Optimal Shape Design For Elliptic Systems
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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.
Optimal Shape Design
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Author : B. Kawohl
language : en
Publisher: Springer
Release Date : 2007-05-06
Optimal Shape Design written by B. Kawohl and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-06 with Mathematics categories.
Optimal Shape Design is concerned with the optimization of some performance criterion dependent (besides the constraints of the problem) on the "shape" of some region. The main topics covered are: the optimal design of a geometrical object, for instance a wing, moving in a fluid; the optimal shape of a region (a harbor), given suitable constraints on the size of the entrance to the harbor, subject to incoming waves; the optimal design of some electrical device subject to constraints on the performance. The aim is to show that Optimal Shape Design, besides its interesting industrial applications, possesses nontrivial mathematical aspects. The main theoretical tools developed here are the homogenization method and domain variations in PDE. The style is mathematically rigorous, but specifically oriented towards applications, and it is intended for both pure and applied mathematicians. The reader is required to know classical PDE theory and basic functional analysis.
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.
Optimization Of Elliptic Systems
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Author : Pekka Neittaanmaki
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-12-08
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 2005-12-08 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.
Optimization Of Structural Topology Shape And Material
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Author : Martin P. Bendsoe
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Optimization Of Structural Topology Shape And Material written by Martin P. Bendsoe 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 2013-03-14 with Technology & Engineering categories.
In the past, the possibilities of structural optimization were restricted to an optimal choice of profiles and shape. Further improvement can be obtained by selecting appropriate advanced materials and by optimizing the topology, i.e. finding the best position and arrangement of structural elements within a construction. The optimization of structural topology permits the use of optimization algorithms at a very early stage of the design process. The method presented in this book has been developed by Martin Bendsoe in cooperation with other researchers and can be considered as one of the most effective approaches to the optimization of layout and material design.
System Modeling And Optimization
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Author : Dietmar Hömberg
language : en
Publisher: Springer
Release Date : 2013-02-20
System Modeling And Optimization written by Dietmar Hömberg and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-02-20 with Computers categories.
This book is a collection of thoroughly refereed papers presented at the 25th IFIP TC 7 Conference on System Modeling and Optimization, held in Dresden, Germany, in September 2011. The 55 revised papers were carefully selected from numerous submissions. They are organized in the following topical sections: control of distributed parameter systems; stochastic optimization and control; stabilization, feedback, and model predictive control; flow control; shape and structural optimization; and applications and control of lumped parameter systems.
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
Coupling Of Fluids Structures And Waves In Aeronautics
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Author : Noel G. Barton
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Coupling Of Fluids Structures And Waves In Aeronautics written by Noel G. Barton 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 Technology & Engineering categories.
This volume contains the proceedings of a workshop held in Melbourne, Australia, entitled "Coupling of Fluids, Structures and Waves in Aeronautics". The 22 papers deal with new computational methods for multi-disciplinary design in aeronautics. They are grouped into chapters on fluids, structures, electromagnetics, optimisation, mathematical methods and tools, and aircraft design. Several papers treat coupling of these themes in a multi-physics setting. Included is a 17-page report of a Round Table discussion entitled "Future Tools for Design and Manufacture of Innovative Products in the Aeronautics Industry", together with a summary of important themes and issues. This research promotes the advanced technologies necessary for continued development of efficient and environmentally sustainable transport systems.
Shapes And Geometries
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Author : Michel C. Delfour
language : en
Publisher: SIAM
Release Date : 2001-01-01
Shapes And Geometries written by Michel 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 2001-01-01 with Mathematics categories.
The tools to use for problems where the modeling, optimization, or control variable is the structure of a geometric object.