Two basic challenges limiting the simulation capabilities of the streamer discharge community are the efficient resolution of Poisson's equation and the proper treatment of photoionization. This paper addresses both of these challenges, beginning with a graphics processing unit executed multigrid (MG) algorithm to efficiently solve Poisson's equation on a massively parallel platform. When utilized in a 3D particle-in-cell (PIC) model with radiation transport, the MG solver is demonstrated to reduce the required simulation time by approximately a factor of three over a conventional Jacobi scheme. Next, a fully theoretical photoionization model, based on the basic properties of N 2 and O 2 molecules is developed as an alternative to widely utilized semi-empirical models. Following a review of N 2 emission properties, a total of eight transitions from only three excited states are reported as a base set of transitions for a practical physics-based photoionization model. A 3D PIC simulation of streamer formation is demonstrated with two dominant transitions included in the radiation transport model.