 publications

(112 reference statements)

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“…The convergence of Gauss-Seidel iterations is improved by Aitken relaxation [1] which uses a dynamically-adapted relaxation factor. Faster convergence is obtained with Newton methods [2] or in case of black-box solvers with the Interface Generalized Minimum Residual method [3] or with quasi-Newton methods like the interface block quasi-Newton method with approximate Jacobians from least-squares models (IBQN-LS) [4] and the interface quasi-Newton method with inverse Jacobian from a least-squares model (IQN-ILS) [5]. In case of weak interaction between the fluid and the solid, e.g.…”

Section: Introductionmentioning

confidence: 99%

Stability analysis of Gauss–Seidel iterations in a partitioned simulation of fluid–structure interaction

Degroote

Annerel

Vierendeels

2010

Computers & Structures

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A stability analysis of Gauss-Seidel coupling iterations for partitioned simulation of fluid-structure interaction is performed for the flow in a flexible tube. In a previous study the inertia of the structure and the interaction between the segments of the structure were not taken into account. It is now demonstrated that especially the structural inertia has a significant effect on the stability of Gauss-Seidel iterations for a certain range of the time step's size.

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Section: Introductionmentioning

confidence: 99%

Stability analysis of Gauss–Seidel iterations in a partitioned simulation of fluid–structure interaction

Degroote

Annerel

Vierendeels

2010

Computers & Structures

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“…We seek to validate and evaluate the accuracy and performance of the proposed Newtonmultigrid solver for a set of FSI benchmark configurations that can be found in the literature (see [3,7,23]). …”

Section: Numerical Resultsmentioning

confidence: 99%

“…In [11] quasi-Newton outer iterations with line search are performed and the Jacobian matrix is computed by a divided difference approach. A Newton method with the analytical computation of the Jacobian using shape-derivative calculus is considered in [6]. A quasi-Newton method in which the variation of the fluid domain in the fluid equations is neglected is proposed in [5,4].…”

Section: Introductionmentioning

confidence: 99%

Multigrid Solver With Domain Decomposition Smoothing for Steady-State Incompressible Fsi Problems

Aulisa¹,

Bnà²,

Bornia³

2015

Proceedings of the 5th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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Abstract. In this paper we investigate the numerical performance of a monolithic Newtonmultigrid solver with domain decomposition smoothers for the solution of a class of stationary incompressible FSI problems. The physics of the problem is described using a monolithic approach, where mass continuity and stress balance are automatically satisfied across the fluidsolid interface. The deformation of the fluid domain is taken into account within the nonlinear Newton iterations according to an Arbitrary Lagrangian Eulerian (ALE) scheme. Due to the complexity and variety of the operators, the implementation of the Jacobian matrix in the nonlinear iterations is not a trivial task. To this purpose, we make use of automatic differentiation tools for an exact computation of the Jacobian matrix. The numerical solution of steady-state problems is particularly challenging, due to the ill-conditioning of the induced stiffness matrix. Moreover, the enforcement of the incompressibility condition calls for the use of incompressible solvers either of mixed or segregated type. At each nonlinear outer iteration the resulting linearized system is solved with a geometric multigrid solver. We consider a GMRES smoother preconditioned by an Additive Schwarz Method (ASM). The domain decomposition of the preconditioner is driven by the natural splitting between fluid and solid domain. The numerical results of some benchmark tests for steady-state cases show agreement with the literature and an increased robustness with our choice of smoothers with respect to standard ones.

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“…The third example is the propagation of a pressure wave in a three-dimensional flexible tube with radius 0.005 m and length 0.05 m, as described by Fernandez and Moubachir [45], Formaggia et al [46], Gerbeau and Vidrascu [47]. This tube is a simplified model for a large artery.…”

Section: Propagation Of a Pressure Wave In A Three-dimensional Flexibmentioning

confidence: 99%

“…end if 44: end for 45: end while 46: for i = 2 to g do 47: start synchronizing F i with F 1 48: end for 49: for j = 2 to h do 50: start synchronizing S j with S j 51: end for ands 0 1 are known. Again, the differences have to be calculated with respect to an input and output that actually comes from a flow solver and not with respect to the extrapolation.…”

Section: Algorithm 4 the Multi-solver Ibqn-ls (Ms-ibqn-ls) Algorithm mentioning

confidence: 99%

Multi-solver algorithms for the partitioned simulation of fluid–structure interaction

Degroote

Vierendeels

2011

Computer Methods in Applied Mechanics and Engineering

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In partitioned fluid-structure interaction simulations, the flow equations and the structural equations are solved separately. As a result, a coupling algorithm is needed to enforce the equilibrium on the fluid-structure interface in cases with strong interaction. This coupling algorithm performs coupling iterations between the solver of the flow equations and the solver of the structural equations. Current coupling algorithms couple one flow solver with one structural solver. Here, a new class of multi-solver quasi-Newton coupling algorithms for unsteady fluidstructure interaction simulations is presented. More than one flow solver and more than one structural solver are used for a single simulation. The numerical experiments demonstrate that the duration of a simulation decreases as the number of solvers is increased.

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A Newton method using exact jacobians for solving fluid–structure coupling

Cited by 264 publications

References 30 publications

Stability analysis of Gauss–Seidel iterations in a partitioned simulation of fluid–structure interaction

Stability analysis of Gauss–Seidel iterations in a partitioned simulation of fluid–structure interaction

Multigrid Solver With Domain Decomposition Smoothing for Steady-State Incompressible Fsi Problems

Multi-solver algorithms for the partitioned simulation of fluid–structure interaction

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