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蔡勇勇教授:Normalized gradient flow for computing ground states of Bose -- Einstein condensates

本站小编 Free考研考试/2021-12-26


Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars
Speaker: 蔡勇勇教授，北京师范大学
Inviter:
Title:
 Normalized gradient flow for computing ground states of Bose -- Einstein condensates
Time & Venue:
 2021.06.18 09:00-22:30 南楼208
Abstract:
 The normalized gradient flow, i.e. the gradient flow with discrete normalization (GFDN) introduced in by W. Bao and Q. Du (or the 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 multi-component BECs. Several widely used time discretizations are demonstrated 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 accepted linearized backward Euler schemes. More precisely, these schemes usually converge to a solution with an error depending on the time step size. To accurately and efficiently compute the ground state solution of BECs, we propose the gradient flow with Lagrange multiplier (GFLM) method which can be viewed as the modified GFDN by introducing the explicit Lagrange multiplier terms or an approximation of the continuous normalized gradient flow (CNGF).

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