有限元法用于含角动量旋转的时间依赖性格鲁斯-皮塔夫斯基方程

Gross-Pitaevskii方程的有限体积法

Finite volumes for the Gross-Pitaevskii equation

本文针对二维带时变势的Gross-Pitaevskii方程，提出半离散有限体积格式，利用离散Sobolev不等式分析误差界，并通过数值模拟验证收敛性。

Gradient Flow Finite Element Discretizations with Energy-Based Adaptivity for the Gross-Pitaevskii Equation

We present an effective adaptive procedure for the numerical approximation of the steady-state Gross-Pitaevskii equation. Our approach is solely based on energy minimization, and consists of a combination of gradient flow iterations and adaptive finite element mesh refinements. Numerical tests show that this strategy is able to provide highly accurate results, with optimal convergence rates with respect to the number of freedom.

关于Gross-Pitaevskii特征值问题的Sobolev梯度流的收敛性

On the convergence of Sobolev gradient flow for the Gross-Pitaevskii eigenvalue problem

本文研究三种投影Sobolev梯度流求解Gross-Pitaevskii特征值问题基态的收敛性，证明了能量耗散、全局收敛到临界点以及局部指数收敛到基态。

Efficient time integration methods for Gross--Pitaevskii equations with rotation term

The objective of this work is the introduction and investigation of favourable time integration methods for the Gross--Pitaevskii equation with rotation term. Employing a reformulation in rotating Lagrangian coordinates, the equation takes the form of a nonlinear Schr{ö}dinger equation involving a space-time-dependent potential. A natural approach that combines commutator-free quasi-Magnus exponential integrators with operator splitting methods and Fourier spectral space discretisations is proposed. Furthermore, the special structure of the Hamilton operator permits the design of specifically …

二维环上Gross-Pitaevskii方程的数值研究及涡旋成核

Numerical study of the Gross-Pitaevskii equation on a two-dimensional ring and vortex nucleation

本文通过Strang分裂与有限体积法数值求解二维环上的Gross-Pitaevskii方程，研究旋转正弦扰动下量子涡旋的成核现象，并开发了相应的涡旋追踪算法。

Deflation-based Identification of Nonlinear Excitations of the 3D Gross--Pitaevskii equation

We present previously unknown solutions to the 3D Gross--Pitaevskii equation describing atomic Bose-Einstein condensates. This model supports elaborate patterns, including excited states bearing vorticity. The discovered coherent structures exhibit striking topological features, involving combinations of vortex rings and multiple, possibly bent vortex lines. Although unstable, many of them persist for long times in dynamical simulations. These solutions were identified by a state-of-the-art numerical technique called deflation, which is expected to be applicable to many problems from other are…