文章基本信息

标题：An Efficient Compact Finite Difference Method for the Solution of the Gross-Pitaevskii Equation
本地全文：下载
作者：Rongpei Zhang ; Jia Liu ; Guozhong Zhao 等
期刊名称：Advances in Condensed Matter Physics
印刷版ISSN：1687-8108
电子版ISSN：1687-8124
出版年度：2015
卷号：2015
DOI：10.1155/2015/127580
出版社：Hindawi Publishing Corporation
摘要：We present an efficient, unconditionally stable, and accurate numerical method for the solution of the Gross-Pitaevskii equation. We begin with an introduction on the gradient flow with discrete normalization (GFDN) for computing stationary states of a nonconvex minimization problem. Then we present a new numerical method, CFDM-AIF method, which combines compact finite difference method (CFDM) in space and array-representation integration factor (AIF) method in time. The key features of our methods are as follows: (i) the fourth-order accuracy in space and rth () accuracy in time which can be achieved and (ii) the significant reduction of storage and CPU cost because of array-representation technique for efficient handling of exponential matrices. The CFDM-AIF method is implemented to investigate the ground and first excited state solutions of the Gross-Pitaevskii equation in two-dimensional (2D) and three-dimensional (3D) Bose-Einstein condensates (BECs). Numerical results are presented to demonstrate the validity, accuracy, and efficiency of the CFDM-AIF method.