Innovative Butterfly-Compressed Microlocal Hadamard-Babich Integrators for Large-Scale High-Frequency Wave Modeling and Inversion in Variable Media

该项目开发并实现了大规模波浪建模和反演的创新快速算法。波无处不在，例如无线信号以电磁波的形式传播，超声CT成像是基于声波的传播。事实上，波浪模拟是一项基础的、不断发展的技术，应用于从合成孔径雷达、声纳、地球物理资源勘探、医学成像、潜艇探测、遥感和电子学到显微镜和纳米技术等各个学科。为这些领域和应用开发快速算法将在许多方面很好地服务于国家利益，例如通过为医学成像提供快速算法来促进国民健康，通过帮助美国石油工业保持其在石油和天然气勘探方面的优势来促进国家能源安全。计算波传播中最具挑战性的问题之一是如何高效准确地进行大规模高频波模拟，研究者将开发新的快速蝴蝶压缩积分器来解决这一关键问题。为了扩大教育影响，该项目将把科学发现与一系列短期课程结合起来，使研究生能够掌握最新的科学工具。将为本科生和研究生开发跨学科的实践培训，重点是增加代表性不足的学生群体对STEM教育的多样性和参与度。该项目将设计新型的快速蝴蝶压缩微局部Hadamard-Babich （HB）积分器，用于工业和军事应用的大规模高频声波、电磁和弹性波建模和反演。本科学计算项目的目标问题是大数据集的大规模波浪建模和逆问题。目标模型方程包括高频亥姆霍兹方程、麦克斯韦方程和非均匀介质中存在焦散的弹性波动方程。该项目将促进至少三个理论和计算方面的突破性创新。首先，新型蝴蝶压缩HB积分器将在存在焦散的大尺度高频波建模和反演中面临重大的科学挑战。其次，将在基于pde的欧拉微局部分析和计算波传播的新型蝴蝶压缩和HB积分器的开发方面取得重大进展。新的快速HB积分器能够产生均匀的超过焦散的渐近解。第三，新的蝴蝶压缩HB积分器将为非均匀介质中的许多与波相关的应用提供有效的工具，例如地震成像和反演。新的蝴蝶压缩微局部HB集成商将首次开发用于这些应用。该项目产生的新方法将在数学和工程应用的多个科学领域产生广泛的影响，并将显著提高大尺度波传播的模拟能力。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。

This project develops and implements innovative fast algorithms for large-scale wave modeling and inversion. Waves are ubiquitous, for example, wireless signals are communicated in the form of electromagnetic waves, and ultrasound CT imaging is based on propagation of acoustic waves. In fact, wave simulation is a fundamental, growing technology in a variety of disciplines ranging from synthetic aperture radar, sonar, geophysical resources exploration, medical imaging, submarine detection, remote sensing and electronics to microscopy and nanotechnology. Developing fast algorithms for these fields and applications will serve the national interest very well in many aspects, such as advancing national health by providing fast algorithms for medical imaging and advancing national energy security by helping the U.S. petroleum industry maintain its edge in oil and gas exploration. One of the most challenging problems in computational wave propagation is how to carry out large-scale high frequency wave simulation efficiently and accurately, and the investigator will develop new fast butterfly-compressed integrator to address this crucial objective. To expand the educational impacts, the project will integrate the scientific discoveries with a series of short courses so that graduate students can be trained on the latest scientific tools. Interdisciplinary hands-on training will be developed for both undergraduate and graduate students, with an emphasis on increasing the diversity and participation of under-represented groups of students for STEM education.The project will design novel fast butterfly-compressed microlocal Hadamard-Babich (HB) integrators for large-scale high-frequency acoustic, electromagnetic, and elastic wave modeling and inversion motivated by industrial and military applications. The targeted problems for this scientific computing project are large-scale wave modeling and inverse problems with big data sets. The aimed model equations include high-frequency Helmholtz equations, Maxwell's equations, and elastic wave equations in inhomogeneous media in the presence of caustics. This project will foster breakthrough innovations in at least three theoretical and computational aspects. First, the new butterfly-compressed HB integrators will meet significant scientific challenges in large-scale high-frequency wave modeling and inversion in the presence of caustics. Second, significant advances will be made in developing novel butterfly compression and HB integrators for PDE-based Eulerian microlocal analysis and computational wave propagation. The new fast HB integrator is capable of producing uniform asymptotic solutions beyond caustics. Third, new butterfly-compressed HB integrators will provide efficient tools for many wave-related applications in inhomogeneous media, such as seismic imaging and inversion. New butterfly-compressed microlocal HB integrators will be developed for the first time for these applications. The new methodology generated by the project will have broad impacts on multiple scientific fields in both mathematics and engineering applications and will significantly improve the simulation capacities of large-scale wave propagation.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.