ATUS-PRO: A FEM-based solver for the time-dependent and stationary Gross-Pitaevskii equation

TL;DR

ATUS-PRO is a versatile C++ solver package utilizing finite element methods for solving both stationary and time-dependent Gross-Pitaevskii equations, capable of handling complex trap geometries and excited states in Bose-Einstein condensate simulations.

Contribution

It introduces a finite element based solver package that can compute ground and excited states of the Gross-Pitaevskii equation, including high non-linearity regimes, with parallel computing support.

Findings

Successfully computes non-ground state solutions.

Handles arbitrary trap geometries and high non-linearity.

Supports simulations in 1D, 2D, and 3D with axial symmetry.

Abstract

ATUS-PRO is a solver-package written in C++ designed for the calculation of numerical solutions of the stationary- and the time dependent Gross--Pitaevskii equation for local two-particle contact interaction utilising finite element methods. These are implemented by means of the deal.II library. The code can be used in order to perform simulations of Bose-Einstein condensates in gravito-optical surface traps, isotropic and full anisotropic harmonic traps, as well as for arbitrary trap geometries. A special feature of this package is the possibility to calculate non-ground state solutions (topological modes, excited states) for an arbitrarily high non-linearity term. The solver- package is designed to run on parallel distributed machines and can be applied to problems in one, two, or three spatial dimensions with axial symmetry or in Cartesian coordinates. The time dependent Gross--Pitaevskii equation is solved by means of the fully implicit Crank- Nicolson method, whereas stationary states are obtained with a modified version based on our own constrained Newton method. The latter method enables to find the excited state solutions.