Introduction to shape optimization: theory, approximation, and computation

J. Haslinger, R. A. E. Mäkinen9780898715361, 0898715369

The efficiency and reliability of manufactured products depend on, among other things, geometrical aspects; it is therefore not surprising that optimal shape design problems have attracted the interest of applied mathematicians and engineers. This self-contained, elementary introduction to the mathematical and computational aspects of sizing and shape optimization enables readers to gain a firm understanding of the theoretical and practical aspects so they may confidently enter this field.

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Table of contents :
Introduction to Shape Optimization……Page 2
Advances in Design and Control……Page 3
ISBN 0-89871-536-9……Page 5
Contents……Page 6
Preface……Page 10
Notation……Page 14
Introduction……Page 18
Part I Mathematical Aspects of Sizing and Shape Optimization……Page 20
1 Why the Mathematical Analysis Is Important……Page 22
2 A Mathematical Introduction to Sizing and Shape Optimization……Page 32
Part II Computational Aspects of Sizing and Shape Optimization……Page 116
3 Sensitivity Analysis……Page 118
4 Numerical Minimization Methods……Page 148
5 On Automatic Differentiation of Computer Programs……Page 172
6 Fictitious Domain Methods in Shape Optimization……Page 188
Part III Applications……Page 218
7 Applications in Elasticity……Page 220
8 Fluid Mechanical and Multidisciplinary Applications……Page 242
Appendix A Weak Formulations and Approximations of Elliptic Equations and Inequalities……Page 264
Appendix B On Parametrizations of Shapes and Mesh Generation……Page 276
Bibliography……Page 282
Index……Page 290