The design of modern devices is impacted heavily by the use and availability of robust, accurate, and efficient computational tools. This includes modeling devices that exploit plasma physics like particle accelerators, klystrons, ion thrusters, and micro-plasma generators among many other applications. While there are a number of current and emerging applications, the common thread between all is the need to accurately and efficiently capture all the relevant physics in geometrically intricate structures. The holy grail is to enable topology optimization to explore the design space. But all this requires rigorous translation from the continuous to the discrete world, while capturing all the underlying physics and not adding spurious artifacts due to discretization. A common computational model to perform this analysis is the particle-in-cell (PIC) method. It provides a straightforward paradigm to self-consistently solve for the distribution of the plasma as a collection of particles. The prevailing approach to solve for the fields in PIC is the finite difference time domain method (FDTD), or EM-FDTDPIC. But this effort leaves much to be desired, given the leaps that have been made in the finite element method; indeed, the latter is the method of choice for most commercial tools that that have become the de-facto workhorse in RF design industry. As a result, in the past decade, considerable effort has been expended in developing finite element (FEM) based PIC schemes, EM-FEMPIC. But we are still not there. One major concern of utilizing EM-FEMPIC over EM-FDTDPIC is the computational cost of FEM, which is greater than FDTD, despite the advantages of field and geometry accuracy FEM affords. This dissertation seeks to develop (i) a theoretically rigorous means to translate from the continuous to the discrete world while ensuring that there are no spurious artifacts, (ii) develops a higher order accurate method in both space and time, and (iii) overcomes cost complexity by introducing a linear scaling domain decomposition scheme. In all of these, the methods developed ensure that the necessary conservation properties are satisfied to machine precision. Numerous examples developed demonstrate these claims.
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