High-order time-splitting Hermite and Fourier spectral methods

JOURNAL OF COMPUTATIONAL PHYSICS

卷:228

Article

Thalhammer, Mechthild¹  Caliari, Marco²  Neuhauser, Christof¹ 

[1] Leopold Franzens Univ Innsbruck, Inst Math, A-6020 Innsbruck, Austria

[2] Univ Verona, Dipartimento Informat, I-37134 Verona, Italy

关键词: Nonlinear Schrodinger equations;    Gross-Pitaevskii equation;    Pseudospectral methods;    Exponential operator splitting methods;   

DOI  :  10.1016/j.jcp.2008.10.008

来源: Elsevier

【 摘 要 】

In this paper, we are concerned with the numerical solution of the time-dependent Gross-Pitaevskii Equation (GPE) involving a quasi-harmonic potential. Primarily, we consider discretisations that are based on spectral methods in space and higher-order exponential operator splitting methods in time. The resulting methods are favourable in view of accuracy and efficiency; moreover, geometric properties of the equation such as particle number and energy conservation are well captured. Regarding the spatial discretisation of the GPE, we consider two approaches. In the unbounded domain, we employ a spectral decomposition of the solution into Hermite basis functions: on the other hand. restricting the equation to a sufficiently large bounded domain, Fourier techniques are applicable. For the time integration of the GPE, we study various exponential operator splitting methods of convergence orders two, four, and six. Our main objective is to provide accuracy and efficiency comparisons of exponential operator splitting Fourier and Hermite pseudospectral methods for the time evolution of the GPE. Furthermore, we illustrate the effectiveness of higher-order time-splitting methods compared to standard integrators in a long-term integration. (c) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

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