Please use this identifier to cite or link to this item: http://dx.doi.org/10.25673/69575
Title: A Newton multigrid framework for optimal control of fluid–structure interactions
Author(s): Failer, L.
Richter, Thomas
Issue Date: 2021
Type: Article
Language: English
URN: urn:nbn:de:gbv:ma9:1-1981185920-715274
Subjects: Fluid-structure interactions
Finite elements
Multigrid
Parallel computing
Abstract: We present a monolithic parallel Newton-multigrid solver for nonlinear nonstationary three dimensional fluid-structure interactions in arbitrary Lagrangian Eulerian (ALE) formulation. We start with a finite element discretization of the coupled problem, based on a remapping of the Navier–Stokes equations onto a fixed reference framework. The strongly coupled fluidstructure interaction problem is discretized with finite elements in space and finite differences in time. The resulting nonlinear and linear systems of equations are large and show a very high condition number. We present a novel Newton approach that is based on two essential ideas: First, a condensation of the solid deformation by exploiting the discretized velocitydeformation relation dtu = v, second, the Jacobian of the fluid-structure interaction system is simplified by neglecting all derivatives with respect to the ALE deformation, an approximation that has shown to have little impact. The resulting system of equations decouples into a joint momentum equation and into two separate equations for the deformation fields in solid and fluid. Besides a reduction of the problem sizes, the approximation has a positive effect on the conditioning of the systems such that multigrid solvers with simple smoothers like a parallel Vanka-iteration can be applied.We demonstrate the efficiency of the resulting solver infrastructure on a well-studied 2d test-case and we also introduce a challenging 3d problem.
URI: https://opendata.uni-halle.de//handle/1981185920/71527
http://dx.doi.org/10.25673/69575
Open Access: Open access publication
License: (CC BY 4.0) Creative Commons Attribution 4.0(CC BY 4.0) Creative Commons Attribution 4.0
Sponsor/Funder: Projekt DEAL 2020
Journal Title: Optimization and engineering
Publisher: Springer Science + Business Media B.V
Publisher Place: Dordrecht [u.a.]
Volume: 22
Original Publication: 10.1007/s11081-020-09498-8
Page Start: 2009
Page End: 2037
Appears in Collections:Fakultät für Mathematik (OA)

Files in This Item:
File Description SizeFormat 
Failer et al._A Newton_2021.pdfZweitveröffentlichung1.94 MBAdobe PDFThumbnail
View/Open