On the Adjoint Equation in Fluid-Structure Interaction

Wick, Thomas

doi:10.23967/wccm-eccomas.2020.268

Cited by 3 publications

(1 citation statement)

References 32 publications

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“…For applications in fluid-structure interaction, we refer to [32,23,54,57,44,46,20,22]. A recent overview of our own work using the adjoint FSI equation in goal-oriented error estimation and optimization was done in [60]. In [49] a variational localization using a partition-of-unity (PU) was proposed, facilitating the application to coupled problems such as fluid-structure interaction.…”

Section: Introductionmentioning

confidence: 99%

Adjoint-based methods for optimization and goal-oriented error control applied to fluid-structure interaction: implementation of a partition-of-unity dual-weighted residual estimator for stationary forward FSI problems in deal.II

Wick¹

2021

Preprint

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In this work, we implement goal-oriented error control and spatial mesh adaptivity for stationary fluid-structure interaction. The a posteriori error estimator is realized using the dual-weighted residual method in which the adjoint equation arises. The fluid-structure interaction problem is formulated within a variational-monolithic framework using arbitrary Lagrangian-Eulerian coordinates. The overall problem is nonlinear and solved with Newton's method. We specifically consider the FSI-1 benchmark problem in which quantities of interest include the elastic beam displacements, drag, and lift. The implementation is provided open-source published on github https://github.com/tommeswick/goal-oriented-fsi. Possible extensions are discussed in the source code and in the conclusions of this paper.

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Section: Introductionmentioning

confidence: 99%

Adjoint-based methods for optimization and goal-oriented error control applied to fluid-structure interaction: implementation of a partition-of-unity dual-weighted residual estimator for stationary forward FSI problems in deal.II

Wick¹

2021

Preprint

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Numerical Modeling and Open-Source Implementation of Variational Partition-of-Unity Localizations of Space-Time Dual-Weighted Residual Estimators for Parabolic Problems

Thiele,

Wick

2024

J Sci Comput

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In this work, we consider space-time goal-oriented a posteriori error estimation for parabolic problems. Temporal and spatial discretizations are based on Galerkin finite elements of continuous and discontinuous type. The main objectives are the development and analysis of space-time estimators, in which the localization is based on a weak form employing a partition-of-unity. The resulting error indicators are used for temporal and spatial adaptivity. Our developments are substantiated with several numerical examples.

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Adjoint-based methods for optimization and goal-oriented error control applied to fluid-structure interaction: implementation of a partition-of-unity dual-weighted residual estimator for stationary forward FSI problems in deal.II

Wick

2021

Proceedings of the YIC 2021 - VI ECCOMAS Young Investigators Conference

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In this presentation, we focuson the adjoint equation in fluid-structure interaction. Derivations for both stationary and nonstationary settings are undertaken. In the latter, the adjoint is running backward-in-time and must access the primal solution due to the nonlinearities.This is a computational challenge, but it is shown that the overall implementationis very promising and numerically robust. We demonstrate the performance in terms of error estimation, space/time adaptivity,and optimal control.

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On the Adjoint Equation in Fluid-Structure Interaction

Cited by 3 publications

References 32 publications

Adjoint-based methods for optimization and goal-oriented error control applied to fluid-structure interaction: implementation of a partition-of-unity dual-weighted residual estimator for stationary forward FSI problems in deal.II

Adjoint-based methods for optimization and goal-oriented error control applied to fluid-structure interaction: implementation of a partition-of-unity dual-weighted residual estimator for stationary forward FSI problems in deal.II

Numerical Modeling and Open-Source Implementation of Variational Partition-of-Unity Localizations of Space-Time Dual-Weighted Residual Estimators for Parabolic Problems

Adjoint-based methods for optimization and goal-oriented error control applied to fluid-structure interaction: implementation of a partition-of-unity dual-weighted residual estimator for stationary forward FSI problems in deal.II

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