AuthorsJ. Haubner, M. Ulbrich and S. Ulbrich
TitleAnalysis of shape optimization problems for unsteady fluid-structure interaction
AfilliationScientific Computing
Project(s)No Simula project
StatusPublished
Publication TypeJournal Article
Year of Publication2020
JournalInverse Problems
Volume36
Number3
Pagination034001
Date Published02/2020
PublisherIOP Publishing
Abstract

Shape optimization via the method of mappings is investigated for unsteady fluid-structure interaction (FSI) problems that couple the Navier–Stokes equations and the Lamé system. Building on recent existence and regularity theory we prove Fréchet differentiability results for the state with respect to domain variations. These results form an analytical foundation for optimization und inverse problems governed by FSI systems. Our analysis develops a general framework for deriving local-in-time continuity and differentiability results for parameter dependent nonlinear systems of partial differential equations. The main part of the paper is devoted to conducting this analysis for the FSI problem, transformed to a shape reference domain. The underlying shape transformation—actually we work with the corresponding shape displacement instead—represents the shape and the main result proves the Fréchet differentiability of the solution of the FSI system with respect to the shape transformation.

DOI10.1088/1361-6420/ab5a11
Citation Key28235