  The finite-amplitude method (FAM) is one of the most promising methods for
optimizing the computational performance of the random-phase approximation
(RPA) calculations in deformed nuclei. In this report, we will mainly focus on
our recent progress in the self-consistent relativistic RPA established by
using the FAM. It is found that the effects of Dirac sea can be taken into
account implicitly in the coordinate-space representation and the rearrangement
terms due to the density-dependent couplings can be treated without extra
computational costs.
