学术报告20251208：Hermite-Galerkin spectral method for Schrödinger-type systems on unbounded domains: Conservation of invariants

报告人：郭士民 教授 西安交通大学

报告题目：Hermite-Galerkin spectral method for Schrödinger-type systems on unbounded domains: Conservation of invariants

摘 要：In this talk, we shall consider the Hermite-Galerkin spectral method for the Schrödinger equation with wave operator. First, we construct the finite difference/spectral method for the d-dimensional Schrödinger 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-Schrödinger 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.

报告人简介：郭士民教授，西安交通大学、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；主持国家青年拔尖人才项目、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。

报告时间：2025年12月8日，09:15--12:15

报告地点：腾讯会议（会议号：627-694-067）

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内蒙古大学数学科学学院

2025年12月3日