H-AMR: A New GPU-accelerated GRMHD Code for Exascale Computing with 3D Adaptive Mesh Refinement and Local Adaptive Time Stepping

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