CUDA programs for solving the time-dependent dipolar Gross-Pitaevskii equation in an anisotropic trap

In this paper we present new versions of previously published numerical programs for solving the dipolar Gross–Pitaevskii (GP) equation including the contact interaction in two and three spatial dimensions in imaginary and in real time, yielding both stationary and non-stationary solutions. New versions of programs were developed using CUDA toolkit and can make use of Nvidia GPU devices. The algorithm used is the same split-step semi-implicit Crank–Nicolson method as in the previous version (Kishor Kumar et al., 2015), which is here implemented as a series of CUDA kernels that compute the solution on the GPU. In addition, the Fast Fourier Transform (FFT) library used in the previous version is replaced by cuFFT library, which works on CUDA-enabled GPUs. We present speedup test results obtained using new versions of programs and demonstrate an average speedup of 12–25, depending on the program and input size. The original version of this program (AEWL_v1_0) may be found at dx.doi.org/10.1016/j.cpc.2015.03.024

本文提出了此前已发表的数值程序的新版本，用于求解含接触相互作用的偶极格罗斯-皮塔耶夫斯基（Gross–Pitaevskii, GP）方程，覆盖二维与三维空间维度，支持虚时与实时求解，可得到定态与非定态两类解。新版本程序基于CUDA工具包开发，可适配英伟达（Nvidia）GPU设备。所采用的算法与此前版本（Kishor Kumar等人，2015）一致，均为分步半隐式克兰克-尼科尔森方法，本次将其实现为一系列可在GPU上完成求解计算的CUDA核函数。此外，此前版本所使用的快速傅里叶变换（Fast Fourier Transform, FFT）库已替换为适用于支持CUDA的GPU的cuFFT库。本文给出了基于新版本程序得到的加速测试结果，结果显示平均加速比可达12至25倍，具体数值取决于程序类型与输入规模。该程序的原始版本（AEWL_v1_0）可在dx.doi.org/10.1016/j.cpc.2015.03.024获取。