Domain Decomposition Methods in Optimal Control of Partial Differential Equation

Description: Domain Decomposition Methods in Optimal Control of Partial Differential Equations by John E. Lagnese, GÜnter Leugering This monograph considers problems of optimal control for partial differential equa tions of elliptic and, more importantly, of hyperbolic types on networked domains. FORMAT Paperback LANGUAGE English CONDITION Brand New Publisher Description 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. Table of Contents 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 Maxwells 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. Promotional Springer Book Archives Long Description This monograph considers problems of optimal control for partial differential equa Feature Emphasis 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 decompositions by an all-at-once approach Development of a general theory for systems of partial differential equations on multi-linked or networked domains Description for Sales People 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. This monograph considers problems of optimal control for partial differential equations 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. Details ISBN3034896107 Author GÜnter Leugering Language English Edition 04200th ISBN-10 3034896107 ISBN-13 9783034896108 Short Title DOMAIN DECOMPOSITION METHODS I Series International Series of Numerical Mathematics Media Book Series Number 148 Year 2012 Publication Date 2012-10-23 Country of Publication Switzerland Illustrations XIII, 443 p. Imprint Birkhauser Verlag AG Place of Publication Basel Pages 443 Publisher Birkhauser Verlag AG Edition Description Softcover reprint of the original 1st ed. 2004 Format Paperback Alternative 9783764321949 DEWEY 515.353 Audience Professional & Vocational We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:96339403;

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