模拟超强短脉冲激光与物质相互作用的高效数值方法及其应用

项目名称： 模拟超强短脉冲激光与物质相互作用的高效数值方法及其应用

项目编号： No.11261065

项目类型： 地区科学基金项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 王汉权

作者单位： 云南财经大学

项目金额： 45万元

中文摘要： 超强短脉冲激光与基本物质（例如原子、分子、团族和等离子体）的相互作用是目前国内国际上非常活跃的前沿研究领域之一。描述二者关系有许多物理理论，例如量子理论、半经典理论、经典理论、运动理论和流体理论等。这些理论为二者相互作用原理提出了许多极端条件下的偏微分方程模型。这些模型显有解析解，而传统的数值方法在数值求解它们时都会遇到或多或少的困难，需要改进和完善。本项目一方面旨在为这些物理理论所提出的偏微分方程模型设计高精度且实用的数值方法,包括求解含时的单粒子薛定谔方程的数值方法、求解含时的多粒子薛定谔方程的数值解法、求解耦合的弗拉索夫（或弗拉索夫-福克-普朗克）方程和麦克斯韦方程组的时间分裂谱方法与格子中含粒子法、求解耦合的流体方程组与麦克斯韦方程组的时间分裂谱方法；另一方面利用所设计的数值方法来模拟二者相互作用后形成的粒子（电子、离子、中子等）运动机理，模拟解释二者相互作用后出现的各种物理现象。

中文关键词： 激光与物质相互作用；薛定谔方程；弗拉索夫方程；克斯韦方程组；谱方法

英文摘要： The interaction between intense short pulse laser with matter(atoms,molecules,clusters and plasma) is one of the most active research fields and one of frontiers both in China and in the world. Many theory in Physic including quantum mechanics, semi-classical theory, classical theory, kinetic theory and fluid theory have successfully explained their interaction. To describe their interaction, physical theory has proposed many partial differential equations in extreme conditions. These mathematical models can rarely be solved exactly and problems have arisen when those traditional numerical methods are applied to solve them numerically. Therefore we need to improve and modify those old numerical methods for our need. In this project, on one hand, we design efficient and higher-order numerical methods for those mathematical models proposed in Physics, such as novel numerical methods for solving time-dependent Schr?dinger equation with either single electron or many electrons,coupled time-splitting spectral method and particle in cell method for Vlasov equation and Maxwell equations,coupled spectral methods and semi-Lagrangian finite difference method for Vlasov-Fokker-Planck equation and Maxwell equations, time-splitting spectral methods for two-fluid Navier-Stoke equations and Maxwell equations. On the other hand

英文关键词： laser-matter interaction；Schrodinger equation；Vlasov equation；Maxwell equation；spectral method