GPELab, a Matlab toolbox to solve Gross-Pitaevskii equations I: computation of stationary solutions

International audienceThis paper presents GPELab (Gross-Pitaevskii Equation Laboratory), an advanced easy-to-use and flexible Matlab toolbox for numerically simulating many complex physics situations related to Bose-Einstein condensation. The model equation that GPELab solves is the Gross-Pitaevskii equation. The aim of this first part is to present the physical problems and the robust and accurate numerical schemes that are implemented for computing stationary solutions, to show a few computational examples and to explain how the basic GPELab functions work. Problems that can be solved include: 1d, 2d and 3d situations, general potentials, large classes of local and nonlocal nonlinearities, multi-components problems, fast rotating gazes. The toolbox is developed in such a way that other physics applications that require the numerical solution of general Schrödinger-type equations can be considered.GPELab also presents some functionalities to compute the dynamics of Bose-Einstein condensates and to numerically include some stochastic effects