Optimal Shape Design For Elliptic Systems

Author : O. Pironneau
Publisher : Springer Science & Business Media
Page : 179 pages
File Size : 51,8 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642877223

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Optimal Shape Design for Elliptic Systems by O. Pironneau Pdf

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).

Author : Professor of Mathematics O Pironneau
Publisher : Unknown
Page : 184 pages
File Size : 53,7 Mb
Release : 1983-12-01
Category : Electronic
ISBN : 3642877230

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Optimal Shape Design for Elliptic Systems by Professor of Mathematics O Pironneau Pdf

Author : Pekka Neittaanmaki,Jürgen Sprekels,Dan Tiba
Publisher : Springer Science & Business Media
Page : 514 pages
File Size : 49,6 Mb
Release : 2007-01-04
Category : Mathematics
ISBN : 9780387272368

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Optimization of Elliptic Systems by Pekka Neittaanmaki,Jürgen Sprekels,Dan Tiba Pdf

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.

Author : John Cagnol,Michael P. Polis,Jean-Paul Zolesio
Publisher : CRC Press
Page : 458 pages
File Size : 51,8 Mb
Release : 2017-08-02
Category : Mathematics
ISBN : 0203904168

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Shape Optimization And Optimal Design by John Cagnol,Michael P. Polis,Jean-Paul Zolesio Pdf

This volume presents developments and advances in modelling passive and active control systems governed by partial differential equations. It emphasizes shape analysis, optimal shape design, controllability, nonlinear boundary control, and stabilization. The authors include essential data on exact boundary controllability of thermoelastic plates with variable transmission coefficients.

Author : Martin P. Bendsoe
Publisher : Springer Science & Business Media
Page : 278 pages
File Size : 53,7 Mb
Release : 2013-03-14
Category : Technology & Engineering
ISBN : 9783662031155

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Optimization of Structural Topology, Shape, and Material by Martin P. Bendsoe Pdf

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.

Author : Il Han Park
Publisher : Springer
Page : 368 pages
File Size : 50,8 Mb
Release : 2018-08-27
Category : Technology & Engineering
ISBN : 9789811302305

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Design Sensitivity Analysis and Optimization of Electromagnetic Systems by Il Han Park Pdf

This book presents a comprehensive introduction to design sensitivity analysis theory as applied to electromagnetic systems. It treats the subject in a unified manner, providing numerical methods and design examples. The specific focus is on continuum design sensitivity analysis, which offers significant advantages over discrete design sensitivity methods. Continuum design sensitivity formulas are derived from the material derivative in continuum mechanics and the variational form of the governing equation. Continuum sensitivity analysis is applied to Maxwell equations of electrostatic, magnetostatic and eddy-current systems, and then the sensitivity formulas for each system are derived in a closed form; an integration along the design interface. The book also introduces the recent breakthrough of the topology optimization method, which is accomplished by coupling the level set method and continuum design sensitivity. This topology optimization method enhances the possibility of the global minimum with minimised computational time, and in addition the evolving shapes during the iterative design process are easily captured in the level set equation. Moreover, since the optimization algorithm is transformed into a well-known transient analysis algorithm for differential equations, its numerical implementation becomes very simple and convenient. Despite the complex derivation processes and mathematical expressions, the obtained sensitivity formulas are very straightforward for numerical implementation. This book provides detailed explanation of the background theory and the derivation process, which will help readers understand the design method and will set the foundation for advanced research in the future.

Author : Jan Sokolowski,Jean-Paul Zolesio
Publisher : Springer Science & Business Media
Page : 254 pages
File Size : 44,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642581069

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Introduction to Shape Optimization by Jan Sokolowski,Jean-Paul Zolesio Pdf

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.

Author : Bijan Mohammadi,Olivier Pironneau
Publisher : Oxford University Press
Page : 292 pages
File Size : 40,6 Mb
Release : 2010
Category : Mathematics
ISBN : 9780199546909

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Applied Shape Optimization for Fluids by Bijan Mohammadi,Olivier Pironneau Pdf

Contents: PREFACE; ACKNOWLEDGEMENTS; 1. Introduction; 2. Optimal shape design; 3. Partial differential equations for fluids; 4. Some numerical methods for fluids; 5. Sensitivity evaluation and automatic differentiation; 6. Parameterization and implementation issues; 7. Local and global optimization; 8. Incomplete sensitivities; 9. Consistent approximations and approximate gradients; 10. Numerical results on shape optimization; 11. Control of unsteady flows; 12. From airplane design to microfluidic; 13. Toplogical optimization for fluids; 14. Conclusion and perspectives; INDEX.

Author : R.P. Gilbert,Panagiotis D. Panagiotopoulos,Panos M. Pardalos
Publisher : Springer Science & Business Media
Page : 395 pages
File Size : 46,9 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461302872

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From Convexity to Nonconvexity by R.P. Gilbert,Panagiotis D. Panagiotopoulos,Panos M. Pardalos Pdf

This collection of papers is dedicated to the memory of Gaetano Fichera, a great mathematician and also a good friend to the editors. Regrettably it took an unusual amount of time to bring this collection out. This was primarily due to the fact that the main editor who had collected all of the materials, for this volume, P. D. Panagiotopoulos, died unexpectedly during the period when we were editing the manuscript. The other two editors in appreciation of Panagiotopoulos' contribution to this field, believe it is therefore fitting that this collection be dedicated to his memory also. The theme of the collection is centered around the seminal research of G. Fichera on the Signorini problem. Variants on this idea enter in different ways. For example, by bringing in friction the problem is no longer self-adjoint and the minimization formulation is not valid. A large portion of this collection is devoted to survey papers concerning hemivariational methods, with a main point of its application to nonsmooth mechanics. Hemivariational inequali ties, which are a generalization of variational inequalities, were pioneered by Panagiotopoulos. There are many applications of this theory to the study of non convex energy functionals occurring in many branches of mechanics. An area of concentration concerns contact problems, in particular, quasistatic and dynamic contact problems with friction and damage. Nonsmooth optimization methods which may be divided into the main groups of subgradient methods and bundle methods are also discussed in this collection.

Author : Paolo Di Barba
Publisher : Springer Science & Business Media
Page : 320 pages
File Size : 42,8 Mb
Release : 2009-12-03
Category : Technology & Engineering
ISBN : 9789048130801

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Multiobjective Shape Design in Electricity and Magnetism by Paolo Di Barba Pdf

Multiobjective Shape Design in Electricity and Magnetism is entirely focused on electric and magnetic field synthesis, with special emphasis on the optimal shape design of devices when conflicting objectives are to be fulfilled. Direct problems are solved by means of finite-element analysis, while evolutionary computing is used to solve multiobjective inverse problems. This approach, which is original, is coherently developed throughout the whole manuscript. The use of game theory, dynamic optimisation, and Bayesian imaging strengthens the originality of the book. Covering the development of multiobjective optimisation in the past ten years, Multiobjective Shape Design in Electricity and Magnetism is a concise, comprehensive and up-to-date introduction to this research field, which is growing in the community of electricity and magnetism. Theoretical issues are illustrated by practical examples. In particular, a test problem is solved by different methods so that, by comparison of results, advantages and limitations of the various methods are made clear.

Author : Jeff Borggaard,John Burkhardt,Max Gunzburger,Janet Peterson
Publisher : Springer Science & Business Media
Page : 298 pages
File Size : 47,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461208396

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Optimal Design and Control by Jeff Borggaard,John Burkhardt,Max Gunzburger,Janet Peterson Pdf

This volume is the proceedings of the Workshop on Optimal Design and Control that was held in Blacksburg, Virginia, April 8-9, 1994. The workshop was spon sored by the Air Force Office of Scientific Research through the Air Force Center for Optimal Design and Control (CODAC) at Virginia Tech. The workshop was a gathering of engineers and mathematicians actively in volved in innovative research in control and optimization, with emphasis placed on problems governed by partial differential equations. The interdisciplinary nature of the workshop and the wide range of subdisciplines represented by the partici pants enabled an exchange of valuable information and also led to significant dis cussions about multidisciplinary optimization issues. One of the goals of the work shop was to include laboratory, industrial, and academic researchers so that anal yses, algorithms, implementations, and applications could all be well-represented in the talks; this interdisciplinary nature is reflected in these proceedings. An overriding impression that can be gleaned from the papers in this volume is the complexity of problems addressed by not only those authors engaged in appli cations, but also by those engaged in algorithmic development and even mathemat ical analyses. Thus, in many instances, systematic approaches using fully nonlin ear constraint equations are routinely used to solve control and optimization prob lems, in some cases replacing ad-hoc or empirically based procedures.

Author : B. Kawohl,O. Pironneau,L. Tartar,J.-P. Zolesio
Publisher : Springer
Page : 397 pages
File Size : 42,6 Mb
Release : 2007-05-06
Category : Mathematics
ISBN : 9783540444862

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Optimal Shape Design by B. Kawohl,O. Pironneau,L. Tartar,J.-P. Zolesio Pdf

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.

Author : Max D. Gunzburger
Publisher : Springer Science & Business Media
Page : 387 pages
File Size : 40,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461225263

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Flow Control by Max D. Gunzburger Pdf

The articles in this volume cover recent work in the area of flow control from the point of view of both engineers and mathematicians. These writings are especially timely, as they coincide with the emergence of the role of mathematics and systematic engineering analysis in flow control and optimization. Recently this role has significantly expanded to the point where now sophisticated mathematical and computational tools are being increasingly applied to the control and optimization of fluid flows. These articles document some important work that has gone on to influence the practical, everyday design of flows; moreover, they represent the state of the art in the formulation, analysis, and computation of flow control problems. This volume will be of interest to both applied mathematicians and to engineers.

Author : J. Borggaard,John Burns,Scott Schreck
Publisher : Springer Science & Business Media
Page : 467 pages
File Size : 42,5 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9781461217800

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Computational Methods for Optimal Design and Control by J. Borggaard,John Burns,Scott Schreck Pdf

This volume contains the proceedings of the Second International Workshop on Optimal Design and Control, held in Arlington, Virginia, 30 September-3 Octo ber, 1997. The First Workshop was held in Blacksburg, Virginia in 1994. The proceedings of that meeting also appeared in the Birkhauser series on Progress in Systems and Control Theory and may be obtained through Birkhauser. These workshops were sponsored by the Air Force Office of Scientific Re search through the Center for Optimal Design and Control (CODAC) at Vrrginia Tech. The meetings provided a forum for the exchange of new ideas and were designed to bring together diverse viewpoints and to highlight new applications. The primary goal of the workshops was to assess the current status of research and to analyze future directions in optimization based design and control. The present volume contains the technical papers presented at the Second Workshop. More than 65 participants from 6 countries attended the meeting and contributed to its success. It has long been recognized that many modern optimal design problems are best viewed as variational and optimal control problems. Indeed, the famous problem of determining the body of revolution that produces a minimum drag nose shape in hypersonic How was first proposed by Newton in 1686. Optimal control approaches to design can provide theoretical and computational insight into these problems. This volume contains a number of papers which deal with computational aspects of optimal control.

Author : Dietmar Hömberg,Fredi Tröltzsch
Publisher : Springer
Page : 580 pages
File Size : 52,9 Mb
Release : 2013-02-20
Category : Computers
ISBN : 9783642360626

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System Modeling and Optimization by Dietmar Hömberg,Fredi Tröltzsch Pdf

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.