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math.NA2026
Structure and symmetry of the Gross-Pitaevskii ground-state manifold
Zixu Feng, Patrick Henning, Qinglin Tang
The structure and degeneracy of ground states of the Gross-Pitaevskii energy functional play a central role in both analysis and computation, yet a precise characterization of the…
math.NA2025
Discrete normalized gradient flow for two-component Bose-Einstein condensates: Energy dissipation, global convergence and sharp local convergence behavior
Zixu Feng, Lunxu Liu, Qinglin Tang
The gradient flow with semi-implicit discretization (GFSI) is the most widely used algorithm for computing the ground state of Gross-Pitaevskii energy functional. We apply GFSI to…
math.NA2025
On preconditioned Riemannian gradient methods for minimizing the Gross-Pitaevskii energy functional: algorithms, global convergence and optimal local convergence rate
Zixu Feng, Qinglin Tang
In this article, we propose a unified framework for preconditioned Riemannian gradient (P-RG) methods to minimize Gross-Pitaevskii (GP) energy functionals with rotation on a Rieman…