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Numerical Methods for Wave Equations in Time and Frequency Domain

时域和频域波动方程的数值方法

基本信息

批准号：
2210286
负责人：
Daniel Appelo
金额：
$ 30.34万
依托单位：
Michigan State University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2021
资助国家：
美国
起止时间：
2021-10-01 至 2023-05-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2210286&HistoricalAwards=false
关键词：
Numerical Methods Wave Equations Time

项目摘要

An intrinsic feature of waves is their ability to propagate over large distances without changing their shape. This ability allows waves to carry information, be it through speech or electronic transmission of data. Waves can also be used to probe the interior of the earth, the human body or engineered structures like buildings or bridges. This probing can be turned into images of the interior by the means of solving inverse problems, and in the extension, mitigate seismic hazards by accurate predictions of ground motion caused by earthquakes. In this project the principal investigator will develop computational simulation tools that increases our ability to exploit the properties of wave propagation for the common good. The tools developed in the project can also be used to design modern materials with exotic properties that cannot be found in nature. Such metamaterials can enable better sensing technologies and faster acoustic and electromagnetic circuit components such as miniaturized speakers, 5G components and other millimeter wave technologies. The research will use a new idea that enables the use of time domain methods for wave equations to design frequency domain Helmholtz type solvers. The approach is remarkable in that the underlying linear operator corresponds to a symmetric positive definite matrix allowing the solution of a coercive problem rather than an indefinite Helmholtz problem. As the proposed Helmholtz solvers rely solely on evolving the wave equation they will be massively parallel, scalable and high order accurate. A goal of the research is to solve the Helmholtz equation in three dimensions at higher frequencies, and on a larger number of cores than is currently possible. The research will also seek to improve the time-step constraints of time domain discontinuous Galerkin methods by exploiting approximation spaces built on discrete periodic extensions from equidistant node data. Such improvements will result in faster simulation times and more accurate predictions. Applications of the methods to modeling of micropolar materials and to simulation of seismic waves will be carried out in collaboration with researchers from academic institutions and national laboratories.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.

波的一个内在特征是它们能够长距离传播而不改变形状。这种能力使电波能够通过语音或电子数据传输来携带信息。波浪还可以用来探测地球内部、人体或建筑、桥梁等工程结构。这种探测可以通过求解逆问题转化为内部的图像，并通过准确预测地震引起的地面运动来减轻地震危害。在这个项目中，首席研究员将开发计算模拟工具，以提高我们为共同利益利用波传播特性的能力。项目中开发的工具也可以用于设计具有自然界中无法找到的奇异特性的现代材料。这种超材料可以实现更好的传感技术和更快的声学和电磁电路组件，如小型化扬声器、5G组件和其他毫米波技术。该研究将采用一种新的思想，即利用波动方程的时域方法来设计频域亥姆霍兹型求解器。该方法的显著之处在于底层的线性算子对应于一个对称的正定矩阵，允许解一个强制问题而不是一个不定的亥姆霍兹问题。由于所提出的亥姆霍兹求解器仅依赖于波动方程的演化，因此它们将具有大规模并行性、可扩展性和高阶精度。这项研究的一个目标是在更高的频率和比目前可能的更多的核上解决三维的亥姆霍兹方程。该研究还将寻求通过利用建立在等距节点数据离散周期扩展上的近似空间来改进时域不连续伽辽金方法的时间步长约束。这样的改进将导致更快的模拟时间和更准确的预测。将与学术机构和国家实验室的研究人员合作，将这些方法应用于微极材料的建模和地震波的模拟。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识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（9）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

A Hermite Method with a Discontinuity Sensor for Hamilton–Jacobi Equations

DOI：
10.1007/s10915-022-01766-2
发表时间：
2021-05
期刊：
Journal of Scientific Computing
影响因子：
2.5
作者：
Allen Alvarez Loya;D. Appelö
通讯作者：
Allen Alvarez Loya;D. Appelö

Taming the CFL Number for Discontinuous Galerkin Methods by Local Exponentiation

通过局部求幂驯服不连续伽辽金方法的 CFL 数

DOI：
发表时间：
2022
期刊：
Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2020+1
影响因子：
0
作者：
Appelö, D.;Hu, M.;Zinchenko, M.
通讯作者：
Zinchenko, M.

An Energy-Based Summation-by-Parts Finite Difference Method For the Wave Equation in Second Order Form

基于能量的二阶波动方程分部求和有限差分法