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Applications of the Topological Derivative Method

  • Antonio André Novotny
  • Jan Sokołowski
  • Antoni Żochowski

Part of the Studies in Systems, Decision and Control book series (SSDC, volume 188)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Antonio André Novotny, Jan Sokołowski, Antoni Żochowski
    Pages 1-12
  3. Antonio André Novotny, Jan Sokołowski, Antoni Żochowski
    Pages 13-39
  4. Antonio André Novotny, Jan Sokołowski, Antoni Żochowski
    Pages 41-50
  5. Antonio André Novotny, Jan Sokołowski, Antoni Żochowski
    Pages 51-60
  6. Antonio André Novotny, Jan Sokołowski, Antoni Żochowski
    Pages 61-84
  7. Antonio André Novotny, Jan Sokołowski, Antoni Żochowski
    Pages 85-107
  8. Antonio André Novotny, Jan Sokołowski, Antoni Żochowski
    Pages 109-128
  9. Antonio André Novotny, Jan Sokołowski, Antoni Żochowski
    Pages 129-148
  10. Antonio André Novotny, Jan Sokołowski, Antoni Żochowski
    Pages 149-164
  11. Antonio André Novotny, Jan Sokołowski, Antoni Żochowski
    Pages 165-181
  12. Antonio André Novotny, Jan Sokołowski, Antoni Żochowski
    Pages 183-200
  13. Back Matter
    Pages 201-212

About this book

Introduction

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.

Keywords

Topological Derivative Method Singularly Perturbed Geometrical Domains Steklov-Poincare´ Operator for Helmholtz Equation Topological Derivatives for Optimal Control Problems Newton-Type Method and Applications

Authors and affiliations

  • Antonio André Novotny
    • 1
  • Jan Sokołowski
    • 2
  • Antoni Żochowski
    • 3
  1. 1.Coordenação de Métodos Matemáticos e ComputacionaisLaboratório Nacional de Computação Científica LNCC/MCTICPetrópolisBrazil
  2. 2.Institut Élie Cartan de Nancy, UMR 7502Université de Lorraine, CNRSVandœuvre-Lès-NancyFrance
  3. 3.Systems Research InstitutePolish Academy of SciencesWarsawPoland

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