*主持人：朱升峰 教授

*讲座内容简介：
Numerical resolution for 6-D Wigner dynamics under the Coulomb potential faces with the combined challenges of high dimensionality, nonlocality, oscillation and singularity. In particular, the extremely huge memory storage of 6-D grids hinders the usage of all existing deterministic numerical scheme, which is well-known as the curse of dimensionality. To surmount these difficulties, we propose a massively parallel solver, termed the Characteristic-Spectral-Mixed (CHASM) scheme, by fully exploiting two distinct features of the Wigner equation: Locality of spatial advection and nonlocality of quantum interaction. Our scheme utilizes the local cubic B-spline basis to interpolate the local spatial advection. The key is to use a perfectly matched boundary condition to give a closure of spline coefficients, so that distributed pieces can recover the global one as accurately as possible owing to the rapid decay of wavelet basis in the dual space, and communication costs are significantly reduced. To resolve the nonlocal pseudodifferential operator with weakly singular symbol, CHASM further adopts the truncated kernel method to attain a highly efficient approximation. Several typical experiments including the quantum harmonic oscillator and Hydrogen 1s state demonstrate the accuracy and efficiency of CHASM. The non-equilibrium electron-proton couplings are also clearly displayed and reveal the uncertainty principle and quantum tunneling in phase space. Finally, the scalability of CHASM up to 16000 cores is presented. This is a joint work with Prof. Yong Zhang at Tianjin University and Prof. Sihong Shao at Peking University.

*主讲人简介：
熊云丰博士2020年毕业于北京大学，获理学博士学位，目前为北京大学博雅博士后，主要研究方向为高维问题的数值方法，包括谱方法和随机粒子方法在高维偏微分方程、随机系统中的应用。目前在国际权威期刊SIAM Journal on Numerical Analysis，SIAM Journal on Scientific Computing， Journal of Computational Physics, Entropy上发表论文多篇。熊云丰博士目前或国家自然基金委青年科学基金项目、中国博士后科学基金会等资助。