An Efficient Compact Finite Difference Method for the Solution of the Gross-Pitaevskii Equation
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...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Advances in Condensed Matter Physics |
| Online Access: | http://dx.doi.org/10.1155/2015/127580 |
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| author | Rongpei Zhang Jia Liu Guozhong Zhao |
| author_facet | Rongpei Zhang Jia Liu Guozhong Zhao |
| author_sort | Rongpei Zhang |
| collection | DOAJ |
| description | 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 (r≥2) 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. |
| format | Article |
| id | doaj-art-ccaa63bcfe2a453ea5e3d64f64f54d03 |
| institution | Kabale University |
| issn | 1687-8108 1687-8124 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Condensed Matter Physics |
| spelling | doaj-art-ccaa63bcfe2a453ea5e3d64f64f54d032025-02-03T07:24:39ZengWileyAdvances in Condensed Matter Physics1687-81081687-81242015-01-01201510.1155/2015/127580127580An Efficient Compact Finite Difference Method for the Solution of the Gross-Pitaevskii EquationRongpei Zhang0Jia Liu1Guozhong Zhao2School of Sciences, Liaoning Shihua University, Fushun 113001, ChinaSchool of Foreign Language, Liaoning Shihua University, Fushun 113001, ChinaFaculty of Mathematics, Baotou Teachers College, Baotou 014030, ChinaWe 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 (r≥2) 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.http://dx.doi.org/10.1155/2015/127580 |
| spellingShingle | Rongpei Zhang Jia Liu Guozhong Zhao An Efficient Compact Finite Difference Method for the Solution of the Gross-Pitaevskii Equation Advances in Condensed Matter Physics |
| title | An Efficient Compact Finite Difference Method for the Solution of the Gross-Pitaevskii Equation |
| title_full | An Efficient Compact Finite Difference Method for the Solution of the Gross-Pitaevskii Equation |
| title_fullStr | An Efficient Compact Finite Difference Method for the Solution of the Gross-Pitaevskii Equation |
| title_full_unstemmed | An Efficient Compact Finite Difference Method for the Solution of the Gross-Pitaevskii Equation |
| title_short | An Efficient Compact Finite Difference Method for the Solution of the Gross-Pitaevskii Equation |
| title_sort | efficient compact finite difference method for the solution of the gross pitaevskii equation |
| url | http://dx.doi.org/10.1155/2015/127580 |
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