Oberwolfach Seminar: Shape Optimization

Date:

November 7th - 13th, 2004

Organizers:

M. Bendsoe, Lyngby

G. Buttazzo, Pisa

A. Henrot, Nancy

Program:

The search of efficient shapes for several problems coming from various kinds of applications has become more and more important in the recent years, the ultimate goal being the identification of the optimal shape for a given cost function. The range of applications is very wide and goes from the design of an efficient insulating layer to the construction of damping devices for vibrating systems, from the shape optimization for elastic materials to the analysis of composite materials, crystal structures and porous media. Some classical problems can also be included into the shape optimization framework, as for instance the Newton's problem of the best aerodynamical shape.

The shape optimization problems will be presented as standard optimization problems, where the unknown runs over a set (the class of admissible domains) that does not have any linear or convex structure. So, new methods are needed to study the existence of solutions and the related necessary conditions of optimality.

The Seminar is intended to give an introduction to the field of shape optimization through the presentation of several problems and of the necessary tools to treat them. The presentation will also include some numerical tools that have been developed recently.

The plan is to have 3 hours of lectures in the mornings, while the afternoons will be used to discuss topics of the morning session and to work on exercises. The planned topics are:

• Introduction to shape optimization and some classical problems
• Newton's best aerodynamical shape
• Optimal insulating layers
• Optimal Dirichlet regions
• Compliance optimization and mass transportation problems
• Rearrangements and symmetrizations
• The derivative with respect to the domain
• The moving plane method
• Hausdorff distance and its use for proving existence of minimizers
• Gamma-convergence and relaxation
• Design parametrization (interpolation schemes, composites,etc.)
• Sensitivity analysis (direct and adjoint methods)
• Algorithms (convex approximation schemes and other methods)
• Computational issues (checkerboards, filters)
• An outline of possible applications in industrial problems

Prerequisites:

The seminar is intended for Ph. D. students or post-docs that already know the basic tools of Functional Analysis.

Deadline for applications:

September 24, 2004

The seminars take place at the Mathematisches Forschungsinstitut Oberwolfach. The number of participants is restricted to 24. Applications including

• full name and address, including e-mail address
• present position, university
• name of supervisor of Ph.D. thesis
• a short summary of previous work and interest

should be sent as hard copy or by e-mail (.ps or .pdf file) to:

Prof. Dr. Gert-Martin Greuel
Universität Kaiserslautern
Fachbereich Mathematik
Erwin Schrödingerstr.
67663 Kaiserslautern, Germany
.