OpenMP Fortran programs for solving the time-dependent dipolar Gross-Pitaevskii equation

In this paper we present Open Multi-Processing (OpenMP) Fortran 90/95 versions of previously published numerical programs for solving the dipolar Gross-Pitaevskii (GP) equation including the contact interaction in one, two and three spatial dimensions. The atoms are considered to be polarized along the z axis and we consider different cases, e.g., stationary and non-stationary solutions of the GP equation for a dipolar Bose-Einstein condensate (BEC) in one dimension (along x and z axes), two dimensions (in x-y and x-z planes), and three dimensions. The algorithm used is the split-step semi-implicit Crank-Nicolson scheme for imaginary- and real-time propagation to obtain stationary states and BEC dynamics, respectively, as in the previous version (Kishor Kumar et al., 2015 [3]). These OpenMP versions have significantly reduced execution time in multicore processors.

The previous version of this program (AEWL_v1_0) may be found at https://doi.org/10.1016/j.cpc.2015.03.024.

本文提出了针对一、二、三维空间中含接触相互作用的偶极格罗斯-皮塔耶夫斯基（dipolar Gross-Pitaevskii，GP）方程求解的开放多处理（Open Multi-Processing，OpenMP）Fortran 90/95版本数值程序，其原型为已发表的同类数值程序。本文假设原子沿z轴极化，并考虑了多种情形：例如一维（沿x轴与z轴方向）、二维（x-y平面与x-z平面）以及三维偶极玻色-爱因斯坦凝聚体（dipolar Bose-Einstein condensate，BEC）的格罗斯-皮塔耶夫斯基方程定态与非定态解。所采用的算法为分步半隐式克兰克-尼科尔森格式，分别通过虚时传播与实时传播来求解定态与玻色-爱因斯坦凝聚体动力学，与此前版本（Kishor Kumar等，2015年[3]）的算法一致。该OpenMP版本程序在多核处理器上的运行时长已得到显著缩短。

该程序的前身版本（AEWL_v1_0）可通过链接https://doi.org/10.1016/j.cpc.2015.03.024获取。