报告题目：A splitting Chebyshev collocation method for Schr\"{o}dinger-Poisson system

报 告 人：王汉权教授（云南财经大学）

报告时间：2018年4月19日 14:30-15:30

报告地点：数统院302学术报告厅

报告摘要：

We develop a splitting Chebyshev collocation (SCC) method for the time-dependant Schr\"{o}dinger-Poisson (SP) system arising from theoretical analysis of quantum plasmas. By means of splitting technique in time, the time-dependant SP system is first reduced to uncoupled Schr\"{o}dinger and Poisson equations at every time step. The space variables in Schr\"{o}dinger and Poisson equations are next represented by high-order Chebyshev polynomials, and the resulting system are discretized by the spectral collocation method. Finally, matrix diagonalization technique is applied to solve the fully discretized system in one dimension, two dimensions and three dimensions, respectively. The newly proposed method not only achieves spectral accuracy in space, but also reduces the computer-memory requirements and the computational time in comparison with conventional solver. Numerical results confirm the spectral accuracy and efficiency of this method, and indicate that the SCC method could be an efficient alternative method for simulating the dynamics of quantum plasmas. Some extension of the proposed method will be briefed too.

报告人简介：

王汉权，现任云南财经大学统计与数学学院特聘教授、云南财经大学统计与数学学院数学专业硕士生导师、云南财经大学统计与数学学院副院长、中国工业与应用数学学会会员、中国计算数学学会会员，2013年入选教育部新世纪优秀人才。曾担任多个国际计算数学期刊论文的通信评审人。在SIAM J. Numer. Anal., SIAM J. Math. Anal., J. Comput. Phys.等杂志发表论文30余篇。