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| Author | : Timo Männikkö |
| Publisher | : |
| Total Pages | : 19 |
| Release | : 1995 |
| Genre | : |
| ISBN | : 9789513405410 |
| Author | : J. Haslinger |
| Publisher | : SIAM |
| Total Pages | : 276 |
| Release | : 2003-01-01 |
| Genre | : Mathematics |
| ISBN | : 0898715369 |
Treats sizing and shape optimization in a comprehensive way, covering everything from mathematical theory through computational aspects to industrial applications.
| Author | : John Cagnol |
| Publisher | : CRC Press |
| Total Pages | : 451 |
| Release | : 2017-08-02 |
| Genre | : Mathematics |
| ISBN | : 0203904168 |
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 | : Volker Schulz |
| Publisher | : Springer |
| Total Pages | : 275 |
| Release | : 2018-09-05 |
| Genre | : Mathematics |
| ISBN | : 3319904698 |
The contributions in this volume give an insight into current research activities in Shape Optimization, Homogenization and Optimal Control performed in Africa, Germany and internationally. Seeds for collaboration can be found in the first four papers in the field of homogenization. Modelling and optimal control in partial differential equations is the topic of the next six papers, again mixed from Africa and Germany. Finally, new results in the field of shape optimization are discussed in the final international three papers. This workshop, held at the AIMS Center Senegal, March 13-16, 2017, has been supported by the Deutsche Forschungsgemeinschaft (DFG) and by the African Institute for Mathematical Sciences (AIMS) in Senegal, which is one of six centres of a pan-African network of centres of excellence for postgraduate education, research and outreach in mathematical sciences.
| Author | : J. Haslinger |
| Publisher | : |
| Total Pages | : 360 |
| Release | : 1988 |
| Genre | : Mathematics |
| ISBN | : |
A text devoted to the mathematical basis of optimal shape design, to finite element approximation and to numerical realization by applying optimization techniques. The aim is to computerize the design process, thus reducing the time needed to design or to improve an existing design.
| Author | : Roland Herzog |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 474 |
| Release | : 2022-03-07 |
| Genre | : Mathematics |
| ISBN | : 3110695987 |
This book highlights new developments in the wide and growing field of partial differential equations (PDE)-constrained optimization. Optimization problems where the dynamics evolve according to a system of PDEs arise in science, engineering, and economic applications and they can take the form of inverse problems, optimal control problems or optimal design problems. This book covers new theoretical, computational as well as implementation aspects for PDE-constrained optimization problems under uncertainty, in shape optimization, and in feedback control, and it illustrates the new developments on representative problems from a variety of applications.
| Author | : Günter Leugering |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 622 |
| Release | : 2012-01-03 |
| Genre | : Mathematics |
| ISBN | : 3034801335 |
This special volume focuses on optimization and control of processes governed by partial differential equations. The contributors are mostly participants of the DFG-priority program 1253: Optimization with PDE-constraints which is active since 2006. The book is organized in sections which cover almost the entire spectrum of modern research in this emerging field. Indeed, even though the field of optimal control and optimization for PDE-constrained problems has undergone a dramatic increase of interest during the last four decades, a full theory for nonlinear problems is still lacking. The contributions of this volume, some of which have the character of survey articles, therefore, aim at creating and developing further new ideas for optimization, control and corresponding numerical simulations of systems of possibly coupled nonlinear partial differential equations. The research conducted within this unique network of groups in more than fifteen German universities focuses on novel methods of optimization, control and identification for problems in infinite-dimensional spaces, shape and topology problems, model reduction and adaptivity, discretization concepts and important applications. Besides the theoretical interest, the most prominent question is about the effectiveness of model-based numerical optimization methods for PDEs versus a black-box approach that uses existing codes, often heuristic-based, for optimization.
| Author | : Hideyuki Azegami |
| Publisher | : Springer Nature |
| Total Pages | : 646 |
| Release | : 2020-09-30 |
| Genre | : Mathematics |
| ISBN | : 9811576181 |
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.
| Author | : Bijan Mohammadi |
| Publisher | : Oxford University Press |
| Total Pages | : 292 |
| Release | : 2010 |
| Genre | : Mathematics |
| ISBN | : 0199546908 |
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 | : Dorin Bucur |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 218 |
| Release | : 2006-09-13 |
| Genre | : Mathematics |
| ISBN | : 0817644032 |
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.
