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.

波的一个固有特征是它们能够在不改变其形状的情况下长距离传播。这种能力使波能够携带信息，无论是通过语音还是电子数据传输。波还可用于探测地球内部、人体或建筑物或桥梁等工程结构。这种探测可以通过求解反问题的方式转化为内部图像，并进一步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，以提高我们为了共同利益而利用波传播特性的能力。该项目开发的工具还可用于设计具有自然界中找不到的奇异特性的现代材料。此类超材料可以实现更好的传感技术以及更快的声学和电磁电路组件，例如微型扬声器、5G 组件和其他毫米波技术。该研究将采用一种新的想法，能够使用波动方程的时域方法来设计频域亥姆霍兹型求解器。该方法的显着之处在于，底层线性算子对应于对称正定矩阵，允许解决强制问题而不是不定亥姆霍兹问题。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。该研究的目标是在更高的频率和比目前更多的内核上求解三个维度的亥姆霍兹方程。该研究还将通过利用基于等距节点数据的离散周期扩展构建的近似空间来寻求改进时域不连续伽辽金方法的时间步约束。这些改进将带来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性材料建模和地震波模拟。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值进行评估，认为值得支持以及更广泛的影响审查标准。