  A new code and methodology are introduced for solving the general
relativistic magnetohydrodynamic (GRMHD) equations in fixed background
spacetimes using time-explicit, finite-volume discretization. The code has
options for solving the GRMHD equations using traditional artificial-viscosity
(AV) or non-oscillatory central difference (NOCD) methods, or a new extended AV
(eAV) scheme using artificial-viscosity together with a dual
energy-flux-conserving formulation. The dual energy approach allows for
accurate modeling of highly relativistic flows at boost factors well beyond
what has been achieved to date by standard artificial viscosity methods. It
provides the benefit of Godunov methods in capturing high Lorentz boosted flows
but without complicated Riemann solvers, and the advantages of traditional
artificial viscosity methods in their speed and flexibility. Additionally, the
GRMHD equations are solved on an unstructured grid that supports local adaptive
mesh refinement using a fully threaded oct-tree (in three dimensions) network
to traverse the grid hierarchy across levels and immediate neighbors. A number
of tests are presented to demonstrate robustness of the numerical algorithms
and adaptive mesh framework over a wide spectrum of problems, boosts, and
astrophysical applications, including relativistic shock tubes, shock
collisions, magnetosonic shocks, Alfven wave propagation, blast waves,
magnetized Bondi flow, and the magneto-rotational instability in Kerr black
hole spacetimes.
