Developing Energy-Conserving Deterministic Solvers for Kinetic Electromagnetic Plasma Simulations
开发用于动力学电磁等离子体模拟的节能确定性求解器
基本信息
- 批准号:1318186
- 负责人:
- 金额:$ 14.27万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:2013
- 资助国家:美国
- 起止时间:2013-07-01 至 2016-06-30
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
In this proposal, the investigator plans to develop and analyze a class of energy-conserving deterministic solvers for kinetic electromagnetic plasma simulations. The proposed methods have several features that overcome the difficulties of many traditional solvers: it conserves the total particle number and energy of the system; it has a systematic way to incorporate explicit or implicit time stepping depending on the stiffness of the equations; and it is designed for implementations on unstructured grids for complex geometries in the physical space. To achieve the objective, the research topics include a range of analytical and computational subjects. The investigator proposes to design a new energy-conserving splitting for the coupled Vlasov-Maxwell system, so that the splitted equations still maintain energy conservation and can be computed in reduced dimensions. The investigator plans to set up a general framework to incorporate various type of energy-conserving temporal and spatial discretizations. Methods to further improve computational efficiency by using various local basis, local time stepping and hybrid solvers will be explored. Issues on how to enforce charge continuity and positivity will be addressed. Analytical aspects such as the numerical dispersion relation, stability and error estimates will be considered.The proposed activity lies between algorithm development, analysis and applications. The resulting numerical schemes can be applied to a wide range of plasma simulations. The theoretical studies will provide foundation and guidance to the design of such numerical methods. The broader impacts of the proposed activity will be its interdisciplinary outreach and educational components. The proposed research is multidisciplinary in its nature. The investigator actively interacts and consults with faculty members in physics, electrical engineering departments. Training opportunities for students and postdocs will be provided. Computational math curriculum development will be incorporated.
在这项提案中,研究人员计划开发和分析一类节能的确定性求解器,用于动态电磁等离子体模拟。所提出的方法克服了许多传统求解方法的困难:它节省了系统的总粒子数和能量;它有一个系统的方法来结合显式或隐式时间步进取决于方程的刚度;它是为物理空间中复杂几何图形的非结构化网格实现而设计的。为了实现这一目标,研究课题包括一系列的分析和计算课题。研究者提出对耦合Vlasov-Maxwell系统设计一种新的节能分裂,使分裂后的方程仍然保持能量守恒,并且可以进行降维计算。研究者计划建立一个综合各种类型的节能时间和空间离散化的总体框架。将探索利用各种局部基、局部时间步进和混合求解方法进一步提高计算效率的方法。将讨论如何加强电荷连续性和正性的问题。分析方面,如数值色散关系,稳定性和误差估计将被考虑。提议的活动介于算法开发、分析和应用之间。所得到的数值格式可广泛应用于等离子体模拟。理论研究将为此类数值方法的设计提供依据和指导。拟议活动的更广泛影响将是其跨学科的推广和教育内容。拟议的研究本质上是多学科的。研究者积极地与物理系、电子工程系的教员进行互动和咨询。为学生和博士后提供培训机会。计算数学课程的发展将被纳入。
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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Yingda Cheng其他文献
Numerical study of one-dimensional Vlasov–Poisson equations for infinite homogeneous stellar systems
无限均匀恒星系统一维Vlasov-Poisson方程的数值研究
- DOI:
- 发表时间:
2012 - 期刊:
- 影响因子:0
- 作者:
Yingda Cheng;I. Gamba - 通讯作者:
I. Gamba
Energy Stable Nodal Discontinuous Galerkin Methods for Nonlinear Maxwell's Equations in Multi-dimensions
- DOI:
https://doi.org/10.1007/s10915-021-01651-4 - 发表时间:
2021 - 期刊:
- 影响因子:
- 作者:
Maohui Lyu;Vrushali A. Bokil;Yingda Cheng;Fengyan Li - 通讯作者:
Fengyan Li
Kraus is king: High-order completely positive and trace preserving (CPTP) low rank method for the Lindblad master equation
克劳斯是王者:用于林德布拉德主方程的高阶完全正且保迹(CPTP)低秩方法
- DOI:
10.1016/j.jcp.2025.114036 - 发表时间:
2025-08-01 - 期刊:
- 影响因子:3.800
- 作者:
Daniel Appelö;Yingda Cheng - 通讯作者:
Yingda Cheng
An adaptive high-order piecewise polynomial based sparse grid collocation method with applications
基于自适应高阶分段多项式的稀疏网格配置方法及其应用
- DOI:
10.1016/j.jcp.2020.109770 - 发表时间:
2019-12 - 期刊:
- 影响因子:0
- 作者:
Zhanjing Tao;Yan Jiang;Yingda Cheng - 通讯作者:
Yingda Cheng
Discontinuous Galerkin methods for the Boltzmann‐Poisson systems in semiconductor device simulations
半导体器件模拟中玻尔兹曼-泊松系统的不连续伽辽金方法
- DOI:
- 发表时间:
2011 - 期刊:
- 影响因子:0
- 作者:
Yingda Cheng;I. Gamba;A. Majorana;Chi - 通讯作者:
Chi
Yingda Cheng的其他文献
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{{ truncateString('Yingda Cheng', 18)}}的其他基金
Development of Adaptive Sparse Grid Discontinuous Galerkin Methods for Multiscale Kinetic Simulations in Plasmas
等离子体多尺度动力学模拟的自适应稀疏网格间断伽辽金方法的发展
- 批准号:
2404521 - 财政年份:2023
- 资助金额:
$ 14.27万 - 项目类别:
Standard Grant
Development of Adaptive Sparse Grid Discontinuous Galerkin Methods for Multiscale Kinetic Simulations in Plasmas
等离子体多尺度动力学模拟的自适应稀疏网格间断伽辽金方法的发展
- 批准号:
2011838 - 财政年份:2020
- 资助金额:
$ 14.27万 - 项目类别:
Standard Grant
OP: Collaborative Research: Compatible Discretizations for Maxwell Models in Nonlinear Optics
OP:协作研究:非线性光学中麦克斯韦模型的兼容离散化
- 批准号:
1720023 - 财政年份:2017
- 资助金额:
$ 14.27万 - 项目类别:
Continuing Grant
CAREER: Development of Discontinuous Galerkin Methods for Kinetic Equations in High Dimensions
职业:高维动力学方程不连续伽辽金方法的发展
- 批准号:
1453661 - 财政年份:2015
- 资助金额:
$ 14.27万 - 项目类别:
Continuing Grant
Development of Discontinuous Galerkin Methods for Kinetic Transport Models and Control Problems with State Constraints
动态输运模型和状态约束控制问题的不连续伽辽金方法的发展
- 批准号:
1217563 - 财政年份:2011
- 资助金额:
$ 14.27万 - 项目类别:
Standard Grant
Development of Discontinuous Galerkin Methods for Kinetic Transport Models and Control Problems with State Constraints
动态输运模型和状态约束控制问题的不连续伽辽金方法的发展
- 批准号:
1016001 - 财政年份:2010
- 资助金额:
$ 14.27万 - 项目类别:
Standard Grant
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