Trends in PDE Constrained Optimization [electronic resource] / edited by Günter Leugering, Peter Benner, Sebastian Engell, Andreas Griewank, Helmut Harbrecht, Michael Hinze, Rolf Rannacher, Stefan Ulbrich.
Contributor(s): Leugering, Günter [editor.] | Benner, Peter [editor.] | Engell, Sebastian [editor.] | Griewank, Andreas [editor.] | Harbrecht, Helmut [editor.] | Hinze, Michael [editor.] | Rannacher, Rolf [editor.] | Ulbrich, Stefan [editor.] | SpringerLink (Online service)Material type: TextSeries: International Series of Numerical Mathematics: 165Publisher: Cham : Springer International Publishing : Imprint: Birkhäuser, 2014Description: XIV, 543 p. 119 illus., 76 illus. in color. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783319050836Subject(s): Mathematics | Partial differential equations | Computer mathematics | Mathematical optimization | Mathematics | Partial Differential Equations | Optimization | Computational Mathematics and Numerical AnalysisAdditional physical formats: Printed edition:: No titleDDC classification: 515.353 LOC classification: QA370-380Online resources: Click here to access online
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Introduction -- Part I: Constrained Optimization, Identification and Control -- Part II: Shape and Topology Optimization -- Part III: Adaptivity and Model Reduction -- Part IV: Discretization: Concepts and Analysis -- Part V: Applications.
Optimization problems subject to constraints governed by partial differential equations (PDEs) are among the most challenging problems in the context of industrial, economical and medical applications. Almost the entire range of problems in this field of research was studied and further explored as part of the Deutsche Forschungsgemeinschaft (DFG) priority program 1253 on “Optimization with Partial Differential Equations” from 2006 to 2013. The investigations were motivated by the fascinating potential applications and challenging mathematical problems that arise in the field of PDE constrained optimization. New analytic and algorithmic paradigms have been developed, implemented and validated in the context of real-world applications. In this special volume, contributions from more than fifteen German universities combine the results of this interdisciplinary program with a focus on applied mathematics. The book is divided into five sections on “Constrained Optimization, Identification and Control”, “Shape and Topology Optimization”, “Adaptivity and Model Reduction”, “Discretization: Concepts and Analysis” and “Applications”. Peer-reviewed research articles present the most recent results in the field of PDE constrained optimization and control problems. Informative survey articles give an overview of topics that set sustainable trends for future research. This makes this special volume interesting not only for mathematicians, but also for engineers and for natural and medical scientists working on processes that can be modeled by PDEs.