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Domain Decomposition Methods in Optimal Control of Partial Differential Equations

  • Book
  • © 2004

Overview

Authors:
  1. John E. Lagnese

    1. Department of Mathematics, Georgetown University, USA

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  2. Günter Leugering

    1. Angewandte Mathematik II, Universität Erlangen Nürnberg, Erlangen, Germany

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  • 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

Part of the book series: International Series of Numerical Mathematics (ISNM, volume 148)

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Introduction

    • John E. Lagnese, Günter Leugering
    Pages 1-7

  3. Background Material on Domain Decomposition

    • John E. Lagnese, Günter Leugering
    Pages 9-69

  4. Partial Differential Equations on Graphs

    • John E. Lagnese, Günter Leugering
    Pages 71-106

  5. Domain Decomposition for Elliptic Optimal Control Problems

    • John E. Lagnese, Günter Leugering
    Pages 107-129

  6. Optimal Control of One-Dimensional Partial Differential Equations on Graphs

    • John E. Lagnese, Günter Leugering
    Pages 131-157

  7. Domain Decomposition in Optimal Final Value Control of Dissipative Wave Equations

    • John E. Lagnese, Günter Leugering
    Pages 159-256

  8. Domain Decomposition in Optimal Final Value Boundary Control of Maxwell’s System

    • John E. Lagnese, Günter Leugering
    Pages 257-320

  9. Optimal Final Value Boundary Control of Conservative Wave Equations

    • John E. Lagnese, Günter Leugering
    Pages 321-374

  10. Domain Decomposition for Distributed Parameter Systems on 2-D Networks

    • John E. Lagnese, Günter Leugering
    Pages 375-433

  11. Back Matter

    Pages 435-446
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Keywords

About this book

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.

Authors and Affiliations

  • Department of Mathematics, Georgetown University, USA

    John E. Lagnese

  • Angewandte Mathematik II, Universität Erlangen Nürnberg, Erlangen, Germany

    Günter Leugering

Bibliographic Information

  • Book Title: Domain Decomposition Methods in Optimal Control of Partial Differential Equations

  • Authors: John E. Lagnese, Günter Leugering

  • Series Title: International Series of Numerical Mathematics

  • DOI: https://doi.org/10.1007/978-3-0348-7885-2

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Birkhäuser Basel 2004

  • Hardcover ISBN: 978-3-7643-2194-9Published: 27 September 2004

  • Softcover ISBN: 978-3-0348-9610-8Published: 23 October 2012

  • eBook ISBN: 978-3-0348-7885-2Published: 06 December 2012

  • Series ISSN: 0373-3149

  • Series E-ISSN: 2296-6072

  • Edition Number: 1

  • Number of Pages: XIII, 443

  • Topics: Calculus of Variations and Optimal Control; Optimization, Engineering, general

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