Fast Huygens Sweeping Methods for Large-Scale High Frequency Wave Propagation and Wave-Related Imaging Problems

大多数信息都是以波浪的形式传递的，进行波浪模拟对于推进科学和工程学科的发展至关重要。事实上，计算波传播已经成为一个基本的，蓬勃发展的技术在不同的学科，从雷达，声纳，地震成像，医学成像，潜艇探测，隐形技术，遥感，电子显微镜和纳米技术。这些领域和应用在石油工业、医学成像和材料科学中具有重要的战略价值。如何高效、准确地进行大规模高频波传播是计算波传播中最具挑战性的问题之一。 该研究项目开发了用于高频波传播的新型快速数值方法，以应对这一长期挑战。研究人员将开发和实施新的数据驱动的快速惠更斯扫描方法，用于大规模高频波建模和成像，其中大数据集由工业和军事应用驱动。目标是在高频区域和存在焦散线的情况下，为非均匀介质中的亥姆霍兹和麦克斯韦方程开发高效和精确的扫描方法。该项目将在至少四个理论和计算方面促进突破性创新：第一，用于计算欧拉几何光学成分（如eikonals和振幅）的快速高阶扫描方法;第二，用于大规模高频波建模和模拟的基于蝴蝶算法的快速惠更斯扫描方法;第三，用于大地震数据集的快速惠更斯扫描成像方法;第四，这些新算法在一系列新颖的并行计算架构上的实现。数据支持的快速惠更斯扫描算法将首次为这些大规模成像应用开发。

Most information is communicated in the form of waves, and it is critical to carry out wave simulations to advance science and engineering disciplines. In fact, computational wave propagation has become a fundamental, vigorously growing technology in diverse disciplines ranging from radar, sonar, seismic imaging, medical imaging, submarine detection, stealth technology, remote sensing, and electronics to microscopy and nanotechnology. These fields and applications are of great strategic value in the petroleum industry, in medical imaging, and in materials science. One of the most challenging problems in computational wave propagation is how to carry out large-scale high frequency wave propagation efficiently and accurately. This research project develops novel, fast numerical methods for high frequency wave propagation to tackle this long-standing challenge. The investigator will develop and implement new data-enabled fast Huygens sweeping methods for large-scale high-frequency wave modeling and imaging with big data sets motivated by industrial and military applications. The goal is to develop efficient and accurate sweeping methods for the Helmholtz and Maxwell equations in inhomogeneous media in the high frequency regime and in the presence of caustics. This project will foster breakthrough innovations in at least four theoretical and computational aspects: first, fast higher-order sweeping methods for computing Eulerian geometrical-optics ingredients, such as eikonals and amplitudes; second, butterfly-algorithm-based fast Huygens sweeping methods for large-scale high-frequency wave modeling and simulation; third, fast Huygens sweeping-imaging methods for big seismic data sets; and fourth, implementations of these new algorithms on a range of novel parallel-computing architectures. Data-enabled fast Huygens sweeping algorithms will be developed for the first time for these large-scale imaging applications.