We report on the development of numerical module for the HiLight simulation platform based on GPGPU supercomputing to solve a system of coupled fields governed by the Generalized Nonlinear Schr¨odinger Equation with local and/or nonlocal nonlinearities. This models plays an important role in describing a plethora of different phenomena in various areas of physics. In optics, this model was initially used to describe the propagation of light through local and/or nonlocal systems under the paraxial approximation, but more recently it has been extensively used as a support model to develop optical analogues. However, establishing the relation between the original system and the analogue, as well as, between their model and the actual experimental setup is not an easy task. First and foremost because in most cases the governing equations are nonintegrable, preventing from obtaining analytical solutions and hindering the optimization of the experiments. Alternatively, despite numerical methods not providing exact solutions, they allow to test different experimental scenarios and provide a better insight to what to expect in an actual experiment, while giving access to all the variables of the optical system being simulated. However, the numerical solution of a system of N-coupled Schr¨odinger fields in systems with two or three spatial dimensions requires massive computation resources, and must employ advanced supercomputing and parallelization techniques, such as GPGPU. This paper focuses on the numerical aspects behind this challenge, describing the structure of our simulation module, its performance and the tests performed.