主講人：郭士民 西安交通大學(xué)教授

時(shí)間：2025年10月18日9：30

地點(diǎn)：徐匯校區(qū)三號(hào)樓332室

舉辦單位：數(shù)理學(xué)院

主講人介紹：郭士民，西安交通大學(xué)教授、博士生導(dǎo)師，主要研究方向?yàn)橛?jì)算等離子體物理、高精度數(shù)值算法；在SIAM Journal on Scientific Computing、Journal of Computational Physics等期刊上發(fā)表多篇學(xué)術(shù)論文，ESI高被引論文2篇；主持國(guó)家級(jí)青年人才類(lèi)項(xiàng)目、國(guó)家自然科學(xué)基金面上項(xiàng)目、國(guó)家重點(diǎn)研發(fā)計(jì)劃子課題、陜西省杰出青年基金等多項(xiàng)科研項(xiàng)目；榮獲陜西省自然科學(xué)獎(jiǎng)二等獎(jiǎng)、陜西省優(yōu)秀博士學(xué)位論文獎(jiǎng)等獎(jiǎng)勵(lì)。

內(nèi)容介紹：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.