报告题目：Notes on Normalized Gradient Flow for Computing Ground States of Bose-Einstein Condensates

报 告 人：刘伟（华南师范大学）

报告时间：2021年8月25日  16:30-18:00

报告地点：数学研究中心报告厅

报告摘要：

The normalized gradient flow, i.e., the gradient flow with discrete normalization (GFDN) introduced in (W. Bao and Q. Du. SIAM J. Sci. Compul., 25 (2004), PP. 1674-1697) or the imaginary time evolution method, is one of the most popular techniques for computing the ground states of Bose-Einstein condensates (BECs). In this talk, we revisit the time discretizations for the GFDN and its generalization to the muti-component BEC. Several widely used time discretizations are demonstrated to be not accurate for computing the ground state solution in the general case, especially for the multi-component BECs with two or more constraints even for the most aceepted lincarized backward Euler schemes. More precisely, these schemes usually converge to a solution with n error depending o0 the time step sie. To accurately and efficienty compute the ground state solution of BECH we propose the gradient flow with Lagrange multiplier (GFL M) method which can be viewed the modified GFDN bhy introducing the explicit Lagrange mutiplier terms or an approximation of the confinuous normalized gradient flow (CNGE). Through analysis and numerieal computation, we elarity that, in order to aecurately compute the ground state solution, the GFDN method must be discretized in very special ways in time such the linearieed backwand Euler scheme, while the GFLM can be discretized by various schemes and works for molticomponent BEC with multiple constraint.

报告人简介：

刘伟，男，华南师范大学博士后。2010-2020年就读于湖南师范大学，分别于2014年和2020年获得学士学位和博士学位。2020年秋进入华南师范大学从事博士后研究工作。曾访问新加坡国立大学数学科学研究所、北京计算科学研究中心等国内外知名大学成科研机构。主要研究领域为计算与应用数学，研究工作沙及非线性偏微分方程多解计算、计算量子物理学、非线性色散方程的数值方法等。主要成果发表在SIAM J. Sci. Comput.、J. Comput. Phys.、 Commun. Math. Sci.、《中国科学:数学》等期刊上。2021年获批国家自然科学基金青年科学基金项目和中国博士后国际交流计划项目各1项。