Efficient Algorithms for Interface Motion and Wave Propagation

波传播中的接触面和相关问题出现在大量的科学、工程和工业问题中。 这些问题包括打破水波，地震波通过地球传播，半导体制造，喷墨绘图仪的设计，以及肿瘤生长和细胞膜边界的生物学方面的问题。在以前的NSF资助的工作中，我们已经建立了日常使用的强大算法来解决这些问题;其中两个包括水平集方法和快速行军方法。 它们在整个半导体行业中用于分析如何使芯片更小，更高效，在喷墨过程中用于模拟更小规模的工业印刷，在石油行业中用于帮助定位石油储量。在这项工作中，我们建议将这些计算技术扩展到更困难的问题，再次将重点放在将它们直接应用于具有挑战性的工业和科学问题。 在这里，我们的重点将超越“初至”解决方案的特点，上述问题，并将旨在设计接口技术，将产生更复杂的多波到达解决方案，复杂的地震和波成像问题，导数相关的控制理论问题，出现在飞机回避和控制问题，以及在机器人技术和半导体器件中的蚀刻和沉积中的高度精细的多尺度问题。

Propagating interfaces and related problems in wave propagation appear in a vast collection of scientific, engineering, and industrial problems. These include problems in breaking water waves, seismic wave propagation through the Earth, semiconductor fabrication, the design of ink jet plotters, and biological aspects of tumor growth and cell membrane boundaries.Under previous NSF-funded work, we have built robust algorithms in everyday use to tackle these problems; two of these include Level Set Methods and Fast Marching Methods. They are used throughout the semiconductor industry to analyze how to make chips smaller and more efficient, in the ink jet process to simulate industrial printing on ever smaller scales, and in the petroleum industry to help locate oil reserves. We propose in this work to extend these computational techniques to significantly more difficult problems, again with a focus on applying them directly to challenging industrial and scientific problems. Here, our focus will go beyond ''first arrival'' solutions which characterize the above problems, and will aim to design interface techniques that will produce the far more complex multiple arrivals solutions to intricate seismic and wave imaging problems, derivative-dependent control theory problems that appear in aircraft avoidance and control problems, and highly refined multiple scale problems in robotics and etching and deposition in semiconductor devices.