Applications Of The Topological Derivative Method

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Applications Of The Topological Derivative Method

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Author : Antonio André Novotny
language : en
Publisher: Springer
Release Date : 2018-12-28

Applications Of The Topological Derivative Method written by Antonio André Novotny and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-28 with Technology & Engineering categories.

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.

Topological Derivatives In Shape Optimization

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Author : Antonio André Novotny
language : en
Publisher: Springer
Release Date : 2012-12-14

Topological Derivatives In Shape Optimization written by Antonio André Novotny and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-14 with Technology & Engineering categories.

The topological derivative is defined as the first term (correction) of the asymptotic expansion of a given shape functional with respect to a small parameter that measures the size of singular domain perturbations, such as holes, inclusions, defects, source-terms and cracks. Over the last decade, topological asymptotic analysis has become a broad, rich and fascinating research area from both theoretical and numerical standpoints. It has applications in many different fields such as shape and topology optimization, inverse problems, imaging processing and mechanical modeling including synthesis and/or optimal design of microstructures, fracture mechanics sensitivity analysis and damage evolution modeling. Since there is no monograph on the subject at present, the authors provide here the first account of the theory which combines classical sensitivity analysis in shape optimization with asymptotic analysis by means of compound asymptotic expansions for elliptic boundary value problems. This book is intended for researchers and graduate students in applied mathematics and computational mechanics interested in any aspect of topological asymptotic analysis. In particular, it can be adopted as a textbook in advanced courses on the subject and shall be useful for readers interested on the mathematical aspects of topological asymptotic analysis as well as on applications of topological derivatives in computation mechanics.

An Introduction To The Topological Derivative Method

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Author : Antonio André Novotny
language : en
Publisher: Springer Nature
Release Date : 2020-01-21

An Introduction To The Topological Derivative Method written by Antonio André Novotny and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-21 with Mathematics categories.

This book presents the topological derivative method through selected examples, using a direct approach based on calculus of variations combined with compound asymptotic analysis. This new concept in shape optimization has applications in many different fields such as topology optimization, inverse problems, imaging processing, multi-scale material design and mechanical modeling including damage and fracture evolution phenomena. In particular, the topological derivative is used here in numerical methods of shape optimization, with applications in the context of compliance structural topology optimization and topology design of compliant mechanisms. Some exercises are offered at the end of each chapter, helping the reader to better understand the involved concepts.

Topology With Applications

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Author : Somashekhar A. Naimpally
language : en
Publisher: World Scientific
Release Date : 2013

Topology With Applications written by Somashekhar A. Naimpally and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Mathematics categories.

The principal aim of this book is to introduce topology and its many applications viewed within a framework that includes a consideration of compactness, completeness, continuity, filters, function spaces, grills, clusters and bunches, hyperspace topologies, initial and final structures, metric spaces, metrization, nets, proximal continuity, proximity spaces, separation axioms, and uniform spaces.This book provides a complete framework for the study of topology with a variety of applications in science and engineering that include camouflage filters, classification, digital image processing, forgery detection, Hausdorff raster spaces, image analysis, microscopy, paleontology, pattern recognition, population dynamics, stem cell biology, topological psychology, and visual merchandising.It is the first complete presentation on topology with applications considered in the context of proximity spaces, and the nearness and remoteness of sets of objects. A novel feature throughout this book is the use of near and far, discovered by F Riesz over 100 years ago. In addition, it is the first time that this form of topology is presented in the context of a number of new applications.

Computational Topology For Data Analysis

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Author : Tamal Krishna Dey
language : en
Publisher: Cambridge University Press
Release Date : 2022-03-10

Computational Topology For Data Analysis written by Tamal Krishna Dey and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-10 with Computers categories.

This book provides a computational and algorithmic foundation for techniques in topological data analysis, with examples and exercises.

Introduction To Shape Optimization

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Author : Jan Sokolowski
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Introduction To Shape Optimization written by Jan Sokolowski and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

This book is motivated largely by a desire to solve shape optimization prob lems that arise in applications, particularly in structural mechanics and in the optimal control of distributed parameter systems. Many such problems can be formulated as the minimization of functionals defined over a class of admissible domains. Shape optimization is quite indispensable in the design and construction of industrial structures. For example, aircraft and spacecraft have to satisfy, at the same time, very strict criteria on mechanical performance while weighing as little as possible. The shape optimization problem for such a structure consists in finding a geometry of the structure which minimizes a given functional (e. g. such as the weight of the structure) and yet simultaneously satisfies specific constraints (like thickness, strain energy, or displacement bounds). The geometry of the structure can be considered as a given domain in the three-dimensional Euclidean space. The domain is an open, bounded set whose topology is given, e. g. it may be simply or doubly connected. The boundary is smooth or piecewise smooth, so boundary value problems that are defined in the domain and associated with the classical partial differential equations of mathematical physics are well posed. In general the cost functional takes the form of an integral over the domain or its boundary where the integrand depends smoothly on the solution of a boundary value problem.

Modern Methods In Topological Vector Spaces

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Author : Albert Wilansky
language : en
Publisher: Courier Corporation
Release Date : 2013-11-26

Modern Methods In Topological Vector Spaces written by Albert Wilansky and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-26 with Mathematics categories.

Geared toward beginning graduate students of mathematics, this text covers Banach space, open mapping and closed graph theorems, local convexity, duality, equicontinuity, operators, inductive limits, and compactness and barrelled spaces. 1978 edition.

Lagrange Multiplier Approach To Variational Problems And Applications

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Author : Kazufumi Ito
language : en
Publisher: SIAM
Release Date : 2008-01-01

Lagrange Multiplier Approach To Variational Problems And Applications written by Kazufumi Ito and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-01 with Mathematics categories.

Lagrange multiplier theory provides a tool for the analysis of a general class of nonlinear variational problems and is the basis for developing efficient and powerful iterative methods for solving these problems. This comprehensive monograph analyzes Lagrange multiplier theory and shows its impact on the development of numerical algorithms for problems posed in a function space setting. The authors develop and analyze efficient algorithms for constrained optimization and convex optimization problems based on the augumented Lagrangian concept and cover such topics as sensitivity analysis, convex optimization, second order methods, and shape sensitivity calculus. General theory is applied to challenging problems in optimal control of partial differential equations, image analysis, mechanical contact and friction problems, and American options for the Black-Scholes model.

Handbook Of Mathematical Methods In Imaging

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Author : Otmar Scherzer
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-11-23

Handbook Of Mathematical Methods In Imaging written by Otmar Scherzer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-23 with Mathematics categories.

The Handbook of Mathematical Methods in Imaging provides a comprehensive treatment of the mathematical techniques used in imaging science. The material is grouped into two central themes, namely, Inverse Problems (Algorithmic Reconstruction) and Signal and Image Processing. Each section within the themes covers applications (modeling), mathematics, numerical methods (using a case example) and open questions. Written by experts in the area, the presentation is mathematically rigorous. The entries are cross-referenced for easy navigation through connected topics. Available in both print and electronic forms, the handbook is enhanced by more than 150 illustrations and an extended bibliography. It will benefit students, scientists and researchers in applied mathematics. Engineers and computer scientists working in imaging will also find this handbook useful.

Shapes And Geometries

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Author : M. C. Delfour
language : en
Publisher: SIAM
Release Date : 2011-01-01

Shapes And Geometries written by M. C. Delfour and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-01-01 with Mathematics categories.

Presents the latest groundbreaking theoretical foundation to shape optimization in a form accessible to mathematicians, scientists and engineers.