  A new domain decomposition method for Maxwell's equations in conductive media
is presented. Using this method reconstruction algorithms are developed for
determination of dielectric permittivity function using time-dependent
scattered data of electric field. All reconstruction algorithms are based on
optimization approach to find stationary point of the Lagrangian. Adaptive
reconstruction algorithms and space mesh refinement indicators are also
presented. Our computational tests show qualitative reconstruction of
dielectric permittivity function using anatomically realistic breast phantom.
