Optimization Of Elliptic Systems
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Optimization Of Elliptic Systems
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Author : Pekka Neittaanmaki
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-01-04
Optimization Of Elliptic Systems written by Pekka Neittaanmaki 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 2007-01-04 with Mathematics categories.
The present monograph is intended to provide a comprehensive and accessible introduction to the optimization of elliptic systems. This area of mathematical research, which has many important applications in science and technology. has experienced an impressive development during the past two decades. There are already many good textbooks dealing with various aspects of optimal design problems. In this regard, we refer to the works of Pironneau [1984], Haslinger and Neittaanmaki [1988], [1996], Sokolowski and Zolksio [1992], Litvinov [2000], Allaire [2001], Mohammadi and Pironneau [2001], Delfour and Zolksio [2001], and Makinen and Haslinger [2003]. Already Lions [I9681 devoted a major part of his classical monograph on the optimal control of partial differential equations to the optimization of elliptic systems. Let us also mention that even the very first known problem of the calculus of variations, the brachistochrone studied by Bernoulli back in 1696. is in fact a shape optimization problem. The natural richness of this mathematical research subject, as well as the extremely large field of possible applications, has created the unusual situation that although many important results and methods have already been est- lished, there are still pressing unsolved questions. In this monograph, we aim to address some of these open problems; as a consequence, there is only a minor overlap with the textbooks already existing in the field.
Optimal Shape Design For Elliptic Systems
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Author : O. Pironneau
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Optimal Shape Design For Elliptic Systems written by O. Pironneau 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 Science categories.
The study of optimal shape design can be arrived at by asking the following question: "What is the best shape for a physical system?" This book is an applications-oriented study of such physical systems; in particular, those which can be described by an elliptic partial differential equation and where the shape is found by the minimum of a single criterion function. There are many problems of this type in high-technology industries. In fact, most numerical simulations of physical systems are solved not to gain better understanding of the phenomena but to obtain better control and design. Problems of this type are described in Chapter 2. Traditionally, optimal shape design has been treated as a branch of the calculus of variations and more specifically of optimal control. This subject interfaces with no less than four fields: optimization, optimal control, partial differential equations (PDEs), and their numerical solutions-this is the most difficult aspect of the subject. Each of these fields is reviewed briefly: PDEs (Chapter 1), optimization (Chapter 4), optimal control (Chapter 5), and numerical methods (Chapters 1 and 4).
Optimal Shape Design For Elliptic Systems
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Author : Professor of Mathematics O Pironneau
language : en
Publisher:
Release Date : 1983-12-01
Optimal Shape Design For Elliptic Systems written by Professor of Mathematics O Pironneau and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983-12-01 with categories.
Optimization In Elliptic Problems With Applications To Mechanics Of Deformable Bodies And Fluid Mechanics
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Author : William G. Litvinov
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Optimization In Elliptic Problems With Applications To Mechanics Of Deformable Bodies And Fluid Mechanics written by William G. Litvinov and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Technology & Engineering categories.
This book is intended to be both a thorough introduction to contemporary research in optimization theory for elliptic systems with its numerous applications and a textbook at the undergraduate and graduate level for courses in pure or applied mathematics or in continuum mechanics. Various processes of modern technology and production are described by el liptic partial differential equations. Optimization of these processes reduces to op timization problems for elliptic systems. The numerical solution of such problems is associated with the solution of the following questions. 1. The setting of the optimization problem ensuring the existence of a solution on a set of admissible controls, which is a subset of some infinite-dimensional vector space. 2. Reduction of the infinite-dimensional optimization problem to a sequence of finite-dimensional problems such that the solutions of the finite-dimensional problems converge, in a sense, to the solution of the infinite-dimensional problem.3. Numerical solution of the finite-dimensional problems.
Analysis And Optimization Of Systems
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Author : A. Bensoussan
language : en
Publisher: Springer
Release Date : 2006-01-20
Analysis And Optimization Of Systems written by A. Bensoussan and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-20 with Technology & Engineering categories.
INRIA, Institut National de Recherche en Informatique et en Automatique
Optimal Control Of Partial Differential Equations
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Author : Karl-Heinz Hoffmann
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Optimal Control Of Partial Differential Equations written by Karl-Heinz Hoffmann and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The application of PDE-based control theory and the corresponding numerical algorithms to industrial problems have become increasingly important in recent years. This volume offers a wide spectrum of aspects of the discipline, and is of interest to mathematicians and scientists working in the field.
Optimization And Differentiation
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Author : Simon Serovajsky
language : en
Publisher: CRC Press
Release Date : 2017-09-13
Optimization And Differentiation written by Simon Serovajsky and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-13 with Mathematics categories.
Optimization and Differentiation is an introduction to the application of optimization control theory to systems described by nonlinear partial differential equations. As well as offering a useful reference work for researchers in these fields, it is also suitable for graduate students of optimal control theory.
Lectures On Elliptic Partial Differential Equations
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Author : Luigi Ambrosio
language : en
Publisher: Springer
Release Date : 2019-01-10
Lectures On Elliptic Partial Differential Equations written by Luigi Ambrosio and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-10 with Mathematics categories.
The book originates from the Elliptic PDE course given by the first author at the Scuola Normale Superiore in recent years. It covers the most classical aspects of the theory of Elliptic Partial Differential Equations and Calculus of Variations, including also more recent developments on partial regularity for systems and the theory of viscosity solutions.
The Finite Element Method For Elliptic Problems
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Author : P.G. Ciarlet
language : en
Publisher: Elsevier
Release Date : 1978-01-01
The Finite Element Method For Elliptic Problems written by P.G. Ciarlet and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978-01-01 with Mathematics categories.
The objective of this book is to analyze within reasonable limits (it is not a treatise) the basic mathematical aspects of the finite element method. The book should also serve as an introduction to current research on this subject. On the one hand, it is also intended to be a working textbook for advanced courses in Numerical Analysis, as typically taught in graduate courses in American and French universities. For example, it is the author's experience that a one-semester course (on a three-hour per week basis) can be taught from Chapters 1, 2 and 3 (with the exception of Section 3.3), while another one-semester course can be taught from Chapters 4 and 6. On the other hand, it is hoped that this book will prove to be useful for researchers interested in advanced aspects of the numerical analysis of the finite element method. In this respect, Section 3.3, Chapters 5, 7 and 8, and the sections on "Additional Bibliography and Comments should provide many suggestions for conducting seminars.
Optimization In Elliptic Problems With Applications To Mechanics Of Deformable Bodies And Fluid Mechanics
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Author : William G Litvinov
language : en
Publisher:
Release Date : 2000-04-01
Optimization In Elliptic Problems With Applications To Mechanics Of Deformable Bodies And Fluid Mechanics written by William G Litvinov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-04-01 with categories.