Numerical Methods and Analysis for Multiscale Kinetic Equations with Uncertainties
具有不确定性的多尺度动力学方程的数值方法与分析
基本信息
- 批准号:1819012
- 负责人:
- 金额:$ 29.28万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Continuing Grant
- 财政年份:2018
- 资助国家:美国
- 起止时间:2018-07-01 至 2018-08-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
Kinetic models provide the bridges between microscopic and macroscopic descriptions for physical systems; they have a wide range of applications, including astronautics, nuclear engineering, plasma physics, and semiconductor device modeling. These models often involve multiple time and spatial scales, which pose tremendous difficulties in numerical simulations. Moreover, since kinetic models arise from approximations, there are intrinsic uncertainties in the equations employed and the data (initial conditions and boundary values) used. This project aims to develop efficient numerical methods and to conduct analysis for multiscale and uncertain kinetic equations. The questions under study concern fundamental issues in scientific and engineering computation in the modern age -- multiscale modeling and simulation and uncertainty quantification. Some of the research results are expected to provide excellent additions for graduate courses in applied mathematics and scientific computing, thus contributing to training of the future generation of researchers in modern applied mathematics and scientific computing.The project aims to develop and analyze numerical methods for multiscale kinetic equations with uncertainties. The work addresses the numerical challenges of multiple time and spatial scales as well as intrinsic model uncertainties in collision kernels, scattering coefficients, initial and boundary data, forcing and source terms, etc. The investigator plans to tackle these numerical challenges via several computational and analytical tools: asymptotic-preserving schemes to deal with multiple scales; polynomial chaos expansion and stochastic Galerkin (and other non-intrusive) methods for the random uncertainties; and hypocoercivity theory to study the regularity, stability, sensitivity, and long-time behavior of these methods. The hypocoercivity analysis provides new numerical analysis tools to study a wide class of physically important nonlinear partial differential equations in mathematical physics.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
动力学模型提供了物理系统的微观和宏观描述之间的桥梁;它们具有广泛的应用,包括物理学,核工程,等离子体物理和半导体器件建模。这些模型往往涉及多个时间和空间尺度,这给数值模拟带来了巨大的困难。 此外,由于动力学模型来自近似,在所采用的方程和所使用的数据(初始条件和边界值)中存在固有的不确定性。 本计画旨在发展有效的数值方法,并对多尺度及不确定性的动力学方程进行分析。 研究的问题涉及现代科学和工程计算的基本问题-多尺度建模和模拟以及不确定性量化。部分研究成果将为应用数学和科学计算研究生课程提供很好的补充,从而有助于培养现代应用数学和科学计算的未来一代研究人员。本项目旨在开发和分析具有不确定性的多尺度动力学方程的数值方法。该工作解决了多时间和空间尺度以及碰撞核,散射系数,初始和边界数据,强迫和源项等内在模型不确定性的数值挑战。研究者计划通过几种计算和分析工具来解决这些数值挑战:处理多尺度的渐近保持方案;多项式混沌展开和随机Galerkin(和其他非侵入性)方法的随机不确定性;和hypovervivity理论研究这些方法的规律性,稳定性,灵敏度和长期行为。次优性分析提供了新的数值分析工具,用于研究数学物理学中广泛的一类重要物理非线性偏微分方程。该奖项反映了NSF的法定使命,并通过使用基金会的智力价值和更广泛的影响审查标准进行评估,被认为值得支持。
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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Shi Jin其他文献
OFDM/OQAM based WDM fiber VLLC system employing improved channel estimation method
基于 OFDM/OQAM 的 WDM 光纤 VLLC 系统采用改进的信道估计方法
- DOI:
10.1016/j.optcom.2018.07.034 - 发表时间:
2018-11 - 期刊:
- 影响因子:2.4
- 作者:
Shi Jin;He Jing;Zhang Rui;Deng Rui;Xiao Yaoqiang - 通讯作者:
Xiao Yaoqiang
A scalable parallel algorithm for the direct numerical simulation of three-dimensional incompressible particulate flow
三维不可压缩颗粒流直接数值模拟的可扩展并行算法
- DOI:
10.1080/10618560902973748 - 发表时间:
2009 - 期刊:
- 影响因子:1.3
- 作者:
Shi Jin;P. Minev;K. Nandakumar - 通讯作者:
K. Nandakumar
Multiuser Massive MIMO AF Relaying: Spectral Efficiency and Power Allocation
多用户大规模 MIMO AF 中继:频谱效率和功率分配
- DOI:
10.1109/access.2018.2816560 - 发表时间:
2018-03 - 期刊:
- 影响因子:3.9
- 作者:
Xi Yang;Tiecheng Song;Wei Xu;Shi Jin;Xuesong Liang - 通讯作者:
Xuesong Liang
Demonstration of Real-Time Software Reconfigurable Dynamic Power-and-Subcarrier Allocation Scheme for OFDM-NOMA-Based Multi-User Visible Light Communications
基于 OFDM-NOMA 的多用户可见光通信的实时软件可重构动态功率和子载波分配方案演示
- DOI:
10.1109/jlt.2019.2924935 - 发表时间:
2019-09 - 期刊:
- 影响因子:4.7
- 作者:
Shi Jin;Hong Yang;Deng Rui;He Jing;Chen Lian-Kuan;Chang Gee-Kung - 通讯作者:
Chang Gee-Kung
Numerical Integrations of Systems of Conservation Laws of Mixed Type
混合型守恒定律系统的数值积分
- DOI:
10.1137/s0036139994268371 - 发表时间:
1995 - 期刊:
- 影响因子:0
- 作者:
Shi Jin - 通讯作者:
Shi Jin
Shi Jin的其他文献
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{{ truncateString('Shi Jin', 18)}}的其他基金
Multiscale Computational Methods for Semiclassical Schrodinger Equations
半经典薛定谔方程的多尺度计算方法
- 批准号:
1114546 - 财政年份:2011
- 资助金额:
$ 29.28万 - 项目类别:
Continuing Grant
FRG: Collaborative Research: Kinetic Description of Multiscale Phenomena: Modeling, Theory and Computation
FRG:协作研究:多尺度现象的动力学描述:建模、理论和计算
- 批准号:
0757285 - 财政年份:2008
- 资助金额:
$ 29.28万 - 项目类别:
Standard Grant
Computation of Multiscaled and Multivalued Solutions to High Frequency Waves in Multimedia
多媒体高频波的多尺度多值解计算
- 批准号:
0608720 - 财政年份:2006
- 资助金额:
$ 29.28万 - 项目类别:
Continuing Grant
Numerical Methods for Multiscale Physical Problems
多尺度物理问题的数值方法
- 批准号:
0305081 - 财政年份:2003
- 资助金额:
$ 29.28万 - 项目类别:
Standard Grant
Numerical Methods for Hyperbolic Systems and Related Problems
双曲系统的数值方法及相关问题
- 批准号:
9704957 - 财政年份:1997
- 资助金额:
$ 29.28万 - 项目类别:
Standard Grant
Mathematical Sciences: NSF-CBMS Regional Conference on Shock Wave Theory, June 9-13, 1997
数学科学:NSF-CBMS 冲击波理论区域会议,1997 年 6 月 9-13 日
- 批准号:
9634874 - 财政年份:1997
- 资助金额:
$ 29.28万 - 项目类别:
Standard Grant
Mathematical Sciences: Numerical Methods for Hyperbolic Systems
数学科学:双曲系统的数值方法
- 批准号:
9404157 - 财政年份:1994
- 资助金额:
$ 29.28万 - 项目类别:
Standard Grant
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