  General-relativistic magnetohydrodynamic (GRMHD) simulations have
revolutionized our understanding of black hole accretion. Here, we present a
graphics processing unit (GPU) accelerated GRMHD code \hammer{} with
multi-faceted optimizations that, collectively, accelerate computation by 2-5
orders of magnitude for a wide range of applications. Firstly, it introduces a
spherical grid with 3D adaptive mesh refinement that operates in each of the 3
dimensions independently. This allows us to circumvent the Courant condition
near the polar singularity, which otherwise cripples high-resolution
computational performance. Secondly, we demonstrate that local adaptive
time-stepping (LAT) on a logarithmic spherical-polar grid accelerates
computation by a factor of $\lesssim10$ compared to traditional hierarchical
time-stepping approaches. Jointly, these unique features lead to an effective
speed of $\sim10^9$ zone-cycles-per-second-per-node on 5,400 NVIDIA V100 GPUs
(i.e., 900 nodes of the OLCF Summit supercomputer). We illustrate \hammer{}'s
computational performance by presenting the first GRMHD simulation of a tilted
thin accretion disk threaded by a toroidal magnetic field around a rapidly
spinning black hole. With an effective resolution of
$13$,$440\times4$,$608\times8$,$092$ cells, and a total of $\lesssim22$ billion
cells and $\sim0.65\times10^8$ timesteps, it is among the largest astrophysical
simulations ever performed. We find that frame-dragging by the black hole tears
up the disk into two independently precessing sub-disks. The innermost sub-disk
rotation axis intermittently aligns with the black hole spin, demonstrating for
the first time that such long-sought alignment is possible in the absence of
large-scale poloidal magnetic fields.
