The simulation of systems involving charged particles moving in the presence of electromagnetic fields is of great interest in a number of domains in physics, with applications including the characterization of pulsed power devices and accelerators, design of high precision etching and sterilization implements.As a result, several methods have been proposed to accurately simulate such systems. One such method is the particle-in-cell (PIC) technique, which characterizes the distribution of a plasma in phase space through a collection of statistically significant macroparticles. While contemporary implementations of electromagnetic PIC (EM-PIC) have typically relied on a finite-difference time-domain (FDTD) stencil to evaluate the fields, there has been a push for the adoption finite element methods that allow for the use of better geometry representations and more robust function spaces. In particular, recent developments in the field have focused on developing implicit finite element solvers that are free of mesh dependent stability constraints while natively conserving fundamental quantities such as charge and energy.The goals of this dissertation are to develop efficient, charge-conserving, implicit finite element particle-in-cell (EM-FEMPIC) methods. First, (i) we construct a formulation of PIC built around expontential predictor-corrector particle integrators. We demonstrate that this approach has significantly better error convergence than equivalent polynomial methods, thus allowing for accurate evaluation of particle trajectories even at the large step-sizes afforded by implicit EM solvers. Next, (ii) for devices of a narrowband tendency, we construct a novel EM-FEMPIC method based on envelope tracking. This allows us to accurately simulate the EM response of such a device while sampling at the narrow bandwidth, rather than at the highest absolute frequency of interest. Furthermore, we explore the consequences on charge-conservation for such a method and propose a rubric to ensure exact satisfaction of Gauss' laws. We then consider (iii) the matter of energy conservation in an implicit EM-FEMPIC scheme and propose a set of guidelines that ensure the conservation of average energy over the course of a simulation. Finally, (iv) we reformulate a parameter extraction method originally proposed for efficient device-agnostic simulation of EM systems attached to lumped nonlinear devices to make it applicable to a system of moving particles. We couple this approach with a domain-decomposition framework to construct an efficient, 'particle-agnostic' extraction framework. Taken together these contributions address several open problems in the field and extend the applicability of EM-FEMPIC methods to larger, more relevant problems.
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