Advertisement

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

  • John E. Lagnese
  • Günter Leugering
Chapter
Part of the ISNM International Series of Numerical Mathematics book series (ISNM, volume 148)

Abstract

This chapter is concerned with domain decomposition in optimal final value control of the heterogeneous Maxwell system
$$ \begin{gathered} \varepsilon E' - rot H + \sigma E = F, \hfill \\ \mu H' + rot E = G in \mathcal{Q}: = \Omega \times (0,T) \hfill \\ H_\tau - \alpha (\nu \wedge E) = J on \Sigma : = \Gamma \times (0,T) \hfill \\ E(0) = E_0 , H(0) = H_0 in \Omega \hfill \\ \end{gathered} $$
(7.1.1.1)
where ′ = ∂/∂t, ⋀ denotes the vector product operation, v denotes the exterior pointing unit normal vector to Γ andHτis the tangential component ofHthat is,
$$ H_\tau = H - (H \cdot \nu )\nu = \nu \wedge (H \wedge \nu ). $$

Keywords

Optimal Control Problem Spatial Domain Optimality System Domain Decomposition Boundary Control 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Basel AG 2004

Authors and Affiliations

  • John E. Lagnese
    • 1
  • Günter Leugering
    • 2
  1. 1.Department of MathematicsGeorgetown UniversityUSA
  2. 2.Angewandte Mathematik IIUniversität Erlangen NürnbergErlangenGermany

Personalised recommendations