Unconditionally Stable Higher Order Electromagnetic Particle-in-cell Method on Unstructured Meshes
Zane Crawford, Michigan State University
Many electromagnetic particle-in-cell (EM-PIC) implementations utilize the finite-difference time-domain (FDTD) method to calculate the electric and magnetic fields in the system. However, using the FDTD method places some unnecessary restrictions. The first is that the time-step size is limited by a Courant-Fredrich-Levy (CFL) condition, where the time-step size is far smaller than is needed to resolve the movement of the particles. Second, the FDTD method utilizes structured grids, which leads to staircasing errors in representing the geometry. Recently, the mixed finite element method (MFEM) has been used to calculate the fields in EM-PIC methods. In this method, Faraday's and Ampere's laws are coupled together and solved using Whitney basis functions. However, the method to couple the equations utilize the same time-stepping scheme that yields the CFL limit in previous EM-PIC methods. In this work, we build upon previous methods by introducing an unconditionally stable time-marching scheme with a higher-order mixed finite element method in three dimensions. These modifications increase the time step size permissible in the simulation, while the higher order basis functions minimize losses in accuracy.
Abstract Author(s): Zane Crawford, Scott O'Connor, John Verboncoeur, Shanker Balasubramaniam (B. Shanker)