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Talk of Dr. Yongyong Cai

Yongyong Cai

蔡勇勇

蔡勇勇博士,本科和硕士就读于北京大学,2012年在新加坡国立大学获得博士学位。他先后在威斯康辛大学麦迪逊分校、马里兰大学帕克分校和普渡大学从事博士后研究工作。从2016年5月起,他在北京计算科学研究中心任特聘研究员,入选第12批青年千人。蔡勇勇博士的研究兴趣主要是偏微分方程的数值方法及其应用。

Title

Numerical methods for Bogoliubov excitations of Bose-Einstein condensates

Abstract

We study the analytical properties and the numerical methods for the Bogoliubov-de Gennes equations (BdGEs) describing the elementary excitation of Bose-Einstein condensates around the mean field ground state, which is governed by the Gross-Pitaevskii equation (GPE). Derived analytical properties of BdGEs can serve as benchmark tests for numerical algorithms and three numerical methods are proposed to solve the BdGEs, including sine-spectral method, central finite difference method and compact finite difference method. Extensive numerical tests are provided to validate the algorithms and confirm that the sine-spectral method has spectral accuracy in spatial discretization, while the central finite difference method and the compact finite difference method are second-order and fourth-order accurate, respectively. Finally, sine spectral method is extended to study the elementary excitations under optical lattice potential and solve the BdGEs around the first excited states of the GPE. The numerical experiments demonstrate the efficiency and accuracy of the proposed methods for solving BdGEs.

Date

2019年5月24日,14:00-14:45

Location

数学科学学院604室

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