Studies in Systems, Decision and Control

Applications of the Topological Derivative Method

Authors: Novotny, Antonio André, Sokołowski, Jan, Żochowski, Antoni

Free Preview
  • Presents new results and applications of the topological derivative method in control theory, topology optimization, and inverse problems
  • Introduces the theory of singularly perturbed geometrical domains using selected examples
  • Describes the first order topology design algorithm with its applications in topology optimization
  • Shares the second order Newton-type reconstruction algorithm of based on higher order topological derivatives for solving inverse reconstruction problems
see more benefits

Buy this book

eBook 106,99 €
price for Spain (gross)
  • ISBN 978-3-030-05432-8
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 135,19 €
price for Spain (gross)
  • ISBN 978-3-030-05431-1
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
About this book

The book presents new results and applications of the topological derivative method in control theory, topology optimization and inverse problems. It also introduces the theory in singularly perturbed geometrical domains using selected examples. Recognized as a robust numerical technique in engineering applications, such as topology optimization, inverse problems, imaging processing, multi-scale material design and mechanical modeling including damage and fracture evolution phenomena, the topological derivative method is based on the asymptotic approximations of solutions to elliptic boundary value problems combined with mathematical programming tools. The book presents the first order topology design algorithm and its applications in topology optimization, and introduces the second order Newton-type reconstruction algorithm based on higher order topological derivatives for solving inverse reconstruction problems. It is intended for researchers and students in applied mathematics and computational mechanics interested in the mathematical aspects of the topological derivative method as well as its applications in computational mechanics.

Reviews

“The book is well written, and the examples treated are carefully motivated. The references are up-to-date. The material presented in the book requires good mathematical background, so that the book could be used, as usefull reference, for researchers and graduate students that are working in the optimization theory.” (Teodor Atanacković, zbMATH 1460.74001, 2021)
“The book under review provides an excellent overview of historical and current developments in the field and, at the same time, is a very good introduction to readers familiar with linear elliptic equations and variational inequalities. … In all chapters, a thorough literature discussion is provided along with a detailed discussion of open problems.” (Guenter Leugering, Mathematical Reviews, October, 2019)

Table of contents (11 chapters)

Table of contents (11 chapters)

Buy this book

eBook 106,99 €
price for Spain (gross)
  • ISBN 978-3-030-05432-8
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 135,19 €
price for Spain (gross)
  • ISBN 978-3-030-05431-1
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
Loading...

Bibliographic Information

Bibliographic Information
Book Title
Applications of the Topological Derivative Method
Authors
Series Title
Studies in Systems, Decision and Control
Series Volume
188
Copyright
2019
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-05432-8
DOI
10.1007/978-3-030-05432-8
Hardcover ISBN
978-3-030-05431-1
Series ISSN
2198-4182
Edition Number
1
Number of Pages
XIV, 212
Number of Illustrations
53 b/w illustrations, 9 illustrations in colour
Topics