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Volume 24, Issue 4
A Preconditioned Conjugated Gradient Method for Computing Ground States of Rotating Dipolar Bose-Einstein Condensates via Kernel Truncation Method for Dipole-Dipole Interaction Evaluation

Xavier Antoine, Qinglin Tang & Yong Zhang

DOI: 10.4208/cicp.2018.hh80.11

Commun. Comput. Phys., 24 (2018), pp. 966-988.

Published online: 2018-06

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  • Abstract

In this paper, we propose an efficient and accurate method to compute the ground state of 2D/3D rotating dipolar BEC by incorporating the Kernel Truncation Method (KTM) for Dipole-Dipole Interaction (DDI) evaluation into the newly-developed Preconditioned Conjugate Gradient (PCG) method [9]. Adaptation details of KTM and PCG, including multidimensional discrete convolution acceleration for KTM, choice of the preconditioners in PCG, are provided. The performance of our method is confirmed with extensive numerical tests, with emphasis on spectral accuracy of KTM and efficiency of ground state computation with PCG. Application of our method shows some interesting vortex lattice patterns in 2D and 3D respectively.

  • Keywords

Rotating dipolar BEC, Dipole-Dipole Interaction, Preconditioned Conjugate Gradient method, Kernel Truncation Method, ground state.

  • AMS Subject Headings

35Q40, 35Q41, 35Q55, 65M70, 65T40, 65T50, 81-08

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-24-966, author = {Xavier Antoine, Qinglin Tang and Yong Zhang}, title = {A Preconditioned Conjugated Gradient Method for Computing Ground States of Rotating Dipolar Bose-Einstein Condensates via Kernel Truncation Method for Dipole-Dipole Interaction Evaluation}, journal = {Communications in Computational Physics}, year = {2018}, volume = {24}, number = {4}, pages = {966--988}, abstract = {

In this paper, we propose an efficient and accurate method to compute the ground state of 2D/3D rotating dipolar BEC by incorporating the Kernel Truncation Method (KTM) for Dipole-Dipole Interaction (DDI) evaluation into the newly-developed Preconditioned Conjugate Gradient (PCG) method [9]. Adaptation details of KTM and PCG, including multidimensional discrete convolution acceleration for KTM, choice of the preconditioners in PCG, are provided. The performance of our method is confirmed with extensive numerical tests, with emphasis on spectral accuracy of KTM and efficiency of ground state computation with PCG. Application of our method shows some interesting vortex lattice patterns in 2D and 3D respectively.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.2018.hh80.11}, url = {http://global-sci.org/intro/article_detail/cicp/12314.html} }
TY - JOUR T1 - A Preconditioned Conjugated Gradient Method for Computing Ground States of Rotating Dipolar Bose-Einstein Condensates via Kernel Truncation Method for Dipole-Dipole Interaction Evaluation AU - Xavier Antoine, Qinglin Tang & Yong Zhang JO - Communications in Computational Physics VL - 4 SP - 966 EP - 988 PY - 2018 DA - 2018/06 SN - 24 DO - http://doi.org/10.4208/cicp.2018.hh80.11 UR - https://global-sci.org/intro/article_detail/cicp/12314.html KW - Rotating dipolar BEC, Dipole-Dipole Interaction, Preconditioned Conjugate Gradient method, Kernel Truncation Method, ground state. AB -

In this paper, we propose an efficient and accurate method to compute the ground state of 2D/3D rotating dipolar BEC by incorporating the Kernel Truncation Method (KTM) for Dipole-Dipole Interaction (DDI) evaluation into the newly-developed Preconditioned Conjugate Gradient (PCG) method [9]. Adaptation details of KTM and PCG, including multidimensional discrete convolution acceleration for KTM, choice of the preconditioners in PCG, are provided. The performance of our method is confirmed with extensive numerical tests, with emphasis on spectral accuracy of KTM and efficiency of ground state computation with PCG. Application of our method shows some interesting vortex lattice patterns in 2D and 3D respectively.

Xavier Antoine, Qinglin Tang and Yong Zhang. (2018). A Preconditioned Conjugated Gradient Method for Computing Ground States of Rotating Dipolar Bose-Einstein Condensates via Kernel Truncation Method for Dipole-Dipole Interaction Evaluation. Communications in Computational Physics. 24 (4). 966-988. doi:10.4208/cicp.2018.hh80.11
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