High Order Wave Equation Algorithms for the Frequency Domain

频域高阶波动方程算法

基本信息

批准号：
2208164
负责人：
Daniel Appelo
金额：
$ 28.35万
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：
2022
资助国家：
美国
起止时间：
2022-09-15 至 2023-09-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2208164&HistoricalAwards=false
关键词：
Order Wave Equation Algorithms Frequency

项目摘要

A defining feature of waves is their ability to carry information over large distances by propagating without changing their shape. It is this ability that allow waves to probe and image the human body, the interior of the earth and engineered structures like bridges and tunnels. Such images can then be turned into scientific and engineering knowledge that can be used to improve medical diagnostics and prevent failure of buildings and mechanical devices. 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 advanced materials that can enable better acoustic, elastic and electromagnetic components as well as faster and more accurate sensing technologies. Students will be trained as a part of this work. The research will further develop and apply advanced computational methods for solving systems of partial differential equations modeling wave propagation. The approximation methods will be designed to be robust and flexible while effectively utilizing emerging computational architectures. The research will dramatically improve the WaveHoltz method, a recently discovered idea that enables the use of time domain methods for wave equations to design frequency domain Helmholtz type solvers. WaveHoltz is remarkable in that its underlying linear operator corresponds to a symmetric positive definite matrix and allows a coercive problem to be solved rather than a highly indefinite Helmholtz problem. The research will analyze and develop wavefront preconditioners and deflation techniques for preconditioning WaveHoltz; design implicit and explicit error corrected methods for removing the temporal error in the WaveHoltz method; and consider multi-frequency versions of the WaveHoltz method.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.

波浪的一个定义特征是它们能够通过不变形状传播而在大距离内携带信息。正是这种能力允许波浪探测和形象人体，地球的内部以及桥梁和隧道等工程结构。然后，这些图像可以变成科学和工程知识，可用于改善医疗诊断并防止建筑物和机械设备的故障。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还可以用于设计高级材料，以实现更好的声学，弹性和电磁组件，以及更快，更准确的传感技术。学生将作为这项工作的一部分接受培训。该研究将进一步开发并应用高级计算方法来求解模拟波传播的部分微分方程的系统。近似方法将设计为鲁棒和灵活，同时有效地利用了新兴的计算体系结构。这项研究将显着改善Waveholtz方法，Waveholtz方法是一个最近发现的想法，它可以使用时域方法来设计频域Helmholtz类型求解器。 WaveHoltz非常引人注目的是，它的基础线性操作员对应于对称的正定矩阵，并允许解决强制性问题，而不是高度不确定的Helmholtz问题。该研究将分析和开发用于预处理Waveholtz的波前预处理和缩放技术；设计隐式和明确校正的校正方法，用于删除WaveHoltz方法中的时间误差；并考虑WaveHoltz方法的多频版本。该奖项反映了NSF的法定任务，并使用基金会的知识分子优点和更广泛的影响审查标准，被认为值得通过评估。

项目成果

期刊论文数量（3）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

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 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