Domain Decomposition Methods in Optimal Control of Partial Differential Equations

2004
ISBN: 978-3-7643-2194-9
Verlag: Springer

Buch, Englisch, Band 148, 443 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 857 g

Reihe: International Series of Numerical Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Leugering, Günter

Lagnese, John E.

Fachgebiete

• Mathematik | Informatik Mathematik Operations Research Spieltheorie
• Technische Wissenschaften Elektronik | Nachrichtentechnik Elektronik Überwachungstechnik

Inhaltsverzeichnis

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.