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Titlebook: Optimal Shape Design for Elliptic Systems; Olivier Pironneau Book 1984 Springer-Verlag New York Inc. 1984 Design.Diskretisation.Elliptisch

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发表于 2025-3-21 18:15:25 | 显示全部楼层 |阅读模式
书目名称Optimal Shape Design for Elliptic Systems
编辑Olivier Pironneau
视频video
丛书名称Scientific Computation
图书封面Titlebook: Optimal Shape Design for Elliptic Systems;  Olivier Pironneau Book 1984 Springer-Verlag New York Inc. 1984 Design.Diskretisation.Elliptisch
描述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).
出版日期Book 1984
关键词Design; Diskretisation; Elliptische Differentialgleichung; Konstruktion; Optimale Regelung; boundary elem
版次1
doihttps://doi.org/10.1007/978-3-642-87722-3
isbn_softcover978-3-642-87724-7
isbn_ebook978-3-642-87722-3Series ISSN 1434-8322 Series E-ISSN 2198-2589
issn_series 1434-8322
copyrightSpringer-Verlag New York Inc. 1984
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发表于 2025-3-21 20:51:27 | 显示全部楼层
Design Problems Solved by Standard Optimal Control Theory,This approach ought to be well understood before proceeding to the general case where the control is looked at as a geometric element of the system. For further details and examples, the reader is referred to [40].
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Book 1984applications-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
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发表于 2025-3-22 16:42:11 | 显示全部楼层
Design Problems Solved by Standard Optimal Control Theory,], [29])..We give three examples of this type and use these examples as an opportunity to review the techniques of optimal control developed in [40]. This approach ought to be well understood before proceeding to the general case where the control is looked at as a geometric element of the system. F
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Optimality Conditions,ms may be developed to find feasible numerical solutions. Although it is sufficient to know how to derive such conditions on discrete problems only, it is useful to begin with the study of the continuous case since it is simpler and it may give a valuable interpretation to the solution.
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Discretization with Finite Elements,rential equations, the finite element method (FEM) is the obvious one to choose to use when the domains are the unknowns. We see that the FEM yields much simpler gradients than either the finite difference method or the boundary element method; these two methods are presented in Chapter 8. The FEM i
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