  We present domain decomposition finite element/finite difference method for
the solution of hyperbolic equation. The domain decomposition is performed such
that finite elements and finite differences are used in different subdomains of
the computational domain: finite difference method is used on the structured
part of the computational domain and finite elements on the unstructured part
of the domain. The main goal of this method is to combine flexibility of finite
element method and efficiency of a finite difference method.
  An explicit discretization schemes for both methods are constructed such that
finite element and finite difference schemes coincide on the common structured
overlapping layer between computational subdomains. Then the resulting scheme
can be considered as a pure finite element scheme which allows avoid
instabilities at the interfaces.
  We illustrate efficiency of the domain decomposition method on the
reconstruction of the conductivity function in the hyperbolic equation in three
dimensions.
