Global convergence of an efficient splitting method for the defocusing Gross–Pitaevskii ground state problem
Published in arXiv preprint, 2026
Proposes two Davis–Yin three-operator splitting schemes for the defocusing Gross–Pitaevskii ground state whose every iteration inverts only a shifted Laplacian (or a shifted Laplacian plus the separable part of the potential), and proves, for monotone discrete Laplacians, global convergence to the unique positive discrete ground state from any positive normalized initial vector at any constant step size below an explicit threshold; 3D tests with up to 9993 unknowns run on a single GPU.
Recommended citation: J. Li, S. Zheng, X. Zhang. (2026). "Global convergence of an efficient splitting method for the defocusing Gross–Pitaevskii ground state problem." arXiv:2609.13509.
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