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

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 (Bangerth et al., 0000) [1], (Bangerth et al., 2007) [2]. 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) (Marojević et al., 2013), (Yukalov et al., 1997, 2004) [3,4] 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 (Marojević et al., 2013). The latter method enables to find the excited state solutions. Program summaryProgram title: ATUS-PROCatalogue identifier: AEZD_v1_0Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEZD_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: GNU General Public License, version 3No. of lines in distributed program, including test data, etc.: 12757No. of bytes in distributed program, including test data, etc.: 412782Distribution format: tar.gzProgramming language: C++.Computer: PCs and distributed memory machines.Operating system: Linux, UNIX.RAM: Depending on the problem; megabytes to gigabytesSupplementary material: A file containing the expected results from the test run can be downloaded.Classification: 4.3, 4.12.External routines: MPI, GSL, LAPACK, P4EST, PETSC, deal.IINature of problem: Solving the Gross–Pitaevskii equation for Bose–Einstein condensates in external traps. Stationary solutions: computation of ground as well as excited states. Real time propagation: calculation of time dependent solutions.Solution method: The method of solving for stationary states is based on an enhanced version of the Newton algorithm developed in [1]. An implicit Crank–Nicolson scheme is used for real-time propagation. Both methods use adaptive finite element methods based on the library deal.II.Restrictions: The one-dimensional programs run only on single core.Additional comments: This package generates 8 executables, (i) breed_1, (ii) breed, (iii) breed_cs, (iv) rtprop_1, (v) rtprop, (vi) rtprop_cs, (vii) gen_params, (viii) gen_params_csRunning time: Depending on size of problem: from seconds (ground state calculations) to minutes (small no. of excited states, short timescale real-time propagation) up to several days (large no. of excited states and large scale real time propagation).