Simulation of the student enrollment system through the reaction-diffusion model and parallel computing with CUDA

The reduction of student segregation should be one of the priorities of any state in terms of educational legislation and regulation since there is empirical evidence that students belonging to families in vulnerable situations, who attend less segregated schools, tend to have better academic results. In this work, we implement the reaction-diffusion model to simulate decentralized student enrollment. Reaction-diffusion equations are used in conjunction with the finite volumes method to generate a discrete domain of space over which students search for a suitable school and the explicit Euler method for the approximation of time. The computational implementation, through CUDA, allows solving for the problem of wide territories, such as cities, taking advantage of the performance benefits offered by parallel computing by GPU at a low cost. In our tests, simulations have a low runtime, converging to the total assignment of students to schools.