Multiscale reduced basis methods for semiclassical Schrodinger equation with multiscale and random potentials

Speaker:     Prof. Jingrun Chen

Time:          Apr.29.2021 16:00-17:00

Location:    SIST 2-415

Host:            Prof. Qifeng Liao

Abstract: 
The semiclassical Schrodinger equation with multiscale and random potentials often appearswhen studying electron dynamics in heterogeneous quantum systems. As time evolves, the wavefunction develops high-frequency oscillations in both the physical space and the random space, which poses severe challenges for numerical methods. We propose a multiscale reduced basis method, where we construct multiscale reduced basis functions using an optimization method and the proper orthogonal decomposition method in the physical space and employ the quasi-Monte Carlo method in the random space. Our method is verified to be efficient: the spatial grid size is only proportional to the semiclassical parameter and (under suitable conditions) almost first order convergence rate is achieved in the random space with respect to the sample number.

Bio:

陈景润，苏州大学数学与交叉科学研究中心教授。主要研究方向为材料性质的多尺度建模、分析、算法与仿真，包括材料力学、材料磁学以及材料电学。主要工作发表在SIAM系列期刊，Math. Comp.，J. Comput. Phys.等应用与计算数学学术期刊以及Materials Horizons，Journal of Magnetism and Magnetic Materials, IEEE Transactions on Magnetics等材料领域学术期刊上。

SIST Seminar 202108