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An Introduction to the Topological Derivative Method
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.
Compressible Navier-Stokes Equations
The book presents the modern state of the art in the mathematical theory of compressible Navier-Stokes equations, with particular emphasis on the applications to aerodynamics. The topics covered include: modeling of compressible viscous flows; modern mathematical theory of nonhomogeneous boundary value problems for viscous gas dynamics equations; applications to optimal shape design in aerodynamics; kinetic theory for equations with oscillating data; new approach to the boundary value problems for transport equations. The monograph offers a comprehensive and self-contained introduction to recent mathematical tools designed to handle the problems arising in the theory.
Optimal Control
February 27 - March 1, 1997, the conference Optimal Control: The ory, Algorithms, and Applications took place at the University of Florida, hosted by the Center for Applied Optimization. The conference brought together researchers from universities, industry, and government laborato ries in the United States, Germany, Italy, France, Canada, and Sweden. There were forty-five invited talks, including seven talks by students. The conference was sponsored by the National Science Foundation and endorsed by the SIAM Activity Group on Control and Systems Theory, the Mathe matical Programming Society, the International Federation for Information Processing (IFIP), and the International Association f...
Topological Derivatives in Shape Optimization
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 evolu...
Differential Geometric Methods in the Control of Partial Differential Equations
This volume contains selected papers that were presented at the AMS-IMS-SIAM Joint Summer Research Conference on "Differential Geometric Methods in the Control of Partial Differential Equations", which was held at the University of Colorado in Boulder in June 1999. The aim of the conference was to explore the infusion of differential-geometric methods into the analysis of control theory of partial differential equations, particularly in the challenging case of variable coefficients, where the physical characteristics of the medium vary from point to point. While a mutually profitable link has been long established, for at least 30 years, between differential geometry and control of ordinary ...
Shapes and Geometries
Presents the latest groundbreaking theoretical foundation to shape optimization in a form accessible to mathematicians, scientists and engineers.
Modelling and Control in Solid Mechanics
This book covers the boundary value problems for a wide range of mathematical models of the mechanics of deformable bodies, in particular, the boundary value problems concerning plates and shells, crack theory, and elastoplastic bodies. An essential feature of the discussed boundary value problems is the availability of the inequality type constraints imposed on solutions such as the impenetration condition for contact problems, the yield plasticity condition, etc. As a consequence, the presence of free boundaries is typical of the boundary value problems concerned. The objective of the book is to display some new methods of analyzing such problems, as well as to perform research on new mode...
Introduction to Shape Optimization
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 giv...
Applications of the Topological Derivative Method
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.
The Towns of Death
The Towns of Death relies on witness reports from survivors, bystanders, and the murderers themselves as found in court testimonies to describe the pogroms of Jews in Eastern Poland in 1941–1942 perpetrated by their Polish neighbors. The author demonstrates the pivotal role of the Catholic clergy and individual priests, the intellectual classes, and political circles in perpetuating anti-Semitism, often leading to the murder of thousands of Polish Jews.
