Efficient spectral computation of the stationary states of rotating Bose-Einstein condensates by the preconditioned nonlinear conjugate gradient methodReportar como inadecuado




Efficient spectral computation of the stationary states of rotating Bose-Einstein condensates by the preconditioned nonlinear conjugate gradient method - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.

1 EDP - Equations aux dérivées partielles IECL - Institut Élie Cartan de Lorraine 2 SPHINX - Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization Inria Nancy - Grand Est 3 CERMICS - Centre d-Enseignement et de Recherche en Mathématiques et Calcul Scientifique 4 MATHERIALS - MATHematics for MatERIALS CERMICS - Centre d-Enseignement et de Recherche en Mathématiques et Calcul Scientifique, Inria de Paris 5 LMRS - Laboratoire de Mathématiques Raphaël Salem

Abstract : We propose a preconditioned nonlinear conjugate gradient method coupled with a spectral spatial dis-cretization scheme for computing the ground states GS of rotating Bose-Einstein condensates BEC, modeled by the Gross-Pitaevskii Equation GPE. We first start by reviewing the classical gradient flow also known as imaginary time IMT method which considers the problem from the PDE standpoint, leading to numerically solve a dissipative equation. Based on this IMT equation, we analyze the forward Euler FE, Crank-Nicolson CN and the classical backward Euler BE schemes for linear problems and recognize classical power iterations, allowing us to derive convergence rates. By considering the alternative point of view of minimization problems, we propose the preconditioned gradient PG and conjugate gradient PCG methods for the GS computation of the GPE. We investigate the choice of the preconditioner, which plays a key role in the acceleration of the convergence process. The performance of the new algorithms is tested in 1D, 2D and 3D. We conclude that the PCG method outperforms all the previous methods, most particularly for 2D and 3D fast rotating BECs, while being simple to implement.

Keywords : optimization algorithms on Riemannian manifolds rotating Gross-Pitaevskii equation preconditioner nonlinear conjugate gradient stationary states Fourier spectral method Bose-Einstein condensation





Autor: Xavier Antoine - Antoine Levitt - Qinglin Tang -

Fuente: https://hal.archives-ouvertes.fr/



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