Gauss-Seidel-type methods for energy states of a multi-component Bose-Einstein condensate

Shu Ming Chang, Wen Wei Lin*, Shih Feng Shieh


研究成果: 雜誌貢獻期刊論文同行評審

41 引文 斯高帕斯(Scopus)


In this paper, we propose two iterative methods, a Jacobi-type iteration (JI) and a Gauss-Seidel-type iteration (GSI), for the computation of energy states of the time-independent vector Gross-Pitaevskii equation (VGPE) which describes a multi-component Bose-Einstein condensate (BEC). A discretization of the VGPE leads to a nonlinear algebraic eigen-value problem (NAEP). We prove that the GSI method converges locally and linearly to a solution of the NAEP if and only if the associated minimized energy functional problem has a strictly local minimum. The GSI method can thus be used to compute ground states and positive bound states, as well as the corresponding energies of a multi-component BEC. Numerical experience shows that the GSI converges much faster than JI and converges globally within 10-20 steps.

頁(從 - 到)367-390
期刊Journal of Computational Physics
出版狀態已發佈 - 2005 1月 1

ASJC Scopus subject areas

  • 數值分析
  • 建模與模擬
  • 物理與天文學(雜項)
  • 一般物理與天文學
  • 電腦科學應用
  • 計算數學
  • 應用數學


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