FUGUE: A New GPU-accelerated General Relativistic Magnetohydrodynamics Code with Weak-Field Multipole Self-Gravity and Quasi-Stationary Kerr Black Hole Evolution

We present FUGUE, a new GPU-accelerated code for general relativistic magnetohydrodynamics (GRMHD). The code supports an optional quasi-stationary update of the Kerr black hole mass and spin, as well as weak-field multipole self-gravity computed with a spherical harmonic Poisson solver. The calculations using high-order multipoles in the Poisson solver are expensive, so the self-gravity solver is well suited for GPU acceleration. The code uses shock-capturing methods and a second-order Runge--Kutta (RK2) scheme for time integration. We validate the code with hydrodynamic, magnetohydrodynamic, general relativistic, and convergence tests for the self-gravity module. We present an application of the code to a simulation of a self-gravitating, Toomre-unstable, magnetized accretion disk with a mass of 1,M-Sun around a Kerr black hole. In our demonstration model, gravitational instabilities are associated with changes in the mass accretion rate and the Blandford--Znajek luminosity, and may contribute to gamma-ray burst variability.The performance of the code is equivalent to or exceeds that of the current state-of-the-art GRMHD codes, achieving more than 470 million zone-cycles per second on a single NVIDIA GH200 GPU with linear reconstruction.