  Simulating accretion and feedback from the horizon scale of supermassive
black holes (SMBHs) out to galactic scales is challenging because of the vast
range of scales involved. We describe and test a "multi-zone" technique which
is designed to tackle this difficult problem in 3D general relativistic
magnetohydrodynamic (GRMHD) simulations. We simulate accretion on a
non-spinning SMBH ($a_*=0$) using initial conditions from a large scale galaxy
simulation, and achieve steady state over 8 decades in radius. The density
scales with radius as $\rho \propto r^{-1}$ inside the Bondi radius $R_B$,
which is located at $R_B=2\times 10^5 \,r_g$ ($\approx 60\,{\rm pc}$ for M87)
where $r_g$ is the gravitational radius of the SMBH; the plasma-$\beta\sim$
unity, indicating an extended magnetically arrested state; the mass accretion
rate $\dot{M}$ is $\approx 1\%$ of the analytical Bondi accretion rate
$\dot{M}_B$; and there is continuous energy feedback out to $\approx 100R_B$
(or beyond $>\,{\rm kpc}$) at a rate $\approx 0.02 \dot{M}c^2$. Surprisingly,
any ordered rotation in the external medium does not survive as the magnetized
gas flows to smaller radii, and the final steady solution is very similar to
when the exterior has no rotation. Using the multi-zone method, we simulate
GRMHD accretion for a wide range of Bondi radii, $R_{\rm B} \sim 10^2 -
10^7\,r_{\rm g}$, and find that $\dot{M}/\dot{M}_B\approx (R_B/6\,
r_g)^{-0.5}$.
