【唐庆粦】On the discrete normalized gradient flow for computing ground states of rotating Bose-Einstein condensates

On the discrete normalized gradient flow for computing ground states of rotating Bose-Einstein condensates

The discrete normalized gradient flow with semi-implicit time discretization (GFSI), introduced in [W. Bao and Q. Du, SIAM J. Sci. Comput., 25 (2004), pp. 1674-1697], has become one of the most widely used numerical method for computing the ground states (GS) of Bose-Einstein condensates (BECs). In spite of strong numerical evidence of its energy dissipation and global convergence, a rigorous proof of these two properties for the GFSI remains an open challenge. In this talk, by reformulating the GFSI into an equivalent form in terms of the normalized numerical solution, we will rigorously establish the energy dissipation property of the algorithm. Based on this, we then establish its global convergence to a stationary state. Furthermore, revisiting the equivalent form in its continuous version, we will propose a more efficient semi-implicit scheme to compute the GS. Mass-preserving and energy-diminishing properties of the scheme will also be proved.

唐庆粦博士毕业于新加坡国立大学，曾先后在维也纳大学、洛林大学等高校从事博士后研究；于2017年加入四川大学数学学院。曾入选四川省和国家高层次人才计划。主要从事量子物理学中的数学模型的计算方法及理论分析方面的研究，在SINUM、SISC、JCP等重要期刊上发表多篇论文，主持国家重点研发计划项目、面上项目等多项项目。