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ATUS-PRO: a FEM-based solver for the time-dependent and stationary Gross-Pitaevskii equation. (English) Zbl 1348.35005

Summary: 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 [W. Bangerth et al., “The deal.II library, version 8.2”, Arch. Numer. Softw. 3, No. 100, 9 p. (2015; doi:10.11588/ans.2015.100.18031)], [W. Bangerth et al., “deal.II – a general purpose object oriented finite element library”, ACM Trans. Math. Softw. 33, No. 4, Article ID 24, 27 p. (2007; doi:10.1145/1268776.1268779)]. 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) [the first author et al., Comput. Phys. Commun. 184, No. 8, 1920–1930 (2013; Zbl 1344.81076)], [V. I. Yukalov et al., “Non-ground-state Bose-Einstein condensates of trapped atoms”, Phys. Rev. A (3) 56, No. 6, 4845–4854 (1997; doi:10.1103/PhysRevA.56.4845); “Resonant generation of topological modes in trapped Bose-Einstein gases”, Phys. Rev. A (3) 69, No. 2, Article ID 023620, 29 p. (2004; doi:10.1103/PhysRevA.69.023620)] 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 first author et al., loc. cit.]. The latter method enables to find the excited state solutions.

MSC:

35-04 Software, source code, etc. for problems pertaining to partial differential equations
35Q55 NLS equations (nonlinear Schrödinger equations)
82-04 Software, source code, etc. for problems pertaining to statistical mechanics
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs

Citations:

Zbl 1344.81076
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References:

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