Accelerating $N$-body simulation of self-gravitating systems with
  limited first-order post-Newtonian approximation
  In this study, an $N$-body simulation code was developed for self-gravitating
systems with a limited first-order post-Newtonian approximation. The code was
applied to a special case in which the system consists of one massive object
and many low-mass objects. Therefore, the behavior of stars around the massive
black hole could be analyzed. A graphics processing unit (GPU) was used to
accelerate the code execution, and it could be accelerated by several tens of
times compared to a single-core CPU for $N \simeq 10^4$ objects.
