A Fourth-Order Time-Splitting Laguerre-Hermite Pseudospectral Method for Bose-Einstein Condensates
A Fourth-Order Time-Splitting Laguerre-Hermite Pseudospectral Method for Bose-Einstein Condensates
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DOI：
10.1137/030601211
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发表时间：
2003-10
期刊：
影响因子：
--
通讯作者：
W. Bao;Jie Shen
中科院分区：
文献类型：
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作者：
W. Bao;Jie Shen
介绍了一种四阶时间分裂Laguerre-Hermite拟谱方法，用于研究柱对称三维玻色-爱因斯坦凝聚体（BEC）。该方法是明确的，时间可逆的，时间横不变的。它保持了位置密度，并且在空间上具有谱精度，在时间上具有四阶精度。此外，新方法还具有另外两个重要的优点：（i）它将具有圆柱对称性的三维（3-D）问题简化为有效的二维（2-D）问题;（ii）它在整个空间而不是在截断的人工计算域中求解问题。该方法适用于矢量Gros-Pitaevskii方程（VGPEs）的多组分BEC。对一维广义相对论、径向对称二维广义相对论、圆柱对称三维广义相对论以及双分量玻色-爱因斯坦凝聚的三维变广义相对论进行了大量的数值试验，验证了新方法的有效性和准确性.
A fourth-order time-splitting Laguerre--Hermite pseudospectral method is introduced for Bose--Einstein condensates (BECs) in three dimensions with cylindrical symmetry. The method is explicit, time reversible, and time transverse invariant. It conserves the position density and is spectral accurate in space and fourth-order accurate in time. Moreover, the new method has two other important advantages: (i) it reduces a three-dimensional (3-D) problem with cylindrical symmetry to an effective two-dimensional (2-D) problem; (ii) it solves the problem in the whole space instead of in a truncated artificial computational domain. The method is applied to vector Gross--Pitaevskii equations (VGPEs) for multicomponent BECs. Extensive numerical tests are presented for the one-dimensional (1-D) GPE, the 2-D GPE with radial symmetry, the 3-D GPE with cylindrical symmetry, as well as 3-D VGPEs for two-component BECs, to show the efficiency and accuracy of the new numerical method.