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
- 来源:
- 关键词:
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.
几何积分涉及的是保持连续动力系统几何结构的数值方法的构建。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,都是高度非线性的,对微小的扰动很敏感,并且具有影响解的定性行为的潜在几何结构。这些动力系统的混沌特性使得精确计算长时间积分的特定轨迹变得非常昂贵。因此,研究保留问题几何形状的数值方法是可取的,因为它们产生更定性准确的模拟。该项目的目标是将基于离散汉密尔顿原理的变分积分器推广到由天体动力学、分子动力学和计算力学引起的更大规模问题。这将涉及结合大规模科学计算的方法,如自适应、光谱方法、多分辨率分层技术和区域分解,同时保留哈密顿ode和偏微分方程的变分积分器的几何保存特性。复杂物理系统的计算机模拟已经成为传统实验技术的重要补充,作为验证和指导科学理论发展的工具,以及技术和工程的实际进步。这项研究将提高我们精确和有效地计算复杂系统长期行为的能力,这是合理设计药物和高性能复合材料的一个基本方面。此外,它有可能通过允许新的和创新的工业设计的快速原型直接在计算机上加速技术发展的步伐。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
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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
- DOI:
10.1007/s10883-025-09730-7 - 发表时间:
2025-02-15 - 期刊:
- 影响因子:0.800
- 作者:
Brian K. Tran;Melvin Leok - 通讯作者:
Melvin Leok
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
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三维流形的Generalized Seifert Fiber分解
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