Optimal Control of a Linear Unsteady Fluid–Structure Interaction Problem

Failer, Lukas; Meidner, Dominik; Vexler, Boris

doi:10.1007/s10957-016-0930-1

Cited by 20 publications

(14 citation statements)

References 41 publications

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“…For shorter notation, we denote by U := (v, u, p f ) ∈ X the solution variable and with X the corresponding ansatz space and by Φ := (φ, ψ f , ψ s , ξ) ∈ Y the test functions and the corresponding test space. For a control q ∈ L 2 (I) and the here given tracking-type functional constrained by linear-fluid structure interaction, we were able to proof in [18] existence of a unique solution and H 1 (I) regularity of the optimal control. In addition an optimality system could be rigorously derived.…”

Section: Governing Equationsmentioning

confidence: 90%

A Newton multigrid framework for optimal control of fluid–structure interactions

Failer

Richter

2020

Optim Eng

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In this paper we consider optimal control of nonlinear time-dependent fluid structure interactions. To determine a time-dependent control variable a BFGS algorithm is used, whereby gradient information is computed via a dual problem. To solve the resulting ill conditioned linear problems occurring in every time step of state and dual equation, we develop a highly efficient monolithic solver that is based on an approximated Newton scheme for the primal equation and a preconditioned Richardson iteration for the dual problem. The performance of the presented algorithms is tested for one 2d and one 3d example numerically.

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Section: Governing Equationsmentioning

confidence: 90%

A Newton multigrid framework for optimal control of fluid–structure interactions

Failer

Richter

2020

Optim Eng

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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. In Failer and Richter (2020) and Wick and Wollner (2020), the authors solve both solid velocity and displacement, together with fluid velocity and pressure using a monolithic Newton solver.…”

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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“…These include goal-oriented techniques employing the dual-weighted residual method [6] with specific findings in fluid-structure interaction, e.g., in [50,38,26,13,14,39,18]. In numerical optimization such as optimal control, optimal design and parameter estimation, we list [37,27,31,16,15,30,40,48,17]. For gradient-based techniques, the usual approach is via the formal Lagrange formalism resulting in an optimality system to compute stationary points [32,1,28,44].…”

Section: Introductionmentioning

confidence: 99%