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的形式传递的，进行波模拟对于推动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项基础技术，在从雷达、声纳、地震成像、医学成像、潜艇探测、隐形技术、遥感、电子到显微镜和纳米技术的不同学科中蓬勃发展。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、准确地进行大规模的高频波传播是计算波传播中最具挑战性的问题之一。这项研究项目开发了新的、快速的高频波传播数值方法，以应对这一长期存在的挑战。研究人员将开发和实施新的数据启用的快速惠更斯扫描方法，用于工业和军事应用驱动的大数据集的大规模高频波建模和成像。其目的是发展有效和准确的扫描方法，在高频和焦散存在的非均匀介质中计算亥姆霍兹方程和麦克斯韦方程。该项目将至少在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的快速高阶扫描方法，例如像函数和振幅；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，用于大型地震数据集的快速惠更斯扫描成像方法；以及第四，在一系列新型并行计算架构上实现这些新算法。数据使能的快速惠更斯扫描算法将首次为这些大规模成像应用而开发。

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.