Fast Fourier Transform Accelerated Multiscale Algorithms for Computational Electromagnetics

在计算科学和工程的几乎所有领域，当面对涉及现实世界系统的问题时，数值算法会陷入停顿；造成这一缺陷的主要原因是“尺度的暴政”。在大长度和时间尺度范围内发生的现象往往对复杂系统的运行至关重要；不幸的是，对于涉及多个感兴趣的尺度的计算，很少有传统算法足够高效和健壮。需要创新的算法来克服多尺度建模和分析所固有的困难。计算电磁学（CEM）是一个从高效多尺度算法的发展中受益的领域。虽然最近开发的快速CEM算法允许解决前所未有的规模问题，但这些算法主要是为几何上的单尺度结构设计的，也就是说，当它们应用于包含多波长和亚波长尺寸特征的多尺度结构时是无效的。本研究涉及基于FFT算法的发展，用于执行高效的多尺度电磁分析。研究人员正在为最先进的算法开发多尺度扩展，并将其纳入CEM模拟器。由此产生的模拟器将允许对各种具有挑战性的电磁问题进行数值严格，快速和稳健的分析，最终将推进复杂工程系统的理解和设计。通过这个项目，研究人员通过在研究生和本科生课程中引入多尺度算法概念，并通过为研究提供先进的计算工具，正在改善德克萨斯大学奥斯汀分校的CEM研究和教育基础设施。这项研究的结果正在德克萨斯州附近大学的研究研讨会上传播，包括那些少数民族人口明显不足的大学，并通过带有图形用户界面的互动网站传播。

In virtually all areas of computational science and engineering, numerical algorithms grind to a halt when confronted with problems involving real-world systems; chief among the reasons for this shortcoming is the "tyranny of scales". Phenomena occurring across large ranges of length and time scales are often critical for the operation of complex systems; unfortunately, few conventional algorithms are efficient and robust enough for computations involving more than a single scale of interest. Innovative algorithms are needed to overcome the difficulties inherent in multiscale modeling and analysis. Computational electromagnetics (CEM) is one area that stands to benefit from the development of efficient multiscale algorithms. While recently developed fast CEM algorithms allow the solution of problems of unprecedented size, these algorithms are designed primarily for geometrically single-scale structures, i.e., they are ineffective when applied to multiscale structures containing both multi- and sub-wavelength size features. This research involves the development of FFT based algorithms for performing efficient multiscale electromagnetic analysis. The investigators are developing multi-scale extensions for state-of-the-art algorithms and incorporating them to CEM simulators. The resulting simulators will permit the numerically rigorous, fast and robust analysis of a variety of challenging electromagnetic problems, which ultimately will advance the understanding and design of complex engineering systems. Through this project, the investigators are improving the CEM research and education infrastructure at The University of Texas at Austin by introducing multiscale algorithmic concepts into graduate and undergraduate courses and by making advanced computing tools available for research. The findings of the study are being disseminated via research seminars at nearby universities in Texas, including those with significant underrepresented minority populations, and via interactive websites with graphical user interfaces.