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Variational Methods In Shape Optimization Problems
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Book Synopsis Variational Methods in Shape Optimization Problems by : Dorin Bucur
Download or read book Variational Methods in Shape Optimization Problems written by Dorin Bucur and published by Springer Science & Business Media. This book was released on 2006-09-13 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: Shape optimization problems are treated from the classical and modern perspectives Targets a broad audience of graduate students in pure and applied mathematics, as well as engineers requiring a solid mathematical basis for the solution of practical problems Requires only a standard knowledge in the calculus of variations, differential equations, and functional analysis Driven by several good examples and illustrations Poses some open questions.
Book Synopsis Shape Optimization Problems by : Hideyuki Azegami
Download or read book Shape Optimization Problems written by Hideyuki Azegami and published by Springer Nature. This book was released on 2020-09-30 with total page 662 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides theories on non-parametric shape optimization problems, systematically keeping in mind readers with an engineering background. Non-parametric shape optimization problems are defined as problems of finding the shapes of domains in which boundary value problems of partial differential equations are defined. In these problems, optimum shapes are obtained from an arbitrary form without any geometrical parameters previously assigned. In particular, problems in which the optimum shape is sought by making a hole in domain are called topology optimization problems. Moreover, a problem in which the optimum shape is obtained based on domain variation is referred to as a shape optimization problem of domain variation type, or a shape optimization problem in a limited sense. Software has been developed to solve these problems, and it is being used to seek practical optimum shapes. However, there are no books explaining such theories beginning with their foundations. The structure of the book is shown in the Preface. The theorems are built up using mathematical results. Therefore, a mathematical style is introduced, consisting of definitions and theorems to summarize the key points. This method of expression is advanced as provable facts are clearly shown. If something to be investigated is contained in the framework of mathematics, setting up a theory using theorems prepared by great mathematicians is thought to be an extremely effective approach. However, mathematics attempts to heighten the level of abstraction in order to understand many things in a unified fashion. This characteristic may baffle readers with an engineering background. Hence in this book, an attempt has been made to provide explanations in engineering terms, with examples from mechanics, after accurately denoting the provable facts using definitions and theorems.
Book Synopsis Variationl Methods in Some Shape Optimization Problems by : Dorin Bucur
Download or read book Variationl Methods in Some Shape Optimization Problems written by Dorin Bucur and published by . This book was released on 2002 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Variational Methods for Structural Optimization by : Andrej Cherkaev
Download or read book Variational Methods for Structural Optimization written by Andrej Cherkaev and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 561 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book bridges a gap between a rigorous mathematical approach to variational problems and the practical use of algorithms of structural optimization in engineering applications. The foundations of structural optimization are presented in sufficiently simple form as to make them available for practical use.
Book Synopsis Variational Methods in Optimization by : Donald R. Smith
Download or read book Variational Methods in Optimization written by Donald R. Smith and published by Courier Corporation. This book was released on 1998-01-01 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: Highly readable text elucidates applications of the chain rule of differentiation, integration by parts, parametric curves, line integrals, double integrals, and elementary differential equations. 1974 edition.
Book Synopsis Introduction to Shape Optimization by : Jan Sokolowski
Download or read book Introduction to Shape Optimization written by Jan Sokolowski and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Variational Analysis in Sobolev and BV Spaces by : Hedy Attouch
Download or read book Variational Analysis in Sobolev and BV Spaces written by Hedy Attouch and published by SIAM. This book was released on 2014-10-02 with total page 794 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is an excellent guide for anyone interested in variational analysis, optimization, and PDEs. It offers a detailed presentation of the most important tools in variational analysis as well as applications to problems in geometry, mechanics, elasticity, and computer vision. This second edition covers several new topics: new section on capacity theory and elements of potential theory now includes the concepts of quasi-open sets and quasi-continuity; increased number of examples in the areas of linearized elasticity system, obstacles problems, convection-diffusion, and semilinear equations; new section on mass transportation problems and the Kantorovich relaxed formulation of the Monge problem; new subsection on stochastic homogenization establishes the mathematical tools coming from ergodic theory; and an entirely new and comprehensive chapter (17) devoted to gradient flows and the dynamical approach to equilibria. The book is intended for Ph.D. students, researchers, and practitioners who want to approach the field of variational analysis in a systematic way.
Book Synopsis Shape Optimization by the Homogenization Method by : Gregoire Allaire
Download or read book Shape Optimization by the Homogenization Method written by Gregoire Allaire and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the theory and numerical developments of the homogenization method. It's main features are: a comprehensive presentation of homogenization theory; an introduction to the theory of two-phase composite materials; a detailed treatment of structural optimization by using homogenization; a complete discussion of the resulting numerical algorithms with many documented test problems. It will be of interest to researchers, engineers, and advanced graduate students in applied mathematics, mechanical engineering, and structural optimization.
Book Synopsis Variational and Non-variational Methods in Nonlinear Analysis and Boundary Value Problems by : Dumitru Motreanu
Download or read book Variational and Non-variational Methods in Nonlinear Analysis and Boundary Value Problems written by Dumitru Motreanu and published by Springer Science & Business Media. This book was released on 2003-05-31 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book reflects a significant part of authors' research activity dur ing the last ten years. The present monograph is constructed on the results obtained by the authors through their direct cooperation or due to the authors separately or in cooperation with other mathematicians. All these results fit in a unitary scheme giving the structure of this work. The book is mainly addressed to researchers and scholars in Pure and Applied Mathematics, Mechanics, Physics and Engineering. We are greatly indebted to Viorica Venera Motreanu for the careful reading of the manuscript and helpful comments on important issues. We are also grateful to our Editors of Kluwer Academic Publishers for their professional assistance. Our deepest thanks go to our numerous scientific collaborators and friends, whose work was so important for us. D. Motreanu and V. Radulescu IX Introduction The present monograph is based on original results obtained by the authors in the last decade. This book provides a comprehensive expo sition of some modern topics in nonlinear analysis with applications to the study of several classes of boundary value problems. Our framework includes multivalued elliptic problems with discontinuities, variational inequalities, hemivariational inequalities and evolution problems. The treatment relies on variational methods, monotonicity principles, topo logical arguments and optimization techniques. Excepting Sections 1 and 3 in Chapter 1 and Sections 1 and 3 in Chapter 2, the material is new in comparison with any other book, representing research topics where the authors contributed. The outline of our work is the following.
Book Synopsis Lagrange Multiplier Approach to Variational Problems and Applications by : Kazufumi Ito
Download or read book Lagrange Multiplier Approach to Variational Problems and Applications written by Kazufumi Ito and published by SIAM. This book was released on 2008-11-06 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analyses Lagrange multiplier theory and demonstrates its impact on the development of numerical algorithms for variational problems in function spaces.
Book Synopsis Convex Analysis and Variational Problems by : Ivar Ekeland
Download or read book Convex Analysis and Variational Problems written by Ivar Ekeland and published by SIAM. This book was released on 1999-12-01 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains different developments of infinite dimensional convex programming in the context of convex analysis, including duality, minmax and Lagrangians, and convexification of nonconvex optimization problems in the calculus of variations (infinite dimension). It also includes the theory of convex duality applied to partial differential equations; no other reference presents this in a systematic way. The minmax theorems contained in this book have many useful applications, in particular the robust control of partial differential equations in finite time horizon. First published in English in 1976, this SIAM Classics in Applied Mathematics edition contains the original text along with a new preface and some additional references.
Book Synopsis Variational Methods for the Numerical Solution of Nonlinear Elliptic Problem by : Roland Glowinski
Download or read book Variational Methods for the Numerical Solution of Nonlinear Elliptic Problem written by Roland Glowinski and published by SIAM. This book was released on 2015-11-04 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: Variational Methods for the Numerical Solution of Nonlinear Elliptic Problems?addresses computational methods that have proven efficient for the solution of a large variety of nonlinear elliptic problems. These methods can be applied to many problems in science and engineering, but this book focuses on their application to problems in continuum mechanics and physics. This book differs from others on the topic by presenting examples of the power and versatility of operator-splitting methods; providing a detailed introduction to alternating direction methods of multipliers and their applicability to the solution of nonlinear (possibly nonsmooth) problems from science and engineering; and showing that nonlinear least-squares methods, combined with operator-splitting and conjugate gradient algorithms, provide efficient tools for the solution of highly nonlinear problems. The book provides useful insights suitable for advanced graduate students, faculty, and researchers in applied and computational mathematics as well as research engineers, mathematical physicists, and systems engineers.
Book Synopsis Real-time PDE-constrained Optimization by : Lorenz T. Biegler
Download or read book Real-time PDE-constrained Optimization written by Lorenz T. Biegler and published by SIAM. This book was released on 2007-01-01 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many engineering and scientific problems in design, control, and parameter estimation can be formulated as optimization problems that are governed by partial differential equations (PDEs). The complexities of the PDEs--and the requirement for rapid solution--pose significant difficulties. A particularly challenging class of PDE-constrained optimization problems is characterized by the need for real-time solution, i.e., in time scales that are sufficiently rapid to support simulation-based decision making. Real-Time PDE-Constrained Optimization, the first book devoted to real-time optimization for systems governed by PDEs, focuses on new formulations, methods, and algorithms needed to facilitate real-time, PDE-constrained optimization. In addition to presenting state-of-the-art algorithms and formulations, the text illustrates these algorithms with a diverse set of applications that includes problems in the areas of aerodynamics, biology, fluid dynamics, medicine, chemical processes, homeland security, and structural dynamics. Audience: readers who have expertise in simulation and are interested in incorporating optimization into their simulations, who have expertise in numerical optimization and are interested in adapting optimization methods to the class of infinite-dimensional simulation problems, or who have worked in "offline" optimization contexts and are interested in moving to "online" optimization.
Author :Hedy Attouch Publisher :Society for Industrial and Applied Mathematics ISBN 13 :9780898716009 Total Pages :650 pages Book Rating :4.7/5 (16 download)
Book Synopsis Variational Analysis in Sobolev and BV Spaces by : Hedy Attouch
Download or read book Variational Analysis in Sobolev and BV Spaces written by Hedy Attouch and published by Society for Industrial and Applied Mathematics. This book was released on 1987-01-01 with total page 650 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained book is excellent for graduate-level courses devoted to variational analysis, optimization, and partial differential equations (PDEs). It provides readers with a complete guide to problems in these fields as well as a detailed presentation of the most important tools and methods of variational analysis. New trends in variational analysis are also presented, along with recent developments and applications in this area. It contains several applications to problems in geometry, mechanics, elasticity, and computer vision, along with a complete list of references. The book is divided into two parts. In Part I, classical Sobolev spaces are introduced and the reader is provided with the basic tools and methods of variational analysis and optimization in infinite dimensional spaces, with applications to classical PDE problems. In Part II, BV spaces are introduced and new trends in variational analysis are presented.
Book Synopsis Numerical Methods for Free Boundary Problems by : VEITTAANMÄKI
Download or read book Numerical Methods for Free Boundary Problems written by VEITTAANMÄKI and published by Birkhäuser. This book was released on 2013-11-22 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: About 80 participants from 16 countries attended the Conference on Numerical Methods for Free Boundary Problems, held at the University of Jyviiskylii, Finland, July 23-27, 1990. The main purpose of this conference was to provide up-to-date information on important directions of research in the field of free boundary problems and their numerical solutions. The contributions contained in this volume cover the lectures given in the conference. The invited lectures were given by H.W. Alt, V. Barbu, K-H. Hoffmann, H. Mittelmann and V. Rivkind. In his lecture H.W. Alt considered a mathematical model and existence theory for non-isothermal phase separations in binary systems. The lecture of V. Barbu was on the approximate solvability of the inverse one phase Stefan problem. K-H. Hoff mann gave an up-to-date survey of several directions in free boundary problems and listed several applications, but the material of his lecture is not included in this proceedings. H.D. Mittelmann handled the stability of thermo capillary convection in float-zone crystal growth. V. Rivkind considered numerical methods for solving coupled Navier-Stokes and Stefan equations. Besides of those invited lectures mentioned above there were 37 contributed papers presented. We shall briefly outline the topics of the contributed papers: Stefan like problems. Modelling, existence and uniqueness.
Book Synopsis Existence and Regularity Results for Some Shape Optimization Problems by : Bozhidar Velichkov
Download or read book Existence and Regularity Results for Some Shape Optimization Problems written by Bozhidar Velichkov and published by Springer. This book was released on 2015-03-21 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study the existence and regularity of optimal domains for functionals depending on the spectrum of the Dirichlet Laplacian or of more general Schrödinger operators. The domains are subject to perimeter and volume constraints; we also take into account the possible presence of geometric obstacles. We investigate the properties of the optimal sets and of the optimal state functions. In particular, we prove that the eigenfunctions are Lipschitz continuous up to the boundary and that the optimal sets subject to the perimeter constraint have regular free boundary. We also consider spectral optimization problems in non-Euclidean settings and optimization problems for potentials and measures, as well as multiphase and optimal partition problems.
Author :Balkrishna S. Annigeri Publisher :Springer Science & Business Media ISBN 13 :3642842380 Total Pages :596 pages Book Rating :4.6/5 (428 download)
Book Synopsis Boundary Element Methods in Engineering by : Balkrishna S. Annigeri
Download or read book Boundary Element Methods in Engineering written by Balkrishna S. Annigeri and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Boundary Element Method (BEM) has become established as an effective tool for the solutions of problems in engineering science. The salient features of the BEM have been well documented in the open literature and therefore will not be elaborated here. The BEM research has progressed rapidly, especially in the past decade and continues to evolve worldwide. This Symposium was organized to provide an international forum for presentation of current research in BEM for linear and nonlinear problems in solid and fluid mechanics and related areas. To this end, papers on the following topics were included: rotary wing aerodynamics, unsteady aerodynamics, design and optimization, elasticity, elasto dynamics and elastoplasticity, fracture mechanics, acoustics, diffusion and wave motion, thermal analysis, mathematical aspects and boundary/finite element coupled methods. A special session was devoted to parallel/vector supercomputing with emphasis on mas sive parallelism. This Symposium was sponsored by United Technologies Research Center (UTRC) , NASA Langley Research Center, and the International Association of Boundary Ele ment Methods (lAB EM) . We thank the UTRC management for their permission to host this Symposium. In particular, we thank Dr. Arthur S. Kesten and Mr. Robert E. Olson for their encouragement and support. We gratefully acknowledge the support of Dr. E. Carson Yates, Jr. of NASA Langley, Prof. Luigi Morino, Dr. Thomas A.
