Hermite-Galerkin spectral method for Schr?dinger-type systems on unbounded domains: conservation of invariants

主讲人：郭士民 西安交通大学教授

时间：2025年10月18日9：30

地点：徐汇校区三号楼332室

举办单位：数理学院

主讲人介绍：郭士民，西安交通大学教授、博士生导师，主要研究方向为计算等离子体物理、高精度数值算法；在SIAM Journal on Scientific Computing、Journal of Computational Physics等期刊上发表多篇学术论文，ESI高被引论文2篇；主持国家级青年人才类项目、国家自然科学基金面上项目、国家重点研发计划子课题、陕西省杰出青年基金等多项科研项目；荣获陕西省自然科学奖二等奖、陕西省优秀博士学位论文奖等奖励。

内容介绍：In this talk, we shall consider the Hermite-Galerkin spectral method for the Schr?dinger equation with wave operator. First, we construct the finite difference/spectral method for the d-dimensional Schr?dinger equation with wave operator to conserve three of the most important invariants, namely, mass, energy, and momentum. Regarding the mass and momentum conservation laws as d+1 globally physical constraints, we carefully combine the exponential scalar auxiliary variable (ESAV) approach and the Lagrange multiplier approach to construct the ESAV-Lagrange multiplier reformulation of the equation, thereby preserving the energy conservation law. Secondly, for the nonlocal-in-space Klein-Gordon-Schr?dinger system in multi- dimensional unbounded domains, we use the Hermite-Galerkin spectral method with a scaling factor for spatial approximation and the Crank-Nicolson scheme for temporal discretization, which conserves the nonlocal energy at the fully discrete level.