  We prove an adiabatic decomposition formula of the zeta-determinant of the
Laplace type operator with respect to Dirichlet boundary condition. We allow
the non-invertible tangential operator. As a result, our adiabatic
decomposition formula involves the scattering matrix over the manifold with
cylindrical end. We also describe the adiabatic limit of the zeta-determinant
of the Dirichlet to Neumann operator, which plays the essential role of
Burghelea-Friedlander-Kappeler's Meyer-Vietoris type formula of the zeta
determinant.
