The standard method to simulate collisionless plasma is known as the Particle-In-Cell (PIC). We have developed a parallel finite element PIC method for different important problems of charging in space, such as the electrostatic levitation of lunar dust and ion thrusters. To address a group of large scale plasma simulation problems, this research combines mathematical modeling, efficient parallelization, benchmark studies, mathematical analysis, and engineering applications into a hybrid system of research which will fully take advantage of the intensive computation as well as the inherent interaction among the mathematics and engineering problems.