We present BEC2HPC which is a parallel HPC spectral solver for computing the ground states of the nonlinear Schrödinger equation and the Gross-Pitaevskii equation (GPE) modeling rotating Bose-Einstein condensates (BEC). Considering a standard pseudo-spectral discretization based on Fast Fourier Transforms (FFTs), the method consists in finding the numerical solution of the energy functional minimization problem under normalization constraint by using a preconditioned nonlinear conjugate gradient method. We present some numerical simulations and scalability results for the 2D and 3D problems to obtain the stationary states of BEC with fast rotation and large nonlinearities. The code takes advantage of existing HPC libraries and can itself be leveraged to implement other numerical methods like e.g. for the dynamics of BECs.

Program summary

Program title: BEC2HPC

CPC Library link to program files: https://doi.org/10.17632/mdzpw4dr4t.1

Licensing provisions: GPLv2

Programming language: C++, Python

Nature of problem: This software computes the stationary states of rotating Bose–Einstein condensates (BEC) modeled by the Gross–Pitaevskii equation (GPE). It implements a numerical method that is particularly effective for BEC with fast rotation and large nonlinearities. The parallel implementation allows to perform large-scale simulations of 2D or 3D problems on parallel computing platforms.

Solution method: The stationary states are computed using an iterative pseudo-spectral method based on Fast Fourier Transforms. The computation takes the form of a constrained minimization problem solved using a preconditioned nonlinear conjugate gradient method. This solver is implemented in distributed memory using MPI and a decomposition of the computational domain.

Additional comments including restrictions and unusual features: The algorithms are implemented in C++ and MPI but a Python interface is provided for defining the physics of the problem. Results can be exported to HDF5 files and visualized with external tools such as ParaView. The code can be used to implement other spectral methods in parallel or to solve problems related to the dynamics of BECs.

中文翻译：

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BEC2HPC：用于非线性Schrödinger和旋转Gross-Pitaevskii方程的HPC频谱求解器。平稳状态计算

我们介绍了BEC2HPC，它是一个并行的HPC频谱求解器，用于计算非线性Schrödinger方程和Gross-Pitaevskii方程（GPE）的基态，该基态模拟旋转的Bose-Einstein凝聚物（BEC）。考虑到基于快速傅里叶变换（FFT）的标准伪谱离散化，该方法包括使用预处理的非线性共轭梯度法找到归一化约束下的能量函数最小化问题的数值解。我们针对2D和3D问题提出了一些数值模拟和可扩展性结果，以获得具有快速旋转和大非线性的BEC的稳态。该代码利用了现有的HPC库，并且可以自身用于实施其他数值方法，例如用于BEC动力学的方法。

计划摘要

程式名称： BEC2HPC

CPC库链接到程序文件： https : //doi.org/10.17632/mdzpw4dr4t.1

许可条款： GPLv2

编程语言： C ++，Python

问题的性质：该软件计算由Gross–Pitaevskii方程（GPE）建模的旋转Bose-Einstein冷凝物（BEC）的稳态。它实现了一种数值方法，该方法对于具有快速旋转和大非线性的BEC特别有效。并行实现允许在并行计算平台上执行2D或3D问题的大规模仿真。

求解方法：使用基于快速傅立叶变换的迭代伪谱方法来计算稳态。该计算采用约束非线性最小化问题的形式，该问题使用预处理的非线性共轭梯度方法求解。此求解器是使用MPI和计算域的分解在分布式内存中实现的。

包括限制和异常功能在内的其他注释：算法在C ++和MPI中实现，但是提供了Python接口来定义问题的物理性质。可以将结果导出到HDF5文件，并可以使用ParaView等外部工具将其可视化。该代码可用于并行实现其他频谱方法或解决与BEC动态相关的问题。