A hybrid finite element-finite difference electromagnetic particle-in-cell simulation framework

Summary form only given. Electromagnetic particle-in-cell (EM-PIC) numerical simulation frameworks are often based upon the finite-difference (FD) method. Although computationally efficient and easily implemented, their accurate treatment of curved or slanted boundaries is limited to the staircase approximation, which results in both an inaccurate electromagnetic field solution and particle behavior. Finite volume, finite element (FE), and Discontinuous Galerkin EM-PIC schemes have all been developed in attempts to overcome this limitation. While such methods promise better accuracy in the presence of curved boundaries, their corresponding meshes can be denser than their FD counterparts, and their codes more complex. As a result, the total number of system unknowns, computation time, and production time can be much greater. In order to simultaneously maintain both accuracy and numerical efficiency regardless of system geometry, we propose a hybrid (FE-FD) EM-PIC framework. Electromagnetic fields are updated using the FE method near curved or slanted boundaries and via FD otherwise. Particles are tracked and their behavior updated within both regions. The resulting total number of system unknowns is less than that of a completely FE-based EM-PIC scheme, yet both electromagnetic fields and particle behavior remain accurate near irregular boundaries. Careful consideration is required when dealing with the interface separating the two solution regions in order to ensure accurate electromagnetic field propagation and efficient particle tracking.