In the mean-field approximation, Bose-Einstein condensates can be described by the Gross-Pitaevskii equation, a Schrödinger-type equation that includes nonlinear terms arising from the system's interactions. In the case of contact interactions, the corresponding nonlinear term is local, while nonlocal terms may stem from long-range interactions, such as dipole-dipole interactions, which are expressed by an integral kernel. In order to study ground states and dynamics of Bose-Einstein condensates with contact and dipolar interactions, we have developed several parallel algorithms and programs based on the Crank-Nicolson semi-implicit split-step method, which use different levels of parallelism: OpenMP, MPI, CUDA, and their hybrid combinations. In this talk we will give an overview of these programs and show how they can be used to study quantum droplets and vortices in strongly dipolar condensates. Such multiscale systems require numerical simulations in high resolution and therefore parallelization is necessary for their realistic description, in particular in 3D. This application will illustrate how quantum fluctuations of the Bogoliubov-Popov type, or other types of terms and interactions can be included in the programs, which are written to address a broad range of problems modeled by GP-like equations.

This is a joint work with V. Lončar, D. Vudragović, R. Kishor Kumar, P. Muruganandam, and S. K. Adhikari. This work was supported by the Ministry of Education, Science, and Technological Development of the Republic of Serbia under project ON171017.