发表机构
Beijing Huairou Laboratory; Capital Normal University（北京怀柔实验室; 首都师范大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出一种正守恒傅里叶优化方法，通过凸正则化和傅里叶伪谱离散化，结合加速一阶法与牛顿细化，高效高精度计算高阶相互作用玻色-爱因斯坦凝聚体的基态。
AI 中文摘要
我们开发了一种正守恒傅里叶优化（PCFO）方法，用于计算具有高阶相互作用的玻色-爱因斯坦凝聚体的基态。该基态问题具有凸密度形式，但零密度附近的奇异行为给高精度计算带来了困难。我们引入了密度能量的凸正则化，并证明了当正则化参数趋近于零时，这些正则化在计算域上具有Γ-收敛性。正则化问题通过一种保持质量守恒和节点正性的傅里叶伪谱方法进行离散化。对于由此产生的约束优化问题，我们使用加速一阶方法进行主要能量降低，随后采用牛顿细化来减少剩余的优化残差。数值实验表明，对于正则化问题具有谱型收敛性，量化了正则化参数对精度和空间分辨率的影响，并展示了两阶段优化方法的有效性。
英文摘要
We develop a positive-conservative Fourier optimization (PCFO) method for computing ground states of Bose--Einstein condensates with higher-order interactions. The ground-state problem admits a convex density formulation, but the singular behavior near zero density poses difficulties for high-accuracy computation. We introduce convex regularizations of the density energy and establish their $Γ$-convergence on the computational domain as the regularization parameters vanish. The regularized problem is discretized by a Fourier pseudospectral method with mass conservation and nodal positivity. For the resulting constrained optimization problem, we use an accelerated first-order method for the main energy reduction, followed by a Newton refinement to reduce the remaining optimality residual. Numerical experiments show spectral-type convergence for regularized problems, quantify the effects of the regularization parameters on accuracy and spatial resolution, and demonstrate the effectiveness of the two-stage optimization method.
