Shapes and Geometries
Shapes and Geometries
Analysis, Differential Calculus, and Optimization
No date available
Hardback
9780898714890
Hardback
This book provides a self-contained presentation of the mathematical foundations, constructions, and tools necessary for studying 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. Shapes and Geometries: Analysis, Differential Calculus, and Optimization presents the extensive, recently developed theoretical foundation to shape optimization in a form that can be used by the engineering community. 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.
Product details
No date availableHardback
9780898714890
499 pages
260 × 182 × 27 mm
1.085kg
Table of Contents
- List of Figures
- Preface
- 1. Introduction
- 2. Classical Descriptions and Properties of Domains
- 3. Relaxation to Measurable Domains
- 4. Topologies Generated by Distance Functions
- 5. Oriented Distance Function and Smoothness of Sets
- 6. Optimization of Shape Functions
- 7. Transformations versus Flows of Velocities
- 8. Shape Derivatives and Calculus, and Tangential Differential Calculus
- 9. Shape Gradients under a State Equation Constraint
- Elements of Bibliography
- Index of Notation
- Index.
