An optimal control method for fluid structure interaction systems via adjoint boundary pressure

Chirco, Leonardo; Vià, Roberto Da; Manservisi, Sandro

doi:10.1088/1742-6596/923/1/012026

Cited by 6 publications

(7 citation statements)

References 17 publications

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“…A particular challenge in achieving optimal FSI control is to formulate the coupling conditions on the fluid-structure interface into the optimality system (Chirco et al 2017;Failer et al 2016). For example, Failer et al (2016) enforce the coupling condition weakly to analyse optimal control for a linear FSI problem, whereas Chirco and Manservisi (2020) and Chierici et al (2019) introduce an auxiliary mesh displacement in the solid domain to enforce the coupling condition.…”

Section: Introductionmentioning

confidence: 99%

An optimal control method for time-dependent fluid-structure interaction problems

Wang

Jimack

Walkley

et al. 2021

Struct Multidisc Optim

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In this article, we derive an adjoint fluid-structure interaction (FSI) system in an arbitrary Lagrangian-Eulerian (ALE) framework, based upon a one-field finite element method. A key feature of this approach is that the interface condition is automatically satisfied and the problem size is reduced since we only solve for one velocity field for both the primary and adjoint system. A velocity (and/or displacement)-matching optimisation problem is considered by controlling a distributed force. The optimisation problem is solved using a gradient descent method, and a stabilised Barzilai-Borwein method is adopted to accelerate the convergence, which does not need additional evaluations of the objective functional. The proposed control method is validated and assessed against a series of static and dynamic benchmark FSI problems, before being applied successfully to solve a highly challenging FSI control problem.

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Section: Introductionmentioning

confidence: 99%

An optimal control method for time-dependent fluid-structure interaction problems

Wang

Jimack

Walkley

et al. 2021

Struct Multidisc Optim

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“…The existence of an optimal FSI control for the problem of minimizing flow turbulence, by controlling a distributed force, is established in [67]. In recent years, many studies of the optimal FSI control focus on numerical methods and implementations: monolithic formulation and Newton multigrid method are presented in [68,69]; a velocity-tracking objective is considered by controlling either a distributed body force [70] or a boundary pressure [71][72][73].…”

Section: Introductionmentioning

confidence: 99%

A monolithic one-velocity-field optimal control formulation for fluid-structure interaction problems with large solid deformation

Wang

2021

Preprint

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In this article, we formulate a monolithic optimal control method for general time-dependent Fluid-Structure Interaction (FSI) systems with large solid deformation. We consider a displacement-tracking type of objective with a constraint of the solid velocity, tackle the time-dependent control problems by a piecewise-in-time control, cope with large solid displacement using a one-velocity fictitious domain method, and solve the fully-coupled FSI and the corresponding adjoint equations in a monolithic manner. We implement the proposed method in the open-source software package FreeFEM++ and assess it by three numerical experiments, in the aspects of stability of the numerical scheme for different regularisation parameters, and efficiency of reducing the objective function with control of the solid velocity.

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“…24 Studies concentrating on theoretical and computational aspects for stationary FSI optimization are. 23,[25][26][27] Here, we notice that the required adjoints are the same as used for adjoint-based error estimation; see, for instance, References 28, 29. Nonlinear (stationary) FSI investigating various partitioned coupling techniques was recently subject in Reference 30.…”

Section: Introductionmentioning

confidence: 99%

“…Studies concentrating on theoretical and computational aspects for stationary FSI optimization are 1 arXiv:1910.03424v1 [math.NA] 8 Oct 2019 [53,57,60,12]. Here, we notice that the required adjoints are the same as used for adjoint-based error estimation; see for instance [62,51].…”

Section: Introductionmentioning

confidence: 99%

“…Specifically, we will formally provide the backward-in-time running adjoint state used for gradient computations.Our algorithmic developments are demonstrated with some numerical examples as for instance extensions of the well-known fluid-structure benchmark settings and a flapping membrane test in a channel flow with elastic walls. arXiv:1910.03424v1 [math.NA] 8 Oct 2019 [53,57,60,12]. Here, we notice that the required adjoints are the same as used for adjoint-based error estimation; see for instance [62,51].…”

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confidence: 99%

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Optimization with nonstationary, nonlinear monolithic fluid‐structure interaction

Wick

Wollner

2020

Numerical Meth Engineering

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Within this work, we consider optimization settings for nonlinear, nonstationary fluid-structure interaction. The problem is formulated in a monolithic fashion using the arbitrary Lagrangian-Eulerian framework to set-up the fluid-structure forward problem. In the optimization approach, either optimal control or parameter estimation problems are treated. In the latter, the stiffness of the solid is estimated from given reference values. In the numerical solution, the optimization problem is solved with a gradient-based solution algorithm. The nonlinear subproblems of the FSI forward problem are solved with a Newton method including line search. Specifically, we will formally provide the backward-in-time running adjoint state used for gradient computations.Our algorithmic developments are demonstrated with some numerical examples as for instance extensions of the well-known fluid-structure benchmark settings and a flapping membrane test in a channel flow with elastic walls. arXiv:1910.03424v1 [math.NA] 8 Oct 2019 [53,57,60,12]. Here, we notice that the required adjoints are the same as used for adjoint-based error estimation; see for instance [62,51]. Nonlinear (stationary) FSI investigating various partitioned coupling techniques was recently subject in [54]. The by far more challenging situation of nonstationary settings is listed in the following. A nonstationary situation assuming a rigid solid was theoretically studied in [48]. Further theoretical results for a boundary control FSI problem were established in [8].Parameter estimation to detect the stiffness of an arterial wall with a well-posedness analysis and numerical simulations was addressed in [49]. Again in blood flow simulations, a data assimilation problem was formulated in [33], in which however, the arterial walls were not considered. A full FSI problem for data assimilation using a Kalman filter was subject in [6]. In [44], the authors used optimization techniques to formulate the FSI coupling conditions. Adjoints for 1D FSI were derived in [16,47]. Reduced basis methods for FSI-based optimization were developed in [45]. Optimal control of nonstationary FSI applied to benchmark settings was investigated in [3]. A linearized FSI optimization problem was addressed in [23] and detailed results for full-time-dependent FSI optimal control were summarized in [22]. In this respect, we also mention [24] in which the adjoints required for optimization were employed for dual-weighted residual error estimation for time adaptivity. Most recently, a uncertainty quantification framework for fluid-structure interaction with applications in aortic biomechanics was developed in [43].The significance of the current work is on the development of a robust fully monolithic formulation for gradient-based optimization for nonstationary, nonlinear FSI problems. Here, the coupled problem is prescribed in the reference configuration with the help of the ALE approach in a variationalmonolithic way. As previously summarized in our literature review, only very few results exis...

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An optimal control method for fluid structure interaction systems via adjoint boundary pressure

Cited by 6 publications

References 17 publications

An optimal control method for time-dependent fluid-structure interaction problems

An optimal control method for time-dependent fluid-structure interaction problems

A monolithic one-velocity-field optimal control formulation for fluid-structure interaction problems with large solid deformation

Optimization with nonstationary, nonlinear monolithic fluid‐structure interaction

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