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

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 andH_τis the tangential component ofHthat is,

$$ H_\tau = H - (H \cdot \nu )\nu = \nu \wedge (H \wedge \nu ). $$