  We recently proposed a new method to calculate the standard nuclear matrix
elements for neutrinoless double-$\beta$ decay ($0\nu\beta\beta$) of
${}^{48}$Ca going beyond the closure approximation. Here we extend this
analysis to the important case of ${}^{82}$Se, which was chosen as the base
isotope for the upcoming SuperNEMO experiment. We demonstrate that using a
mixed method that considers information from closure and non-closure
approaches, one can get excellent convergence properties for the nuclear matrix
elements, which allows one to avoid unmanageable computational costs. We show
that in contrast with the closure approximation the mixed approach has a very
weak dependence on the average closure energy. The matrix elements for the
heavy neutrino-exchange mechanism that could contribute to the $0\nu\beta\beta$
decay of ${}^{82}$Se are also presented.
