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Moving Shape Analysis and Control

Applications to Fluid Structure Interactions

Moving Shape Analysis and Control by Marwan Moubachir
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Introduction
Classical and Moving Shape Analysis
Fluid–Structure Interaction Problems
Plan of the Book
Detailed Overview of the Book
An Introductory Example: The Inverse Stefan Problem
The Mechanical and Mathematical Settings
The Inverse Problem Setting
The Eulerian Derivative and the Transverse Field
The Eulerian Material Derivative of the State
The Eulerian Partial Derivative of the State
The Adjoint State and the Adjoint Transverse Field
Weak Evolution of Sets and Tube Derivatives
Introduction
Weak Convection of Characteristic Functions
Tube Evolution in the Context of Optimization Problems
Tube Derivative Concepts
A First Example: Optimal Trajectory Problem
Shape Differential Equation and Level Set Formulation
Introduction
Classical Shape Differential Equation Setting
The Shape Control Problem
The Asymptotic Behavior
Shape Differential Equation for the Laplace Equation
Shape Differential Equation in Rd+1
The Level Set Formulation
Dynamical Shape Control of the Navier–Stokes Equations
Introduction
Problem Statement
Elements of Noncylindrical Shape Calculus
Elements of Tangential Calculus
State Derivative Strategy
Min-Max and Function Space Parameterization
Min-Max and Function Space Embedding
Conclusion
Tube Derivative in a Lagrangian Setting
Introduction
Evolution Maps
Navier–Stokes Equations in Moving Domain
Sensitivity Analysis for a Simple Fluid–Solid Interaction System
Introduction
Mathematical Settings
Well-Posedness of the Coupled System
Inverse Problem Settings
KKT Optimality Conditions
Conclusion
Sensitivity Analysis for a General Fluid–Structure Interaction System
Introduction
Mechanical Problem and Main Result
KKT Optimality Conditions
Appendix A: Functional Spaces and Regularity of Domains
Appendix B: Distribution Spaces
Appendix C: The Fourier Transform
Appendix D: Sobolev Spaces
References
Index
CRC Press; January 2006
312 pages; ISBN 9781420003246
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Title: Moving Shape Analysis and Control
Author: Marwan Moubachir; Jean-Paul Zolesio
 
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