To describe such extreme astrophysical systems, proper physics needs to be taken into account. For example, general relativity is required to account for the extremely strong gravitational fields, relativistic magnetohydrodynamics is necessary to describe the dynamics of plasma. Since the corresponding equations are highly non-linear and fully coupled with each other, they cannot be described analytically. First-principles numerical simulation is probably the only possible way to accurately model the evolution of these extreme compact objects. To accurately model these astrophysical systems, I develop and implement large-scale high-performance computing general-relativistic simulation codes.