Novel Finite Element Methods for Nonlinear Eigenvalue Problems - A Holomorphic Operator-Valued Function Approach
非线性特征值问题的新颖有限元方法 - 全纯算子值函数方法
基本信息
- 批准号:2109949
- 负责人:
- 金额:$ 10万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:2023
- 资助国家:美国
- 起止时间:2023-09-01 至 2026-08-31
- 项目状态:未结题
- 来源:
- 关键词:
项目摘要
Eigenvalue problems of partial differential equations have many important applications in science and engineering, e.g., design of solar cells for clean energy, calculation of electronic structure in condensed matter, extraordinary optical transmission, non-destructive testing, photonic crystals, and biological sensing. Due to the flexibility in treating complex structures and rigorous theoretical justification, finite element methods have been widely used to compute eigenvalue problems. The study of the finite element methods for linear eigenvalue problems started in the 1970s and has been an active research area since then. The main functional analysis tool is the spectral perturbation theory for linear operators. In contrast, for nonlinear eigenvalue problems, a systematic numerical approach does not exist. Effective finite element methods are highly desirable. Both graduate and undergraduate students are expected to receive training in the topics of analysis, modeling, and programming.This project focuses on the development of new finite element methods for nonlinear eigenvalue problems. These problems are recast as the eigenvalue problems of holomorphic Fredholm operator functions. The convergence will be analyzed using the abstract operator approximation theory. Effective numerical methods will be developed to compute the eigenvalues and/or eigenvectors for practical applications. Two important model problems will be studied: the band structure calculation of dispersive photonic crystals and the transmission eigenvalue problem for anisotropic media. Since the eigenvalues of nonlinear problems are complex in general, efficient algorithms to search eigenvalues on the complex plane for large problems in three dimensions will be developed. The novelty is the combination of the spectral theory for holomorphic operator functions and the finite element approximations. The results will advance the finite element theory and enable the scientists and engineers to effectively compute nonlinear eigenvalue problems. The project will also provide a new approach to prove the convergence of finite element methods (both conforming and non-conforming) for linear eigenvalue problems.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.
偏微分方程本征值问题在科学和工程中有许多重要的应用,如清洁能源太阳能电池的设计、凝聚态电子结构的计算、特殊光传输、无损检测、光子晶体和生物传感。由于处理复杂结构的灵活性和严格的理论论证,有限元方法已被广泛应用于特征值问题的计算。线性特征值问题的有限元方法的研究始于20世纪70年代,此后一直是一个活跃的研究领域。主要的泛函分析工具是线性算子的谱微扰理论。相比之下,对于非线性特征值问题,并不存在系统的数值方法。有效的有限元方法是非常必要的。研究生和本科生都应该接受分析、建模和编程方面的培训。这个项目专注于非线性特征值问题的新的有限元方法的发展。这些问题被转化为全纯Fredholm型算子函数的特征值问题。我们将使用抽象算子逼近理论来分析收敛。将开发有效的数值方法来计算实际应用中的特征值和/或特征向量。我们将研究两个重要的模型问题:色散光子晶体的能带结构计算和各向异性介质的传输本征值问题。由于非线性问题的特征值一般是复杂的,因此将发展有效的算法在复平面上搜索三维大型问题的特征值。其新颖之处在于将全纯算子函数的谱理论与有限元近似相结合。所得结果将促进有限元理论的发展,使科学家和工程师能够有效地计算非线性特征值问题。该项目还将提供一种新的方法来证明线性特征值问题的有限元方法(包括协调和非协调)的收敛。该奖项反映了NSF的法定使命,并通过使用基金会的智力优势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)
数据更新时间:{{ journalArticles.updateTime }}
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
数据更新时间:{{ journalArticles.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ monograph.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ sciAawards.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ conferencePapers.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ patent.updateTime }}
Jiguang Sun其他文献
A deterministic-statistical approach to reconstruct moving sources using sparse partial data
使用稀疏部分数据重建移动源的确定性统计方法
- DOI:
10.1088/1361-6420/abf813 - 发表时间:
2021-01 - 期刊:
- 影响因子:2.1
- 作者:
Yanfang Liu;Yukun Guo;Jiguang Sun - 通讯作者:
Jiguang Sun
A new finite element approach for the Dirichlet eigenvalue problem
狄利克雷特征值问题的一种新的有限元方法
- DOI:
10.1016/j.aml.2020.106295 - 发表时间:
2020-01 - 期刊:
- 影响因子:3.7
- 作者:
Wenqiang Xiao;Bo Gong;Jiguang Sun;Zhimin Zhang - 通讯作者:
Zhimin Zhang
A mixed FEM for the quad-curl eigenvalue problem
- DOI:
10.1007/s00211-015-0708-7 - 发表时间:
2013-10 - 期刊:
- 影响因子:2.1
- 作者:
Jiguang Sun - 通讯作者:
Jiguang Sun
Regular Convergence and Finite Element Methods for Eigenvalue Problems
- DOI:
10.48550/arxiv.2206.00626 - 发表时间:
2022-06 - 期刊:
- 影响因子:0
- 作者:
Jiguang Sun - 通讯作者:
Jiguang Sun
Integral EquationMethod for a Non-Selfadjoint Steklov Eigenvalue Problem
非自伴Steklov特征值问题的积分方程法
- DOI:
- 发表时间:
2022 - 期刊:
- 影响因子:0
- 作者:
Yunyun Ma;Jiguang Sun - 通讯作者:
Jiguang Sun
Jiguang Sun的其他文献
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
{{ truncateString('Jiguang Sun', 18)}}的其他基金
International Conference on Computational Mathematics and Inverse Problems
计算数学与反问题国际会议
- 批准号:
1632364 - 财政年份:2016
- 资助金额:
$ 10万 - 项目类别:
Standard Grant
Finite Element Methods for High Order Eigenvalue Problems
高阶特征值问题的有限元方法
- 批准号:
1521555 - 财政年份:2015
- 资助金额:
$ 10万 - 项目类别:
Standard Grant
US-China-Germany Planning Visits: Direct and Inverse Scattering Methods for Periodic Structures with Arbitrary Profiles and Defects
美中德规划访问:具有任意轮廓和缺陷的周期性结构的直接和逆散射方法
- 批准号:
1427665 - 财政年份:2014
- 资助金额:
$ 10万 - 项目类别:
Standard Grant
Numerical Methods for Transmission Eigenvalues
传输特征值的数值方法
- 批准号:
1321391 - 财政年份:2013
- 资助金额:
$ 10万 - 项目类别:
Standard Grant
Numerical Methods for Transmission Eigenvalues
传输特征值的数值方法
- 批准号:
1016092 - 财政年份:2010
- 资助金额:
$ 10万 - 项目类别:
Standard Grant
相似国自然基金
Finite-time Lyapunov 函数和耦合系统的稳定性分析
- 批准号:11701533
- 批准年份:2017
- 资助金额:22.0 万元
- 项目类别:青年科学基金项目
相似海外基金
Finite Element Assessment of Novel High-Performance Building Panels
新型高性能建筑板材的有限元评估
- 批准号:
567551-2021 - 财政年份:2022
- 资助金额:
$ 10万 - 项目类别:
Alliance Grants
Analysis and Novel Finite Element Methods for Elliptic Equations with Complex Boundary Conditions
复杂边界条件椭圆方程的分析和新颖的有限元方法
- 批准号:
2208321 - 财政年份:2022
- 资助金额:
$ 10万 - 项目类别:
Standard Grant
A novel hybrid finite-discrete element modeling approach to assess the impact of drilling-induced core damage on laboratory properties of hard brittle rocks
一种新颖的混合有限离散元建模方法,用于评估钻井引起的岩心损伤对硬脆性岩石实验室特性的影响
- 批准号:
580759-2022 - 财政年份:2022
- 资助金额:
$ 10万 - 项目类别:
Alliance Grants
Novel imaging metrics and finite element methods for understanding role of bone in osteoarthritis
用于了解骨在骨关节炎中的作用的新颖成像指标和有限元方法
- 批准号:
RGPIN-2015-06420 - 财政年份:2021
- 资助金额:
$ 10万 - 项目类别:
Discovery Grants Program - Individual
Finite Element Assessment of Novel High-Performance Building Panels
新型高性能建筑板材的有限元评估
- 批准号:
567551-2021 - 财政年份:2021
- 资助金额:
$ 10万 - 项目类别:
Alliance Grants
Development of a 3D anatomical database of the human lower limb using novel dissection, digitization, and scanning techniques for the construction of a high fidelity finite element model to simulate n
使用新颖的解剖、数字化和扫描技术开发人体下肢 3D 解剖数据库,以构建高保真度有限元模型来模拟
- 批准号:
565027-2021 - 财政年份:2021
- 资助金额:
$ 10万 - 项目类别:
Alexander Graham Bell Canada Graduate Scholarships - Master's
Novel imaging metrics and finite element methods for understanding role of bone in osteoarthritis
用于了解骨在骨关节炎中的作用的新颖成像指标和有限元方法
- 批准号:
RGPIN-2015-06420 - 财政年份:2020
- 资助金额:
$ 10万 - 项目类别:
Discovery Grants Program - Individual
A Novel Finite Element Method Toolbox for Interface Phenomena in Plasmonic Structures
用于等离子体结构界面现象的新型有限元方法工具箱
- 批准号:
2009366 - 财政年份:2020
- 资助金额:
$ 10万 - 项目类别:
Standard Grant
The application of high resolution peripheral quantitative computed tomography and finite element modeling as a novel diagnostic tool for osteoporosis and fracture risk
高分辨率外周定量计算机断层扫描和有限元建模的应用作为骨质疏松症和骨折风险的新型诊断工具
- 批准号:
519724-2018 - 财政年份:2020
- 资助金额:
$ 10万 - 项目类别:
Postgraduate Scholarships - Doctoral
Novel Finite Element Methods for Elliptic Distributed Optimal Control Problems
椭圆分布最优控制问题的新颖有限元方法
- 批准号:
1913035 - 财政年份:2019
- 资助金额:
$ 10万 - 项目类别:
Standard Grant