Shapes and Geometries
Society for Industrial & Applied Mathematics,U.S. (Verlag)
978-0-89871-936-9 (ISBN)
A self-contained presentation of the mathematical foundations, constructions and tools necessary for studying problems where the modeling, optimization or control variable is no longer a set of parameters or functions but the shape or the structure of a geometric object. This second edition presents the latest ground breaking theoretical foundation to shape optimization in a form that can used by the engineering and scientific communities. It also clearly explains the state-of-the-art developments in a mathematical language that will attract mathematicians to open questions in this important field. The area of research is very broad, rich and fascinating from both theoretical and numerical standpoints and this book reflects this exciting expanding field. This book will be of great importance to applied mathematicians, as well as advanced engineers and scientists working in this area.
M. C. Delfour is a Professor of Mathematics and Statistics at the University of Montreal in Canada, a member of the Canadian Academy of Sciences (FRSC), a former Guggenheim and Killam Fellow and a SIAM Fellow. J.-P. Zolésio is Research Director in Mathematics at the CNRS. He is member of the Institut Non Linéaire de Nice (INLN) associated with the Institut National de Recherche en Informatique et Automatique (INRIA) In Sophia Antipolis (France).
List of figures; Preface; 1. Introduction: examples, background, and perspectives; 2. Classical descriptions of geometries and their properties; 3. Courant metrics on images of a set; 4. Transformations generated by velocities; 5. Metrics via characteristic functions; 6. Metrics via distance functions; 7. Metrics via oriented distance functions; 8. Shape continuity and optimization; 9. Shape and tangential differential calculuses; 10. Shape gradients under a state equation constraint; Elements of bibliography; Index of notation; Index.
| Erscheint lt. Verlag | 13.1.2011 |
|---|---|
| Reihe/Serie | Advances in Design and Control |
| Verlagsort | New York |
| Sprache | englisch |
| Maße | 183 x 260 mm |
| Gewicht | 1270 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| ISBN-10 | 0-89871-936-4 / 0898719364 |
| ISBN-13 | 978-0-89871-936-9 / 9780898719369 |
| Zustand | Neuware |
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