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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.
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.
Gegenstand der Algorithmischen Mathematik ist die Konstruktion und
Analyse effizienter Algorithmen zur Loesung mathematischer
Problemstellungen mit Hilfe des Computers. Sie ist damit im Bereich
der Angewandten Mathematik anzusiedeln.Ziel dieses Lehrbuchs ist
es, Studierenden der Mathematik einen Einblick in unterschiedliche
Gebiete der Angewandten Mathematik und in deren algorithmische
Aspekte zu geben. Hierbei liegt das Hauptaugenmerk auf
Graphentheorie, Numerik und Wahrscheinlichkeitstheorie. Die
einschlagige Lehrbuchliteratur befasst sich zumeist jeweils nur mit
einem dieser Gebiete. Im Gegensatz dazu bemuht sich dieses Buch um
eine ganzheitliche Darstellung von Graphentheorie, Numerik und
Wahrscheinlichkeitstheorie und arbeitet so ihre Gemeinsamkeiten und
ihr Zusammenspiel heraus. Gerade die Verschmelzung der
unterschiedlichen Gebiete der Angewandten Mathematik gehoert zu
einer modernen Ausbildung der Mathematik, denn es ist heutzutage
unerlasslich, dass ein Numeriker ein grundlegendes Wissen uber
diskrete Algorithmen besitzt oder ein Stochastiker etwas von
numerischer Simulation versteht. Dieses Buch eignet sich fur
Studierende, aber auch fur alle, die ihr Wissen in Algorithmischer
Mathematik auffrischen oder vertiefen wollen.
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