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Field name	Details
Dewey Class	515.64
Title	Domain Decomposition Methods in Optimal Control of Partial Differential Equations ([EBook] /) / by John E. Lagnese, Günter Leugering.
Author	Lagnese, John E.
Added Personal Name	Leugering, Günter author.
Other name(s)	SpringerLink (Online service)
Publication	Basel : : Birkhäuser Basel : : Imprint: Birkhäuser, , 2004.
Physical Details	XIII, 443 p. : online resource.
Series	ISNM International Series of Numerical Mathematics ; 148
ISBN	9783034878852
Summary Note	This monograph considers problems of optimal control for partial differential equa tions of elliptic and, more importantly, of hyperbolic types on networked domains. The main goal is to describe, develop and analyze iterative space and time domain decompositions of such problems on the infinite-dimensional level. While domain decomposition methods have a long history dating back well over one hundred years, it is only during the last decade that they have become a major tool in numerical analysis of partial differential equations. A keyword in this context is parallelism. This development is perhaps best illustrated by the fact that we just encountered the 15th annual conference precisely on this topic. Without attempting to provide a complete list of introductory references let us just mention the monograph by Quarteroni and Valli [91] as a general up-to-date reference on domain decomposition methods for partial differential equations. The emphasis of this monograph is to put domain decomposition methods in the context of so-called virtual optimal control problems and, more importantly, to treat optimal control problems for partial differential equations and their decom positions by an all-at-once approach. This means that we are mainly interested in decomposition techniques which can be interpreted as virtual optimal control problems and which, together with the real control problem coming from an un derlying application, lead to a sequence of individual optimal control problems on the subdomains that are iteratively decoupled across the interfaces.:
Contents note	1 Introduction -- 2 Background Material on Domain Decomposition -- 2.1 Introduction -- 2.2 Domain Decomposition for 1-d Problems -- 2.3 Domain Decomposition Methods for Elliptic Problems -- 3 Partial Differential Equations on Graphs -- 3.1 Introduction -- 3.2 Partial Differential Operators on Graphs -- 3.3 Elliptic Problems on Graphs -- 3.4 Hyperbolic Problems on Graphs -- 4 Optimal Control of Elliptic Problems -- 4.1 Introduction -- 4.2 Distributed Controls -- 4.3 Boundary Controls -- 5 Control of Partial Differential Equations on Graphs -- 5.1 Introduction -- 5.2 Elliptic Problems -- 5.3 Hyperbolic Problems -- 6 Control of Dissipative Wave Equations -- 6.1 Introduction -- 6.2 Optimal Dissipative Boundary Control -- 6.3 Time Domain Decomposition -- 6.4 Decomposition of the Spatial Domain -- 6.5 Space and Time Domain Decomposition -- 7 Boundary Control of Maxwell’s System -- 7.1 Introduction -- 7.2 Optimal Dissipative Boundary Control -- 7.3 Time Domain Decomposition -- 7.4 Decomposition of the Spatial Domain -- 7.5 Time and Space Domain Decomposition -- 8 Control of Conservative Wave Equations -- 8.1 Introduction -- 8.2 Optimal Boundary Control -- 8.3 Time Domain Decomposition -- 8.4 Decomposition of the Spatial Domain -- 8.5 The Exact Reachability Problem -- 9 Domain Decomposition for 2-D Networks -- 9.1 Elliptic Systems on 2-D Networks -- 9.2 Optimal Control on 2-D Networks -- 9.3 Decomposition of the Spatial Domain.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-3-0348-7885-2
Links to Related Works	Subject References: Calculus of variations . Calculus of variations and optimal control; optimization . Engineering . Engineering, general . Mathematics . Authors: Lagnese, John E. . Leugering, Günter . Corporate Authors: SpringerLink (Online service) . Series: ISNM International Series of Numerical Mathematics . Classification: 515.64 .

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Domain Decomposition Methods in Optimal Control of Partial Differential Equations

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