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：
1913076
负责人：
Daniel Appelo
金额：
$ 30.34万
依托单位：
University of Colorado at Boulder
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2019
资助国家：
美国
起止时间：
2019-06-15 至 2022-04-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1913076&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.

波浪的固有特征是它们在不改变形状的情况下在大距离上传播的能力。这种能力允许波浪携带信息，无论是通过语音还是电子传输数据。波还可以用来探测地球，人体或工程结构（例如建筑物或桥梁）的内部。该探测可以通过解决反问题的手段，并通过对地震引起的地面运动的准确预测来改变内部图像。在该项目中，主要研究人员将开发计算模拟工具，以提高我们利用波传播特性的能力。该项目中开发的工具也可用于设计具有自然界中无法找到的异国特性的现代材料。这样的超材料可以实现更好的感应技术，并可以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。该研究将使用一个新想法，该想法可以将时域方法用于波动方程来设计频域Helmholtz类型求解器。该方法非常明显，因为基础线性算子对应于对称的正定矩阵，允许解决强制性问题而不是无限期的Helmholtz问题。由于提出的Helmholtz求解器仅依赖于发展波方程，它们将非常平行，可扩展和高阶准确。该研究的一个目的是在较高的频率下以三个维度和更大数量的核心来解决Helmholtz方程。这项研究还将寻求通过利用基于等距节点数据的离散周期扩展的近似空间来利用时间域不连续的Galerkin方法的时间步长限制。这种改进将导致更快的模拟时间和更准确的预测。该方法在微极材料建模和模拟地震波的应用中的应用将与学术机构和国家实验室的研究人员合作进行。该奖项反映了NSF的法定任务，并被认为是值得通过基金会的知识分子优点通过评估来支持的。和更广泛的影响审查标准。