An ongoing challenge in computational electromagnetics is correctly representing active sources in simulations. The particle-in-cell method in particular has been used to examine plasma-related phenomena using a number of different discretizations. Commonly, the finite-difference time-domain (FDTD) method is used to find the electromagnetic fields due to a system with some charged media and find the movement of the particles due to those fields. The FDTD method efficiently solves plasma-related problems defined on simple geometries. However, it poses limitations on the representation of more complex geometries and the order of the fields. For this reason, alternative techniques, such as the finite element method, have been proposed to evolve the system.
The finite element method has been shown to be an effective tool to solve electromagnetic problems. Conditionally stable and unconditionally stable formulations exist using basis functions of mixed order to represent the fields and sources. In this work, I will present a novel three-dimensional formulation for a finite element-based particle-in-cell code. The formulation utilizes different spaces to represent the fields and sources that remain consistent with the de Rahm complex. A detailed discussion will examine the noise characteristics and charge conservation of the method.
