The electron source in the University of Maryland Electron Ring (UMER) injector employs a grid 0.15 mm from the cathode to control the current waveform. Under nominal operating conditions, the grid voltage during the current pulse is sufficiently positive relative to the cathode potential to form a virtual cathode downstream of the grid. Three-dimensional computer simulations have been performed that use the mesh refinement capability of the WARP particle-in-cell code to examine a small region near the beam center in order to illustrate some of the complexity that can result from such a gridded structure. These simulations have been found to reproduce the hollowed velocity space that is observed experimentally. The simulations also predict a complicated time dependent response to the waveform applied to the grid during the current turn-on. This complex temporal behavior appears to result from the dynamics of the virtual cathode formation and may therefore be representative of the expected behavior in other sources, such as some photoinjectors, that are characterized by a rapid turnon of the beam current.