  We report Monte Carlo simulations of critical dynamics far from equilibrium
on a perfect and non-perfect surface in the 3d Ising model. For an ordered
initial state, the dynamic relaxation of the surface magnetization, the line
magnetization of the defect line, and the corresponding susceptibilities and
appropriate cumulant is carefully examined at the ordinary, special and surface
phase transitions. The universal dynamic scaling behavior including a dynamic
crossover scaling form is identified. The exponent $\beta_1$ of the surface
magnetization and $\beta_2$ of the line magnetization are extracted. The impact
of the defect line on the surface universality classes is investigated.
