The goal of my project was to develop an optimized linear system solver to shorten the runtime of a computer simulation. The simulation was created to study the thermonuclear burning of Type I X-ray Bursts in low-mass X-ray binary star systems (LMXBs). To study these systems, thousands of X-ray bursts need to be simulated. Currently, the simulation can complete around one X-ray burst per day. I worked on accelerating the main bottleneck of the simulation by using very powerful graphics cards (GPUs) instead of the central processing unit (CPU) to perform the necessary calculations. I made steady progress over the summer towards this goal and eventually developed a solution that was four to five times faster than the original code.