Spectral and spectral collocation methods for Hamiltonian systems

哈密​​顿系统的谱和谱搭配方法

• 批准号: 1115530
• 负责人: Zhimin Zhang
• 金额: $ 12万
• 依托单位: Wayne State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-09-01 至 2014-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1115530&HistoricalAwards=false
• 关键词: Spectral; spectral; collocation; methods; Hamiltonian

The objective of this project is to develop some robust and high accuracy numerical algorithms and related mathematical theory for Hamiltonian systems. The research efforts will be devoted to constructing "essentially" (accuracy is in a range of the computer round-off error) volume conserving (symplectic) and energy conserving algorithms. Some recent mathematical theory in spectral methods, finite element superconvergence, as well as discontinuous Galerkin methods will be employed in the project.Phenomena in different scientific disciplines such as classical mechanics, molecular dynamics, hydrodynamics, electrodynamics, plasma physics, relativity, and astronomy, etc. can be described by Hamiltonian dynamical systems. The success of the project will impact science and engineering practices. This research will widen the body of knowledge in the scientific community on both mathematical theory and practical algorithmic design. The project contains solid multi- and interdisciplinary components and has wide application in scientific computing.

本计画的目标是发展一些强健且高精度的数值演算法及相关的数学理论。研究工作将致力于构建“本质上”（精度在计算机舍入误差范围内）的体积守恒（辛）和能量守恒算法。该计划将应用谱方法、有限元超收敛和间断Galerkin方法等最新的数学理论，不同科学学科中的现象，如经典力学、分子动力学、流体力学、电动力学、等离子体物理、相对论和天文学等，都可以用Hamilton动力系统来描述。该项目的成功将影响科学和工程实践。这项研究将拓宽科学界在数学理论和实用算法设计方面的知识体系。该项目包含坚实的多学科和跨学科的组成部分，并在科学计算中有广泛的应用。