Horizontal ribbon growth is method for producing sheets of single crystal silicon for solar cells. In HRG, the sheet floats on its melt and is pulled horizontally while sheet growth is driven by an impinging helium jet. Although, production of silicon sheets has been experimentally demonstrated, producing uniform and thin sheets has proven challenging. In this study, a computational model of HRG was used that includes the moving solid-melt and melt-gas interfaces, solidification kinetics, and the physics of the triple-phase line (TPL) where the three phases meet. For spatial discretization, an hp-finite element method was utilized with an arbitrary Lagrangian-Eulerian moving mesh and local mesh adaptation were employed. This study uses the computational model to investigate the stability of the growth process as a function of the production velocity and the thermal boundary conditions. It is shown that there are two types of instability that can affect the process, the first is a turning point that occurs with increasing production rate [1]. Beyond this turning point, no steady production process exists so the turning point limits the maximum production rate of the system. The second instability is convective where perturbations can grow at an exponential rate and subsequently interfere with the growth process [2]. In this case, the maximum production velocity is limited by the convective instability rather than the turning point behavior of the system. Both types of instability must be avoided to create a stable production process. Simulations were performed to optimized the thermal conditions such that the production rate can be maximized. Results indicate that a narrow heat removal profile with high intensity increases the turning point production velocity, but also exacerbates the convective instability. Adding heat from the bottom of the melt reduce the convective instability at the cost of a reduced production velocity at the turning point. [1] B. T. Helenbrook, P. Kellerman, F. Carlson, N. Desai, and D. Sun. “Experimental and Numerical Investigation of the Horizontal Ribbon Growth Process”. In: Journal of Crystal Growth 453 (Nov. 2016), pp. 163–172. ISSN: 0022-0248. DOI: 10.1016/j.jcrysgro.2016.08.034. [2] B. T. Helenbrook and N. S. Barlow. “Spatial-Temporal Stability Analysis of Faceted Growth with Application to Horizontal Ribbon Growth”. In: Journal of Crystal Growth 454 (Nov. 2016), pp. 35– 4