论文标题
加速的数值算法，用于与微波相结合的GROSS-PITAEVSKII方程的稳态
Accelerated numerical algorithms for steady states of Gross-Pitaevskii equations coupled with microwaves
论文作者
论文摘要
我们提出了两种用于单组分和二进制Gross-pitaevskii（GP）方程的加速数值算法，并在稳态状态下与微波（电磁场）结合。一个基于归一化梯度流式公式，称为ASGF方法，而另一个在非线性约束优化的扰动，投影的共轭梯度方法上，称为PPNCG方法。耦合的GP方程在空间中是非局部性的，描述了与电磁场相互作用的伪螺旋体冷凝物（BEC）。我们对这项研究的兴趣是开发非本地GP方程系统的稳定对称和中央涡流状态的有效的迭代数值方法。在算法中，GP方程在二维（2D）空间中的极坐标中通过Legendre-Galerkin光谱法离散。新算法被证明可以通过许多基准示例胜过现有的算法，其中PPNCG方法在其中表现最好。提供了中央涡流状态的其他数值模拟，以证明新算法的有用性和效率。
We present two accelerated numerical algorithms for single-component and binary Gross-Pitaevskii (GP) equations coupled with microwaves (electromagnetic fields) in steady state. One is based on a normalized gradient flow formulation, called the ASGF method, while the other on a perturbed, projected conjugate gradient approach for the nonlinear constrained optimization, called the PPNCG method. The coupled GP equations are nonlocal in space, describing pseudo-spinor Bose-Einstein condensates (BECs) interacting with an electromagnetic field. Our interest in this study is to develop efficient, iterative numerical methods for steady symmetric and central vortex states of the nonlocal GP equation systems. In the algorithms, the GP equations are discretized by a Legendre-Galerkin spectral method in a polar coordinate in two-dimensional (2D) space. The new algorithms are shown to outperform the existing ones through a host of benchmark examples, among which the PPNCG method performs the best. Additional numerical simulations of the central vortex states are provided to demonstrate the usefulness and efficiency of the new algorithms.
