Optimal Shape Design

Lectures given at the joint C.I.M./C.I.M.E. Summer School held in Tróia, Portugal, June 1–6, 1998

  • Authors
  • Bernhard Kawohl
  • Olivier Pironneau
  • Luc Tartar
  • Jean-Paul Zolésio
  • Editors
  • Arrigo Cellina
  • António Ornelas

Part of the Lecture Notes in Mathematics book series (LNM, volume 1740)

Table of contents

  1. Front Matter
    Pages I-IX
  2. Arrigo Cellina
    Pages 1-5
  3. Jean-Paul Zolésio
    Pages 157-341
  4. Olivier Pironneau
    Pages 343-384
  5. Back Matter
    Pages 385-389

About this book

Introduction

Optimal Shape Design is concerned with the optimization of some performance criterion dependent (besides the constraints of the problem) on the "shape" of some region. The main topics covered are: the optimal design of a geometrical object, for instance a wing, moving in a fluid; the optimal shape of a region (a harbor), given suitable constraints on the size of the entrance to the harbor, subject to incoming waves; the optimal design of some electrical device subject to constraints on the performance. The aim is to show that Optimal Shape Design, besides its interesting industrial applications, possesses nontrivial mathematical aspects. The main theoretical tools developed here are the homogenization method and domain variations in PDE. The style is mathematically rigorous, but specifically oriented towards applications, and it is intended for both pure and applied mathematicians. The reader is required to know classical PDE theory and basic functional analysis.

Keywords

differential equation functional analysis homogenization numerical methods optimization partial differential equation

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0106739
  • Copyright Information Springer-Verlag Berlin Heidelberg 2000
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-67971-4
  • Online ISBN 978-3-540-44486-2
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book