  We investigate the nonequilibrium coarsening dynamics in two-dimensional
overdamped superconducting arrays under zero external current, where ohmic
dissipation occurs on junctions between superconducting islands through uniform
resistance. The nonequilibrium relaxation of the unfrustrated array and also of
the fully frustrated array, quenched to low temperature ordered states or
quasi-ordered ones, is dominated by characteristic features of coarsening
processes via decay of point and line defects, respectively. In the case of
unfrustrated arrays, it is argued that due to finiteness of the friction
constant for a vortex (in the limit of large spatial extent of the vortex), the
typical length scale grows as $\ell_s \sim t^{1/2}$ accompanied by the number
of point vortices decaying as $N_v \sim 1/t $. This is in contrast with the
case that dominant dissipation occurs between each island and the substrate,
where the friction constant diverges logarithmically and the length scale
exhibits diffusive growth with a logarithmic correction term. We perform
extensive numerical simulations, to obtain results in reasonable agreement. In
the case of fully frustrated arrays, the domain growth of Ising-like chiral
order exhibits the low-temperature behavior $\ell_q \sim t^{1/z_q}$, with the
growth exponent $1/z_q$ apparently showing a strong temperature dependence in
the low-temperature limit.
