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Optimal Shape Design

Lectures given at the Joint C.I.M./C.I.M.E. Summer School held in Troia (Portugal), June 1-6, 1998

  • Book
  • © 2000

Overview

Authors:
  1. Bernhard Kawohl
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  2. Olivier Pironneau
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  3. Luc Tartar
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  4. Jean-Paul Zolésio
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Editors:
  1. Arrigo Cellina
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  2. António Ornelas
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1740)

Part of the book sub series: C.I.M.E. Foundation Subseries (LNMCIME)

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Table of contents (5 chapters)

  1. Front Matter

    Pages I-IX
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  2. Introduction

    • Arrigo Cellina
    Pages 1-5

  3. Some nonconvex shape optimization problems

    • Bernd Kawohl
    Pages 7-46

  4. An introduction to the homogenization method in optimal design

    • Luc Tartar
    Pages 47-156

  5. Shape analysis and weak flow

    • Jean-Paul Zolésio
    Pages 157-341

  6. Optimal shape design by local boundary variations

    • Olivier Pironneau
    Pages 343-384

  7. Back Matter

    Pages 385-389
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Keywords

About this book

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.

Bibliographic Information

  • Book Title: Optimal Shape Design

  • Book Subtitle: Lectures given at the Joint C.I.M./C.I.M.E. Summer School held in Troia (Portugal), June 1-6, 1998

  • Authors: Bernhard Kawohl, Olivier Pironneau, Luc Tartar, Jean-Paul Zolésio

  • Editors: Arrigo Cellina, António Ornelas

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0106739

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2000

  • Softcover ISBN: 978-3-540-67971-4Published: 16 November 2000

  • eBook ISBN: 978-3-540-44486-2Published: 06 May 2007

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XII, 392

  • Topics: Analysis, Calculus of Variations and Optimal Control; Optimization

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