Particle-in-Cell approach is first-principle simulation method. The unabridged set of Maxwell equations for electromagnetic fields is solved together with motion equations for the relativistic particles. In addition, one might have to include inelastic processes, such as ionization, collisions, QED effects, etc.
Only massively parallel processing can provide enough computational power for full three dimensional simulations. We use our local Intel-cluster with 512 i7 cores and have access to super-computers.