Shape Variation and Optimization
A Geometrical Analysis
Seiten
2018
EMS Press (Verlag)
978-3-03719-178-1 (ISBN)
EMS Press (Verlag)
978-3-03719-178-1 (ISBN)
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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.
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.
| Erscheinungsdatum | 28.02.2018 |
|---|---|
| Reihe/Serie | EMS Tracts in Mathematics ; 28 |
| Sprache | englisch |
| Maße | 170 x 240 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Schlagworte | Calculus of Variations • continuity with respect to domains • Gamma convergence • geometry of optimal shapes • Hausdorff convergence • homogenization • Isoperimetric inequality • Laplace-Dirichlet problem • Neumann problem • Optimum Design • overdetermined problems • Potential Theory • shape derivative • shape optimization • variations of domains |
| ISBN-10 | 3-03719-178-3 / 3037191783 |
| ISBN-13 | 978-3-03719-178-1 / 9783037191781 |
| Zustand | Neuware |
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