Computational Challenges in Geometrical Flows: Numerical Methods and Analysis, Algorithmic Development and Software Engineering
几何流中的计算挑战:数值方法和分析、算法开发和软件工程
基本信息
- 批准号:0410266
- 负责人:
- 金额:--
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:2004
- 资助国家:美国
- 起止时间:2004-08-01 至 2008-07-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
This research is an attempt to conduct an extensive and comprehensive numerical study of geometrical flows, such as the mean curvature flow, the inverse mean curvature flow, the Gauss curvature flow, the surface diffusion flow, the Willmore flow, and the Ricci flow, from differential geometry, fluid mechanics, materials science, and cosmology, and to address theoretically and numerically challenging issues arising from geometrical flow computations. The goal of this project is to develop accurate, robust, and efficient adaptive finite element discretization methods, parallel iterative solution algorithms and computer codes for computing geometrical flows based on both level set and phase field formulations. The investigator aims to carry out a balanced numerical study for the geometrical flows by emphasizing both qualitative analysis and quantitative computation, and thus to provide reliable computational tools for discovering and analyzing fine properties such as dynamics of the singularities of the geometrical flows, which often are difficult and even may not be possible to predicate and characterize by analytical means. The methods and algorithms resulting from this research will have the following attractive features: high accuracy, strong stability, low cost, and high efficiency. In addition, the proposed methods are also capable of accurately and efficiently approximating the geometrical flows not only before but also beyond the onset of singularities.As critical applications from fluid mechanics, cosmology, and materials science are directly tied to the solutions of geometrical flows, it is expected that successful completion of the proposed research has the potential to significantly impact these applied sciences not only by presenting new methods for solving underlying mathematical problems but also providing insights for the understanding of each of these applications. Furthermore, the methods to be developed will find applications in other fields such as cell biology, geophysics, image processing, and computer vision. The educational component of the project consists of graduate graduate course development, training and mentoring both graduate and undergraduate students through the project.
本研究试图从微分几何、流体力学、材料科学和宇宙学的角度对几何流动进行广泛而全面的数值研究,包括平均曲率流、逆平均曲率流、高斯曲率流、表面扩散流、Willmore流和Ricci流,并解决几何流动计算所产生的理论和数值挑战问题。该项目的目标是开发准确、稳健和高效的自适应有限元离散方法、并行迭代求解算法和计算机代码,用于计算基于水平集和相场公式的几何流动。研究者的目标是通过强调定性分析和定量计算,对几何流动进行平衡的数值研究,从而为发现和分析几何流动奇异性的动力学等精细性质提供可靠的计算工具,这些性质往往很难甚至可能无法用分析手段来预测和表征。本研究提出的方法和算法具有精度高、稳定性强、成本低、效率高等特点。由于流体力学、宇宙学和材料科学的关键应用都直接与几何流的解联系在一起,因此,拟议的研究的成功完成有望对这些应用科学产生重大影响,不仅为解决基本的数学问题提供了新的方法,而且还为理解这些应用提供了见解。此外,即将开发的方法还将在其他领域得到应用,如细胞生物学、地球物理学、图像处理和计算机视觉。该项目的教育部分包括通过该项目开发研究生课程、培训和指导研究生和本科生。
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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Xiaobing Feng其他文献
DNNTune: Automatic Benchmarking DNN Models for Mobile-cloud Computing
DNNTune:移动云计算 DNN 模型的自动基准测试
- DOI:
10.1145/3368305 - 发表时间:
2019 - 期刊:
- 影响因子:1.6
- 作者:
Chunwei Xia;Jiacheng Zhao;Huimin Cui;Xiaobing Feng;Jingling Xue - 通讯作者:
Jingling Xue
Associations of urinary 1,3-butadiene metabolite with glucose homeostasis, prediabetes, and diabetes in the US general population: Role of alkaline phosphatase.
美国普通人群尿 1,3-丁二烯代谢物与葡萄糖稳态、糖尿病前期和糖尿病的关联:碱性磷酸酶的作用。
- DOI:
10.1016/j.envres.2023.115355 - 发表时间:
2023 - 期刊:
- 影响因子:8.3
- 作者:
Ruyi Liang;Xiaobing Feng;Da Shi;Linling Yu;Meng Yang;Min Zhou;Yongfang Zhang;Bin Wang;Weihong Chen - 通讯作者:
Weihong Chen
Depth Camera Based Fluid Reconstruction and its Solid-fluid Interaction
基于深度相机的流体重建及其固液相互作用
- DOI:
10.1145/3328756.3328761 - 发表时间:
2019 - 期刊:
- 影响因子:0
- 作者:
Xiaobing Feng;Juan Zhang;Dengming Zhu;Min Shi;Zhaoqi Wang - 通讯作者:
Zhaoqi Wang
CloudRaid: Detecting Distributed Concurrency Bugs via Log Mining and Enhancement
CloudRaid:通过日志挖掘和增强检测分布式并发错误
- DOI:
10.1109/tse.2020.2999364 - 发表时间:
2022-02 - 期刊:
- 影响因子:7.4
- 作者:
Jie Lu;Feng Li;Chen Liu;Lian Li;Xiaobing Feng;Jingling Xue - 通讯作者:
Jingling Xue
Cascade Wide Activation Multi-Scale Networks for Single Image Super-Resolution
用于单图像超分辨率的级联宽激活多尺度网络
- DOI:
- 发表时间:
2019 - 期刊:
- 影响因子:0
- 作者:
Yiwei Zhang;He Huang;Qingliang Chen;Xu Zhang;Jianxing Liang;H. Yin;Xiaobing Feng;Shasha Wang - 通讯作者:
Shasha Wang
Xiaobing Feng的其他文献
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{{ truncateString('Xiaobing Feng', 18)}}的其他基金
Novel Numerical Methods for Nonlinear Stochastic PDEs and High Dimensional Computation
非线性随机偏微分方程和高维计算的新数值方法
- 批准号:
2309626 - 财政年份:2023
- 资助金额:
-- - 项目类别:
Continuing Grant
Efficient Numerical Methods and Algorithms for Nonlinear Stochastic Partial Differential Equations
非线性随机偏微分方程的高效数值方法和算法
- 批准号:
2012414 - 财政年份:2020
- 资助金额:
-- - 项目类别:
Standard Grant
Novel numerical methods for fully nonlinear second order elliptic and parabolic Monge-Ampere and Hamilton-Jacobi-Bellman equations
全非线性二阶椭圆和抛物线 Monge-Ampere 和 Hamilton-Jacobi-Bellman 方程的新颖数值方法
- 批准号:
1620168 - 财政年份:2016
- 资助金额:
-- - 项目类别:
Continuing Grant
Novel Discontinuous Galerkin Finite Element Methods for Second Order Fully Nonlinear Equations and High Frequency Wave Equations
二阶完全非线性方程和高频波动方程的新型间断伽辽金有限元方法
- 批准号:
1318486 - 财政年份:2013
- 资助金额:
-- - 项目类别:
Standard Grant
Conference: Recent Developments in Discontinuous Galerkin Finite Element Methods for Partial Differential Equations
会议:偏微分方程不连续伽辽金有限元方法的最新进展
- 批准号:
1203237 - 财政年份:2012
- 资助金额:
-- - 项目类别:
Standard Grant
Numerical Methods and Algorithms for Fully Nonlinear Second Order Evolution Equations with Applications
全非线性二阶演化方程的数值方法和算法及其应用
- 批准号:
1016173 - 财政年份:2010
- 资助金额:
-- - 项目类别:
Continuing Grant
Numerical Methods and Algorithms for Second Order Fully Nonlinear Partial Differential Equations
二阶完全非线性偏微分方程的数值方法和算法
- 批准号:
0710831 - 财政年份:2007
- 资助金额:
-- - 项目类别:
Standard Grant
International Workshop on Computational Methods in Geosciences
地球科学计算方法国际研讨会
- 批准号:
0715713 - 财政年份:2007
- 资助金额:
-- - 项目类别:
Standard Grant
The Barrett Lectures May, 2001 "New Directions and Developments in Computational Mathematics
巴雷特讲座,2001 年 5 月“计算数学的新方向和发展
- 批准号:
0107159 - 财政年份:2001
- 资助金额:
-- - 项目类别:
Standard Grant
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