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.本文提出了已发表数值程序的开放多处理（Open Multi-Processing, OpenMP）Fortran 90/95版本，用于求解包含接触相互作用的一维、二维及三维空间维度下的偶极格罗斯-皮塔耶夫斯基（Gross-Pitaevskii, GP）方程。本文假设原子沿z轴极化，并考虑多种情形：例如一维（沿x轴与z轴方向）、二维（x-y平面与x-z平面）及三维空间中偶极玻色-爱因斯坦凝聚（Bose-Einstein condensate, BEC）的GP方程驻态与非驻态解。所采用的算法为分步半隐式克兰克-尼科尔森（Crank-Nicolson）格式，分别通过虚时传播与实时传播以获取驻态与BEC动力学特性，与此前版本（Kishor Kumar等人，2015年[3]）一致。这些OpenMP版本在多核处理器上的执行时间显著缩短。本程序的旧版本（AEWL_v1_0）可于https://doi.org/10.1016/j.cpc.2015.03.024获取。