SIAM Conference on Control and its Applications, July 11-14, 2001, Town and Country Resort Hotel, San Diego, CA

Short Course: Shapes and Geometries: an Introduction

Half day short course: July 10, 2001, Town and Country Resort Hotel, San Diego, California

Organizer and Instructor:

Michel C. Delfour
University of Montreal


Advanced engineers in a number of applications domains have used basic ideas of shape optimization, but have often encountered difficulties due to the sophisticated mathematical foundations for the field. The mathematics community has made extraordinary progress in establishing a rational foundation for shape optimization during the past decades. This area of research has become very broad, rich and fascinating from the theoretical and numerical standpoints with a high potential for applications in many different areas such as fluid mechanics, elasticity theory, modern optimal design, free and moving boundary problems, optimal location and shape of geometric objects, and image processing.


This shortcourse aims at giving a very basic introduction to the foundations, constructions and tools to study 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. It is planned to use generic examples which will serve as motivation and illustration of some of the material contained in the forthcoming book.

M. Delfour and J. P. Zolesio, Shapes and Geometries: analysis, differential calculus and optimization, SIAM Publications, July 2001.

Level of Material

40% introductory; 40% intermediate; 20% advanced

Recommended Background

Familiarity with Partial Differential Equations, Optimization, and Finite Element Analysis.

Who Should Attend?

Scientists, engineers, program developers -- anyone interested in learning about shapes and geometries in the modelization, design or optimization of physical and technological systems.

About the Instructor

Michel C. Delfour is a Professor of Mathematics and Statistics at the University of Montreal, and a Fellow of the Royal Society of Canada. His areas of research are differential equations, control, optimization, and numerical methods. His recent interests include shape optimal design, modeling of thin and asymptotic shells, and problems in frequency spectrum assignments to land mobiles systems. He is the coauthor with Jean-Paul Zolésio of a recent book entitled "Shapes and Geometries: Analysis, Differential Calculus and Optimization" which should be available in July 2001 through SIAM. He has been a P. Eng. since 1966 and is still actively involved in consulting for Canadian organizations.

Short Course Program

I. Problem Formulations and Shape Calculus

II. Shape Gradient Under a State Equation Constraint: Min and Min-max Formulations

III. Relaxed Formulations of Free Boundary Problems


Seats are limited. Please register before the deadline. To register, please submit the Preregistration Form. Submit completed form with registration payment to reach SIAM on or before June 7, 2001. Registration fee includes coffee breaks and lunch on Sunday, July 10.

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