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 (1, 2) , Qinglin Tang (3) , Yong Zhang (4, 5)

1 SPHINX - Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization
2 IECL - Institut Élie Cartan de Lorraine
3 Department of Mathematics [Singapore]
4 WPI - Wolfgang Pauli Institute
5 CIMS - Courant Institute of Mathematical Sciences [New York]

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.

Mots clés: ground state; Dipole-Dipole Interaction; Preconditioned Conjugate Gradient method; rotating dipolar BEC; Kernel Truncation Method

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

Xavier Antoine, Qinglin Tang, Yong Zhang. 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, 2018, 24 (4), pp.966-988. ⟨10.4208/cicp.2018.hh80.11⟩. ⟨hal-01649724⟩