Optimal Shape Design for Elliptic Systems

✍ Scribed by Olivier Pironneau (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 1984
• Tongue: English
• Leaves: 178
• Series: Springer Series in Computational Physics
• Edition: 1
• Category: Library

✦ Synopsis

The study of optimal shape design can be arrived at by asking the following question: "What is the best shape for a physical system?" This book is an applications-oriented study of such physical systems; in particular, those which can be described by an elliptic partial differential equation and where the shape is found by the minimum of a single criterion function. There are many problems of this type in high-technology industries. In fact, most numerical simulations of physical systems are solved not to gain better understanding of the phenomena but to obtain better control and design. Problems of this type are described in Chapter 2. Traditionally, optimal shape design has been treated as a branch of the calculus of variations and more specifically of optimal control. This subject interfaces with no less than four fields: optimization, optimal control, partial differential equations (PDEs), and their numerical solutions-this is the most difficult aspect of the subject. Each of these fields is reviewed briefly: PDEs (Chapter 1), optimization (Chapter 4), optimal control (Chapter 5), and numerical methods (Chapters 1 and 4).

✦ Table of Contents

Front Matter....Pages i-xii
Elliptic Partial Differential Equations....Pages 1-15
Problem Statement....Pages 16-29
Existence of Solutions....Pages 30-44
Optimization Methods....Pages 45-67
Design Problems Solved by Standard Optimal Control Theory....Pages 68-80
Optimality Conditions....Pages 81-98
Discretization with Finite Elements....Pages 99-120
Other Methods....Pages 121-142
Two Industrial Examples....Pages 143-162
Back Matter....Pages 163-168

✦ Subjects

Fluid- and Aerodynamics;Mathematical Methods in Physics;Numerical and Computational Physics;Numerical Analysis