  We present the newly developed code, GAMER (GPU-accelerated Adaptive MEsh
Refinement code), which has adopted a novel approach to improve the performance
of adaptive mesh refinement (AMR) astrophysical simulations by a large factor
with the use of the graphic processing unit (GPU). The AMR implementation is
based on a hierarchy of grid patches with an oct-tree data structure. We adopt
a three-dimensional relaxing TVD scheme for the hydrodynamic solver, and a
multi-level relaxation scheme for the Poisson solver. Both solvers have been
implemented in GPU, by which hundreds of patches can be advanced in parallel.
The computational overhead associated with the data transfer between CPU and
GPU is carefully reduced by utilizing the capability of asynchronous memory
copies in GPU, and the computing time of the ghost-zone values for each patch
is made to diminish by overlapping it with the GPU computations. We demonstrate
the accuracy of the code by performing several standard test problems in
astrophysics. GAMER is a parallel code that can be run in a multi-GPU cluster
system. We measure the performance of the code by performing purely-baryonic
cosmological simulations in different hardware implementations, in which
detailed timing analyses provide comparison between the computations with and
without GPU(s) acceleration. Maximum speed-up factors of 12.19 and 10.47 are
demonstrated using 1 GPU with 4096^3 effective resolution and 16 GPUs with
8192^3 effective resolution, respectively.
