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Optimal Shape Design for Elliptic Systems

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 equati...

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Bibliographic Details
Main Author: Pironneau, O.
Format: eBook
Language:English
Published: Berlin, Heidelberg Springer Berlin Heidelberg 1984, 1984
Edition:1st ed. 1984
Series:Scientific Computation
Subjects:
Numerical Analysis
Continuum Mechanics
Mathematical Physics
Theoretical, Mathematical And Computational Physics
Mathematical Methods In Physics
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 1. Elliptic Partial Differential Equations
  • 1.1 Introduction
  • 1.2 Green’s Formula
  • 1.3 Sobolev Spaces
  • 1.4 Linear Elliptic PDE of Order 2
  • 1.5 Numerical Solutions of Linear Elliptic Equations of Order 2
  • 1.6 Other Elliptic Equations
  • 1.7 Continuous Dependence on the Boundary
  • 2. Problem Statement
  • 2.1 Introduction
  • 2.2 Definition
  • 2.3 Examples
  • 2.4 Principles of Solution
  • 2.5 Future of Optimal Design Applications in Industry
  • 2.6 Historical Background and References
  • 3. Existence of Solutions
  • 3.1 Introduction
  • 3.2 Dirichlet Conditions
  • 3.3 Neumann Boundary Conditions
  • 3.4 Conclusion
  • 4. Optimization Methods
  • 4.1 Orientation
  • 4.2 Problem Statement
  • 4.3 Gradients
  • 4.4 Method of Steepest Descent
  • 4.5 Newton Method
  • 4.6 Conjugate Gradient Method
  • 4.7 Optimization with Equality Constraints
  • 4.8 Optimization with Inequality Constraints
  • 5. Design Problems Solved by Standard Optimal Control Theory
  • 5.1 Introduction
  • 5.2 Optimization of a Thin Wing
  • 5.3 Optimization of an Almost Straight Nozzle
  • 5.4 Thickness Optimization Problem
  • 6. Optimality Conditions
  • 6.1 Introduction
  • 6.2 Distributed Observation on a Fixed Domain
  • 6.3 Other Cases with Linear PDE
  • 7. Discretization with Finite Elements
  • 7.1 Introduction
  • 7.2 Neumann Problem
  • 7.3 Dirichlet Conditions
  • 7.4 Other Problems
  • 7.5 Convergence
  • 8. Other Methods
  • 8.1 Introduction
  • 8.2 Method of Mappings
  • 8.3 Finite Difference Discretization
  • 8.4 Method of Characteristic Functions
  • 8.5 Discretization by the Boundary Element Method
  • 9. Two Industrial Examples
  • 9.1 Introduction
  • 9.2 Optimization of Electromagnets
  • 9.3 Optimization of Airfoils
  • 9.4 Conclusion
  • References

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