A Monolithic FEM/Multigrid Solver for an ALE Formulation of Fluid-Structure Interaction with Applications in Biomechanics

Hron, J.; Turek, Stefan

doi:10.1007/3-540-34596-5_7

Cited by 175 publications

(202 citation statements)

References 20 publications

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“…(16) where the test functions are defined on H 1 0 (Ω sf (d)), thus on a domain which overlaps with both the solid and fluid parts. It is worth noting that, by the coupling conditions (12), the two boundary terms that result from integration by parts at the solid-fluid interface Γ i cancel out. This assures that stresses at the interface are correctly balanced.…”

Section: Weak Formulationmentioning

confidence: 99%

“…Monolithic algorithms solve simultaneously for the fluid and the structure unknowns in a unique solver, so that the solid and fluid regions are treated as a single continuum and the boundary conditions at the interface are automatically satisfied ( [9,12]). Monolithic algorithms are CPU-time expensive.…”

Section: Introductionmentioning

confidence: 99%

“…Other variants have been proposed in literature for the linearization. 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].…”

Section: Introductionmentioning

confidence: 99%

“…In [12] a geometric multigrid solver with a Multilevel Pressure Schur Complement (MPSC) Vanka-like smoother is considered, with applications to nonstationary FSI problems in biomechanics. Applications of this scheme to hemodynamics are also addressed in [22,14].…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Weak Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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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“…Moreover this method has a solid mathematical background and the existence of local optimal solutions can be investigated in many interesting cases, see for examples [21,22,24]. We are interested in a monolithic approach to the solution of the FSI system leading to a stable and well defined solution in a finite element setting [25,26]. Inside this framework we study a distributed optimal control problem applied to the monolithic FSI system.…”

Section: Introductionmentioning

confidence: 99%

Adjoint Optimal Control Problems for Fluid-Structure Interaction Systems

Cerroni¹,

Davià²,

Manservisi³

et al. 2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract. In the last years adjoint optimal control has been increasingly used for design and simulations in several research fields. Applications to Computational Fluid Dynamics problems dedicated to the study of transient-diffusion equations, shape optimization problems, fluid-solid conjugate heat transfer and turbulent flows can be found in literature. The study of FluidStructure Interaction problems gained popularity recently because of many interesting applications in engineering and biomedical fields. In this paper we study adjoint optimal control problems for Fluid-Structure Interaction systems in order to improve the advantages of using FSI simulations when designing engineering devices where fluid-dynamical interactions between a fluid and a solid play a significant role. We assess distributed optimal control problems with the purpose to control the fluid behavior by moving the solid region to obtain a desired fluid velocity in specific parts of the domain. The adjoint equations of the FSI monolithic system are derived and the optimality system solved for some simple cases with an in-house finite element code with mesh-moving capabilities for the study of large displacements in the solid. The approach presented in this work is general and can be used to assess different objectives and types of control in future works.

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Implicit Partitioned Coupling in Fluid–Structure Interaction

Schäfer¹

2013

Arbitrary Lagrangian‐Eulerian and Fluid–Structure Interaction

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A Monolithic FEM/Multigrid Solver for an ALE Formulation of Fluid-Structure Interaction with Applications in Biomechanics

Cited by 175 publications

References 20 publications

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

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

Adjoint Optimal Control Problems for Fluid-Structure Interaction Systems

Implicit Partitioned Coupling in Fluid–Structure Interaction

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