Shape variation and optimization : a geometrical analysis / Antoine Henrot, Michel Pierre.

Format:

Book

Author/Creator:

Henrot, Antoine, 1957- author.

Pierre, Michel, 1949- author.

Contributor:

European Mathematical Society, issuing body.

Series:

EMS tracts in mathematics ; 28.

EMS Tracts in Mathematics ; 28

Standardized Title:

Variation et optimisation de formes. English

Language:

English

French

Subjects (All):

Manifolds (Mathematics).

Calculus of variations.

Mathematical optimization.

Minimal surfaces.

Physical Description:

xi, 365 pages : illustrations ; 25 cm.

Place of Publication:

Zürich, Switzerland : European Mathematical Society, [2018]

Summary:

Optimizing the shape of an object to make it the most efficient, resistant, streamlined, lightest, noiseless, stealthy or the cheapest is clearly a very old task. But the recent explosion of modeling and scientific computing have given this topic new life. Many new and interesting questions have been asked. A mathematical topic was born - shape optimization (or optimum design). This book provides a self-contained introduction to modern mathematical approaches to shape optimization, relying only on undergraduate level prerequisite but allowing to tackle open questions in this vibrant field. The analytical and geometrical tools and methods for the study of shapes are developed. In particular, the text presents a systematic treatment of shape variations and optimization associated with the Laplace operator and the classical capacity. Emphasis is also put on differentiation with respect to domains and a FAQ on the usual topologies of domains is provided. The book ends with geometrical properties of optimal shapes, including the case where they do not exist.

Notes:

"This book is essentially the English version of the one published in French by the same authors [188], except for some additions and updates. It originated from graduate courses given in past years at the Universities of Nancy, Besançon, and Rennes in France"--Page v.

Includes bibliographical references (pages 341-359) and indexes.

Other Format:

Online version: Henrot, Antoine, 1957- . Shape variation and optimization

ISBN:

9783037191781

3037191783

OCLC:

1028220247