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Shapes and Geometries: Metrics, Analysis, Differential Calculus, and Optimization, Second Edition

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by M. C. Delfour and J.-P. ZolŽésio


2011 / xvii + 622 / Hardcover / ISBN 978-0-898719-36-9 / List Price $127.00 / SIAM Member Price $88.90 / Order Code DC22

Keywords: shape, geometry, design, imaging, control

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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: Metrics, Analysis, Differential Calculus, and Optimization 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 endosprotheses in interventional cardiology.

This book is intended for applied mathematicians and advanced engineers and scientists, but the book is also structured as an initiation to shape analysis and calculus techniques for a broader audience of mathematicians. Some chapters are self-contained and can be used as lecture notes for a minicourse. The material at the beginning of each chapter is accessible to a broad audience, while the subsequent sections may sometimes require more mathematical maturity.

About the Authors
The authors are among the most advanced mathematicians in the field of shape optimization. They are vastly experienced in fields of applications at significant levels of depth in both engineering and science. Their unique combination of mathematical and applications knowledge makes this book of great importance to both the mathematics and applications communities.

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. He is the author or coauthor of 10 books and more than 165 journal and proceedings papers. He was president of the Canadian Mathematical Society from 1992 to 1994. He has served on numerous Canadian advisory boards and granting committees and on international panels and committees. He has been a Professional Engineer (P. Eng.) since 1966 and is actively involved in consulting for Canadian organizations. His areas of research are shape optimal design, the analysis and control of delay and distributed parameter systems, the control and stabilization of large flexible space structures, and numerical methods in differential equations and optimization. His recent interests include the modeling of thin and asymptotic shells, the design of endoprotheses in interventional cardiology, and the assignment of frequency spectrums to land mobile systems.

J.-P. Zolésio is Research Director in Mathematics at the CNRS. He is member of the Institut Non LinŽaire de Nice (INLN) associated with the Institut National de Recherche en Informatique et Automatique (INRIA) in Sophia Antipolis (France). In 1986 he became Research Director in the Laboratoire de Physique MathŽmatique of the CNRS (Montpellier) for his work on the plasma model of Grad. In 1990 he was invited by G. Loss to join the new INLN. He chairs the IFIP 7.2 working group, organized numerous international conferences on shape analysis for the IFIP and COMCON federations, and received the IFIP Silver Core in 1992. He was one of the founders of the e-Laboratory OpRaTel in collaboration with three French industrial partners in the area of radar and communications. He is the coauthor of four books on shape optimization and fluid structure interactions, 93 journal articles, and 121 chapters in edited books. His area of research is control and optimization through the geometrical domain of systems governed by partial differential equations. His recent interests include asymptotic geometry evolution with topological changes and applications to electromagnetics.

This second edition replaces Shapes and Geometries: Analysis, Differential Calculus, and Optimization (Order Code DC04, ISBN 978-0-898714-89-0), which is no longer available.

ISBN 978-0-898719-36-9

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