Numerical Methods for Waves: Nonlocal, Nonlinear, and Multiscale Systems
波的数值方法:非局部、非线性和多尺度系统
基本信息
- 批准号:2012296
- 负责人:
- 金额:$ 34.25万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Continuing Grant
- 财政年份:2020
- 资助国家:美国
- 起止时间:2020-07-01 至 2024-06-30
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
The reliable simulation of complex physical phenomena can benefit society and help satisfy human curiosity in countless ways. Examples range from the very small, such as the design of nanoscale devices and emerging applications of quantum systems, to the very large, such as natural disasters caused by earthquakes and tsunamis, as well as our understanding of the dynamics and evolution of the cosmos. Although computational capabilities are increasing, with a push towards exascale systems, the computer hardware itself is becoming more heterogeneous and difficult to use efficiently, and the challenges posed by the models one wishes to solve are also rapidly growing. The need to develop and deploy better algorithms is urgent if the tremendous promise of the new computing technologies is to be realized. This research program is focused on the invention of new fast and accurate methods for solving comprehensive models of physical systems where wave propagation plays a central role, with applications throughout the range of problems outlined above.A primary obstacle to simulating waves is the multiscale nature of most applied problems. On the one hand, the defining feature of waves is their ability to propagate long distances relative to their wavelength, effectively leading to problems posed on unbounded domains. On the other, waves interact with media that may vary at or below the wavelength scale. A central theme in such models is the appearance of nonlocal operators; one main goal of the project is the construction of fast, accurate, and memory-efficient algorithms to evaluate them. This includes the development of (i) effective and mathematically justified domain truncation algorithms for general wave propagation problems, which at present are only available for a limited class of systems, (ii) methods for numerically constructing accurate reduced-order models of wave propagation in the presence of subwavelength variations in material properties, capable of efficiently treating engineered materials without assumptions of scale separation or periodicity, and (iii) low-memory algorithms for fractional and other operator functions. The second goal of this project is the extension of robust and efficient discretization schemes to second-order nonlinear wave equations derived from action principles, yielding, in particular, new methods to solve equations arising in general relativity and gauge theories.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.
对复杂物理现象的可靠模拟可以造福社会,并在无数方面帮助满足人类的好奇心。例子从非常小的,如纳米设备的设计和量子系统的新兴应用,到非常大的,如地震和海啸造成的自然灾害,以及我们对宇宙动力学和演化的理解。虽然计算能力正在提高,但随着对亿级系统的推动,计算机硬件本身正变得更加异质,难以有效使用,人们希望解决的模型带来的挑战也迅速增长。如果要实现新计算技术的巨大前景,迫切需要开发和部署更好的算法。这项研究计划的重点是发明新的快速和准确的方法来求解物理系统的综合模型,其中波传播起核心作用,并在上述问题的所有范围内应用。模拟波的一个主要障碍是大多数应用问题的多尺度性质。一方面,波的定义特征是它们能够相对于其波长传播很远的距离,这有效地导致了在无界区域上提出的问题。另一方面,波与可能在波长尺度上或低于波长尺度变化的介质相互作用。这类模型的一个中心主题是非局部运算符的出现;该项目的一个主要目标是构建快速、准确和内存高效的算法来评估它们。这包括发展(I)用于一般波传播问题的有效的和数学上合理的域截断算法,这些算法目前仅适用于有限类别的系统;(Ii)用于在材料性质存在亚波长变化的情况下数值构建准确的波传播降阶模型的方法,能够有效地处理工程材料,而不需要假设尺度分离或周期性;以及(Iii)用于分数和其他算子函数的低存储量算法。该项目的第二个目标是将稳健和高效的离散化方案扩展到源自作用力原理的二阶非线性波动方程,特别是产生了求解广义相对论和规范理论中的方程的新方法。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(4)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Discontinuous Galerkin Galerkin Differences for the Wave Equation in Second-Order Form
二阶形式波动方程的间断伽辽金伽辽金差分
- DOI:10.1137/20m1328671
- 发表时间:2021
- 期刊:
- 影响因子:3.1
- 作者:Banks, J. W.;Buckner, B. Brett;Hagstrom, T.;Juhnke, K.
- 通讯作者:Juhnke, K.
An energy-based discontinuous Galerkin method with tame CFL numbers for the wave equation
波动方程中具有温和 CFL 数的基于能量的间断伽辽金方法
- DOI:10.1007/s10543-023-00954-2
- 发表时间:2023
- 期刊:
- 影响因子:1.5
- 作者:Appelö, Daniel;Zhang, Lu;Hagstrom, Thomas;Li, Fengyan
- 通讯作者:Li, Fengyan
Complete radiation boundary conditions for the Helmholtz equation II: domains with corners
亥姆霍兹方程 II 的完整辐射边界条件:有角的域
- DOI:10.1007/s00211-023-01352-0
- 发表时间:2023
- 期刊:
- 影响因子:2.1
- 作者:Hagstrom, Thomas;Kim, Seungil
- 通讯作者:Kim, Seungil
Continuous/Discontinuous Galerkin Difference Discretizations of High-Order Differential Operators
- DOI:10.1007/s10915-022-01891-y
- 发表时间:2022-06
- 期刊:
- 影响因子:2.5
- 作者:J. Banks;B. B. Buckner-B.;T. Hagstrom
- 通讯作者:J. Banks;B. B. Buckner-B.;T. Hagstrom
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Thomas Hagstrom其他文献
Energy-Conserving Hermite Methods for Maxwell’s Equations
- DOI:
10.1007/s42967-024-00469-9 - 发表时间:
2025-02-26 - 期刊:
- 影响因子:1.400
- 作者:
Daniel Appelö;Thomas Hagstrom;Yann-Meing Law - 通讯作者:
Yann-Meing Law
Perfectly matched layers in photonics computations: 1D and 2D nonlinear coupled mode equations
- DOI:
10.1016/j.jcp.2006.10.002 - 发表时间:
2007-05-01 - 期刊:
- 影响因子:
- 作者:
Tomáš Dohnal;Thomas Hagstrom - 通讯作者:
Thomas Hagstrom
Locating Discontinuities of a Bounded Function by the Partial Sums of Its Fourier Series
- DOI:
10.1023/a:1023204330916 - 发表时间:
1999-12-01 - 期刊:
- 影响因子:3.300
- 作者:
George Kvernadze;Thomas Hagstrom;Henry Shapiro - 通讯作者:
Henry Shapiro
High-order discretization of a stable time-domain integral equation for 3D acoustic scattering
- DOI:
10.1016/j.jcp.2019.109047 - 发表时间:
2020-02-01 - 期刊:
- 影响因子:
- 作者:
Alex Barnett;Leslie Greengard;Thomas Hagstrom - 通讯作者:
Thomas Hagstrom
Thomas Hagstrom的其他文献
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{{ truncateString('Thomas Hagstrom', 18)}}的其他基金
Robust and Efficient Numerical Methods for Wave Equations in the Time Domain: Nonlinear and Multiscale Problems
时域波动方程的鲁棒高效数值方法:非线性和多尺度问题
- 批准号:
2309687 - 财政年份:2023
- 资助金额:
$ 34.25万 - 项目类别:
Standard Grant
Robust High-Order Methods for Wave Equations in the Time Domain
时域波动方程的鲁棒高阶方法
- 批准号:
1418871 - 财政年份:2014
- 资助金额:
$ 34.25万 - 项目类别:
Standard Grant
Collaborative Research: Simulation and Analysis of Turbulent Jet Noise Using Arbitrary-Order Hermite Methods
合作研究:使用任意阶 Hermite 方法模拟和分析湍流射流噪声
- 批准号:
0904773 - 财政年份:2009
- 资助金额:
$ 34.25万 - 项目类别:
Standard Grant
Numerical Methods for Wave Propagation Problems: Efficient Resolution of Multiple Scales
波传播问题的数值方法:多尺度的有效解决
- 批准号:
0929241 - 财政年份:2008
- 资助金额:
$ 34.25万 - 项目类别:
Standard Grant
Numerical Methods for Wave Propagation Problems: Efficient Resolution of Multiple Scales
波传播问题的数值方法:多尺度的有效解决
- 批准号:
0610067 - 财政年份:2006
- 资助金额:
$ 34.25万 - 项目类别:
Standard Grant
Numerical Methods for Multiple Scale Problems in Wave Propagation: Efficient Approximation of Integral Operators in the Time Domain
波传播中多尺度问题的数值方法:时域积分算子的有效逼近
- 批准号:
0306285 - 财政年份:2003
- 资助金额:
$ 34.25万 - 项目类别:
Standard Grant
New Methods for the Simulation and Analysis of Waves
波浪模拟和分析的新方法
- 批准号:
9971772 - 财政年份:1999
- 资助金额:
$ 34.25万 - 项目类别:
Standard Grant
Scientific Computing Research Environments in the Mathematical Sciences
数学科学中的科学计算研究环境
- 批准号:
9977396 - 财政年份:1999
- 资助金额:
$ 34.25万 - 项目类别:
Standard Grant
Mathematical Sciences: Computational Analysis of Multiple Scales Problems in Wave Propagation
数学科学:波传播中多尺度问题的计算分析
- 批准号:
9600146 - 财政年份:1996
- 资助金额:
$ 34.25万 - 项目类别:
Standard Grant
Scientific Computing Research Developments for the Mathematical Sciences
数学科学的科学计算研究进展
- 批准号:
9508285 - 财政年份:1995
- 资助金额:
$ 34.25万 - 项目类别:
Standard Grant
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