LTB: Generalized Variational Integrators for Large-Scale Scientific Computation

LTB:用于大规模科学计算的广义变分积分器

基本信息

  • 批准号:
    1001521
  • 负责人:
  • 金额:
    $ 13.11万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Standard Grant
  • 财政年份:
    2009
  • 资助国家:
    美国
  • 起止时间:
    2009-09-04 至 2011-08-31
  • 项目状态:
    已结题

项目摘要

Geometric integration is concerned with the construction of numerical methods that preserve the geometric structure of a continuous dynamical system. Many problems arising in science and engineering, such as solar system dynamics and molecular dynamics, are highly nonlinear, sensitive to small perturbations, and have underlying geometric structure that affects the qualitative behavior of solutions. The chaotic properties of these dynamical systems render prohibitively expensive the accurate computation of particular trajectories for long-time integration. As such, it is instead desirable to study numerical methods that preserve the geometry of a problem as they yield more qualitatively accurate simulations. The goal of this project is to generalize variational integrators based on a discrete Hamilton's principle to larger-scale problems arising from astrodynamics, molecular dynamics, and computational mechanics. This will involve incorporating methods from large-scale scientific computation, such as adaptivity, spectral methods, multi-resolution hierarchical techniques, and domain decomposition, while retaining the geometric preservation properties of variational integrators for Hamiltonian ODEs and PDEs.Computer simulations of complex physical systems have become an increasingly important complement to traditional experimental techniques as a tool for validating and guiding theoretical developments in science, as well as practical advances in technology and engineering. This research will improve our ability to accurately and efficiently compute the long-time behavior of complex systems, which is a fundamental aspect of the rational design of pharmaceuticals and high-performance composite materials. In addition, it has the potential to accelerate the pace of technological development by allowing the rapid prototyping of new and innovative industrial designs directly on the computer.
几何积分关注的是保持连续动力系统几何结构的数值方法的构造。在科学和工程中出现的许多问题,如太阳系动力学和分子动力学,是高度非线性的,对小扰动敏感,并具有潜在的几何结构,影响解决方案的定性行为。这些动力系统的混沌特性使得长时间积分的特定轨迹的精确计算过于昂贵。因此,相反,希望研究保留问题的几何形状的数值方法,因为它们产生更定性准确的模拟。这个项目的目标是推广基于离散汉密尔顿原理的变分积分器,以解决天体动力学、分子动力学和计算力学中的大规模问题。这将涉及纳入大规模科学计算的方法,如自适应性,光谱方法,多分辨率分层技术和区域分解,同时保留了Hamilton常微分方程和偏微分方程的变分积分器的几何保持性质。复杂物理系统的计算机模拟作为验证和指导理论的工具,已经成为传统实验技术的日益重要的补充。科学的发展,以及技术和工程的实际进展。这项研究将提高我们准确有效地计算复杂系统长期行为的能力,这是药物和高性能复合材料合理设计的一个基本方面。此外,它有可能通过允许直接在计算机上快速原型制作新的和创新的工业设计来加快技术发展的步伐。

项目成果

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Melvin Leok其他文献

Safe Stabilizing Control for Polygonal Robots in Dynamic Elliptical Environments
动态椭圆环境中多边形机器人的安全稳定控制
  • DOI:
  • 发表时间:
    2023
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Kehan Long;Khoa Tran;Melvin Leok;Nikolay Atanasov
  • 通讯作者:
    Nikolay Atanasov
On Properties of Adjoint Systems for Evolutionary PDEs
演化偏微分方程伴随系统的性质
  • DOI:
  • 发表时间:
    2024
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Brian K. Tran;Benjamin Southworth;Melvin Leok
  • 通讯作者:
    Melvin Leok
A Type II Hamiltonian Variational Principle and Adjoint Systems for Lie Groups

Melvin Leok的其他文献

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{{ truncateString('Melvin Leok', 18)}}的其他基金

Hierarchical Geometric Accelerated Optimization, Collision-based Constraint Satisfaction, and Sensitivity Analysis for VLSI Chip Design
VLSI 芯片设计的分层几何加速优化、基于碰撞的约束满足和灵敏度分析
  • 批准号:
    2307801
  • 财政年份:
    2023
  • 资助金额:
    $ 13.11万
  • 项目类别:
    Standard Grant
Geometric Numerical Integration of Plasma Physics and General Relativity
等离子体物理与广义相对论的几何数值积分
  • 批准号:
    1813635
  • 财政年份:
    2018
  • 资助金额:
    $ 13.11万
  • 项目类别:
    Standard Grant
Geometric Numerical Discretizations of Gauge Field Theories and Interconnected Systems
规范场论和互连系统的几何数值离散
  • 批准号:
    1411792
  • 财政年份:
    2014
  • 资助金额:
    $ 13.11万
  • 项目类别:
    Standard Grant
Collaborative Research: Ergodic Trajectories in Discrete Mechanics
协作研究:离散力学中的遍历轨迹
  • 批准号:
    1334759
  • 财政年份:
    2013
  • 资助金额:
    $ 13.11万
  • 项目类别:
    Standard Grant
Collaborative Research: Computational Geometric Uncertainty Propagation for Hamiltonian Systems on a Lie Group
合作研究:李群上哈密顿系统的计算几何不确定性传播
  • 批准号:
    1029445
  • 财政年份:
    2010
  • 资助金额:
    $ 13.11万
  • 项目类别:
    Standard Grant
CAREER: Computational Geometric Mechanics: Foundations, Computation, and Applications
职业:计算几何力学:基础、计算和应用
  • 批准号:
    1010687
  • 财政年份:
    2009
  • 资助金额:
    $ 13.11万
  • 项目类别:
    Continuing Grant
CAREER: Computational Geometric Mechanics: Foundations, Computation, and Applications
职业:计算几何力学:基础、计算和应用
  • 批准号:
    0747659
  • 财政年份:
    2008
  • 资助金额:
    $ 13.11万
  • 项目类别:
    Continuing Grant
LTB: Generalized Variational Integrators for Large-Scale Scientific Computation
LTB:用于大规模科学计算的广义变分积分器
  • 批准号:
    0714223
  • 财政年份:
    2007
  • 资助金额:
    $ 13.11万
  • 项目类别:
    Standard Grant
Computational Geometric Mechanics and its Applications to Geometric Control Theory
计算几何力学及其在几何控制理论中的应用
  • 批准号:
    0726263
  • 财政年份:
    2007
  • 资助金额:
    $ 13.11万
  • 项目类别:
    Standard Grant
Computational Geometric Mechanics and its Applications to Geometric Control Theory
计算几何力学及其在几何控制理论中的应用
  • 批准号:
    0504747
  • 财政年份:
    2005
  • 资助金额:
    $ 13.11万
  • 项目类别:
    Standard Grant

相似国自然基金

三维流形的Generalized Seifert Fiber分解
  • 批准号:
    11526046
  • 批准年份:
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  • 资助金额:
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"Nonsmooth dynamics associated to variational inequalities, generalized Nash games and applications"
“与变分不等式相关的非光滑动力学、广义纳什博弈和应用”
  • 批准号:
    262899-2012
  • 财政年份:
    2016
  • 资助金额:
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  • 项目类别:
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"Nonsmooth dynamics associated to variational inequalities, generalized Nash games and applications"
“与变分不等式相关的非光滑动力学、广义纳什博弈和应用”
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"Nonsmooth dynamics associated to variational inequalities, generalized Nash games and applications"
“与变分不等式相关的非光滑动力学、广义纳什博弈和应用”
  • 批准号:
    262899-2012
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    2014
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  • 项目类别:
    Discovery Grants Program - Individual
"Nonsmooth dynamics associated to variational inequalities, generalized Nash games and applications"
“与变分不等式相关的非光滑动力学、广义纳什博弈和应用”
  • 批准号:
    262899-2012
  • 财政年份:
    2013
  • 资助金额:
    $ 13.11万
  • 项目类别:
    Discovery Grants Program - Individual
"Nonsmooth dynamics associated to variational inequalities, generalized Nash games and applications"
“与变分不等式相关的非光滑动力学、广义纳什博弈和应用”
  • 批准号:
    262899-2012
  • 财政年份:
    2012
  • 资助金额:
    $ 13.11万
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    Discovery Grants Program - Individual
Development and implementation of numerical algorithm for variational methods and generalized gradient flows for geometric evolution problems of higher order for surface processing in computer graphics
计算机图形学表面处理高阶几何演化问题的变分法和广义梯度流数值算法的开发和实现
  • 批准号:
    190140394
  • 财政年份:
    2010
  • 资助金额:
    $ 13.11万
  • 项目类别:
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LTB: Generalized Variational Integrators for Large-Scale Scientific Computation
LTB:用于大规模科学计算的广义变分积分器
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An analysis of dissipative phenomena and intermittency in complex systems via a generalized variational principle
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  • 批准号:
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Minimax inequalities and fixed point theorems, equilibria of abstract economies and iterative solutions of generalized variational inequalities
极小极大不等式和不动点定理、抽象经济的均衡和广义变分不等式的迭代解
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