Shapes and Geometries

Metrics, Analysis, Differential Calculus, and Optimization

M. Delfour, J.-P. Zolésio (Autoren)

Buch | Hardcover

645 Seiten

2010 | Second Edition
Society for Industrial & Applied Mathematics,U.S. (Verlag)
978-0-89871-936-9 (ISBN)

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Presents the latest ground-breaking theoretical foundation to shape optimization in a form that can be 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.

This considerably enriched new edition provides a self-contained presentation of the mathematical foundations, constructions, and tools necessary for studying problems where the modeling, optimization, or control variable is the shape or the structure of a geometric object.

Shapes and Geometries presents the latest ground-breaking theoretical foundation to shape optimization in a form that can be 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. A series of generic examples has been added to the introduction and special emphasis has been put on the construction of important metrics.

Advanced engineers in various application areas use basic ideas of shape optimization, but often encounter difficulties due to the sophisticated mathematical foundations for the field. This new version of the book challenges these difficulties by showing how the mathematics community has made extraordinary progress in establishing a rational foundation for shape optimization. This area of research is very broad, rich, and fascinating from both theoretical and numerical standpoints. It is applicable in many different areas such as fluid mechanics, elasticity theory, modern theories of optimal design, free and moving boundary problems, shape and geometric identification, image processing, and design of endoprotheses in interventional cardiology.

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
Chapter 1: Introduction: Examples, Background, and Perspectives
Chapter 2: Classical Descriptions of Geometries and Their Properties
Chapter 3: Courant Metrics on Images of a Set
Chapter 4: Transformations Generated by Velocities
Chapter 5: Metrics via Characteristic Functions
Chapter 6: Metrics via Distance Functions
Chapter 7: Metrics via Oriented Distance Functions
Chapter 8: Shape Continuity and Optimization
Chapter 9: Shape and Tangential Differential Calculuses
Chapter 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	182 x 259 mm
Gewicht	1283 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
ISBN-10	0-89871-936-4 / 0898719364
ISBN-13	978-0-89871-936-9 / 9780898719369
Zustand	Neuware