A new model is developed for three-dimensional global simulations of plasma flow in an entire subscale ion optics. This model explicitly includes apertures located near the edge of the grid surface and fully accounts for the effects of multiple ion beamlets and geometric asymmetry. This model is based on a new algorithm, the streamline hybrid-grid immersed-finite-element particle-in-cell. This algorithm is capable of achieving the same accuracy as an unstructured body-fit mesh-based particle-in-cell with a faster computational speed. Simulation results are presented to understand the plasma sheath upstream of the screen grid, direct impingement of beam ions, the crossover limit, the perveance limit, and the electron backstreaming onset. Nomenclature e = electron charge F = force vector I = current k = Boltzmann constant m = mass q = charge T = temperature t = time v = velocity vector x = position vector = IFE mesh stretching parameter 0 = electric permittivity of vacuum D = Debye length = charge density = electrostatic potential Subscripts a = accelerator grid b= beamlet cc = center-to-center e = electron g = gap between ion optics grids i = ion, or impingement s = screen grid w = grid wall 0 = upstream plasma condition 1 = downstream plasma condition