Overview

Many things have properties that depend on their shape, such as the drag characteristics of a rigid body in a flow. This self-contained overview of differential geometry explains how to differentiate a function with respect to a 'shape variable'. This approach, useful for understanding mathematical models containing geometric PDEs, allows readers to obtain formulas for geometric quantities (such as curvature) that are clearer than those usually offered in differential geometry texts. Readers will learn how to compute geometric sensitivities by developing basic calculus on surfaces alongside calculus of variations, aided by plenty of applications and illustrations. This book, a convenient reference for various shape derivative formulas, will be valuable to anyone interested in surface geometry and shape optimization. Graduate students can use it to quickly get acquainted with shape differentiation while scientists will find the book helpful for problems where surface geometry is critical or geometry evolves in time.

Full Product Details

Author:   Shawn W. Walker (Louisiana State University)
Publisher:   Society for Industrial & Applied Mathematics,U.S.
Imprint:   Society for Industrial & Applied Mathematics,U.S.
Volume:   28
Dimensions:   Width: 18.00cm , Height: 1.20cm , Length: 25.50cm
Weight:   0.360kg
ISBN:  

9781611973952

ISBN 10:   1611973953
Pages:   162
Publication Date:   17 December 2015
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

Preface; 1. Introduction; 2. Surfaces and differential geometry; 3. The fundamental forms of differential geometry; 4. Calculus on surfaces; 5. Shape differential calculus; 6. Applications; 7. Willmore flow; Appendix A. Vectors and matrices; Appendix B. Derivatives and integrals; Bibliography; Index.

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Author Information

Shawn Walker is an assistant professor of mathematics at Louisiana State University (LSU), with a joint appointment in the Center for Computation and Technology (CCT). He held a postdoctoral position at the Courant Institute (New York University) and joined the LSU faculty in 2010 in the computational mathematics group. He is a member of SIAM, AMS, MRS, and APS. His research interests include PDEs for fluids and moving/free boundaries, geometric evolution problems, numerical analysis and finite element methods, mesh generation, and optimal PDE control of shape.

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