Simulation of Stark broadened hydrogen Balmer line shapes for DA white dwarf synthetic spectra

White Dwarfs (WD) are useful across a surprisingly wide range of astrophysical contexts from cosmochronology to piecing together the chemical enrichment history of a galaxy throughout the cycles of star formation to their use as spectrophotometric standards for many major astronomical observatories. In all of these contexts, the fidelity of the information we can extract is predicated on the accuracy of our model atmosphere calculations. Interpretations of actual WD stellar spectral and photometric data depend in one way or another on fits to grids of model atmospheres. The codes used to construct these grids have relied on the basic model of Vidal et al. (1970) (VCS), known as the Unified Theory of line broadening for line shape calculations. There have since been significant advancements in the theory, however, the calculations used in WD model atmospheres have only received minor updates. Meanwhile, continued advances in spectroscopic instrumentation and signal-to-noise of stellar spectral data have uncovered indications of inaccuracies in the VCS theory. The improvements in the fidelity of our data have signaled a simultaneous decline in the fidelity of our spectral fits and fundamental parameter determinations. The inaccuracies manifest as discrepancies in mean mass estimates made using different mass determination techniques. Additionally, fits performed using individual spectral lines as opposed to the entire set of lines Hβ-H8 also yield highly discrepant inferred values for mass and temperature. Motivated by this, Gomez et al. (2016) developed a simulation based line profile calculation code Xenomorph using an improved theoretical treatment of Stark Broadened line profiles themselves. This code made the theoretical line shape advancements available to the WD community for the first time. However, the code required a series of revisions to make it more physically realistic as well as to the numerical methods to make the calculations computationally tractable for the large grids needed for model atmosphere calculations. Comparisons against the standard Tremblay & Bergeron (2009) line shape calculations also demanded an implementation of a simulation based approach to occupation probability. This thesis presents a detailed description of these changes which now make full grids of new and improved line profile calculations feasible and appropriate for use in WD model atmosphere calculations.