High Order Wave Equation Algorithms for the Frequency Domain

频域高阶波动方程算法

• 批准号: 2345225
• 负责人: Daniel Appelo
• 金额: $ 28.35万
• 依托单位: Virginia Polytechnic Institute and State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-08-15 至 2025-08-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2345225&HistoricalAwards=false
• 关键词: Order; Wave; Equation; Algorithms; Frequency

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.

波的一个决定性特征是它们能够通过传播而不改变其形状来长距离携带信息。正是这种能力使得波能够探测人体、地球内部以及桥梁和隧道等工程结构并对其进行成像。然后，这些图像可以转化为科学和工程知识，可用于改进医疗诊断并防止建筑物和机械设备发生故障。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先进材料，从而实现更好的声学、弹性和电磁组件以及更快、更准确的传感技术。作为这项工作的一部分，学生将接受培训。该研究将进一步开发和应用先进的计算方法来求解模拟波传播的偏微分方程组。近似方法将被设计为稳健且灵活，同时有效利用新兴的计算架构。这项研究将极大地改进 WaveHoltz 方法，这是最近发现的一种想法，可以使用波动方程的时域方法来设计频域亥姆霍兹型求解器。 WaveHoltz 的非凡之处在于其底层线性算子对应于对称正定矩阵，并且允许解决强制问题而不是高度不定的亥姆霍兹问题。该研究将分析和开发用于预处理 WaveHoltz 的波前预处理器和放气技术；设计隐式和显式误差校正方法来消除 WaveHoltz 方法中的时间误差；并考虑 WaveHoltz 方法的多频率版本。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力优点和更广泛的影响审查标准进行评估，被认为值得支持。