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

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


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


Optimal Control Problem Spatial Domain Optimality System Domain Decomposition Boundary Control 
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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

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