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

Publication date: 24 May 2021

Abstract: 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.

Has companion code repository: https://github.com/tommeswick/goal-oriented-fsi

Mathematics Subject Classification ID

Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) (74F10) Proceedings, conferences, collections, etc. pertaining to numerical analysis (65-06) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Software, source code, etc. for problems pertaining to numerical analysis (65-04)

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