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

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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.