报告题目：Hermite-Galerkin spectral method for Klein-Gordon-Schrodinger system on unbounded domains: Conservation of invariants

报 告 人：郭士民（西安交通大学）

报告时间：2024年12月13日  9:30-10:30

报告地点：腾讯会议（691203563）

报告摘要：

In this talk, we shall consider the Hermite-Galerkin spectral method for the Klein-Gordon-Schrodinger (KGS) system. First, we construct the finite difference/spectral method for the d-dimensional KGS system to conserve three of the most important invariants, namely, mass, energy, and momentum. Reganding the mass and momentum conservation laws as d+1 globally physical constrants, we carefully combine the exponential scalar auxiliary variable (ESAV) approach and Lagrange multiplier approach to construct the ESAV-Lagrange multiplier reformulation of the KGS system, thereby preserving its original energy conservation law. Secondly, for the nonlocal-in-space KGS 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，西安交通大学教授、博士生导师，主要研究方向为高精度数值算法、计算等离子体物理；在SIAM Journal on Scientific Computing、Journal of Computational Physics等期刊上发表多篇学术论文，主持国家自然科学基金面上项目、国家重点研发计划子课题等多项科研项目；博士学位论文入选“2016年度陕西省优秀博士学位论文”，荣获2019年度陕西省自然科学奖二等奖。