Fast Fourier Transform Accelerated Multiscale Algorithms for Computational Electromagnetics

计算电磁学的快速傅里叶变换加速多尺度算法

• 批准号: 0728828
• 负责人: Ali Yilmaz
• 金额: $ 15万
• 依托单位: University of Texas at Austin
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-09-15 至 2011-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0728828&HistoricalAwards=false
• 关键词: Fast; Fourier; Transform; Accelerated; Multiscale

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.

在计算科学和工程的几乎所有领域，当遇到涉及真实世界系统的问题时，数值算法都会陷入停顿;造成这种缺点的主要原因是“规模的暴政”。在大范围的长度和时间尺度上发生的现象对于复杂系统的操作通常是至关重要的;不幸的是，很少有传统算法对于涉及多于一个感兴趣尺度的计算是足够有效和鲁棒的。需要创新的算法来克服多尺度建模和分析中固有的困难。计算电磁学（CEM）是一个受益于高效多尺度算法发展的领域。虽然最近开发的快速CEM算法允许解决前所未有大小的问题，但这些算法主要是针对几何单尺度结构设计的，即，当应用于包含多波长和亚波长尺寸特征的多尺度结构时，它们是无效的。本研究涉及基于FFT的算法进行有效的多尺度电磁分析的发展。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严格、快速和鲁棒的数值分析，最终将促进对复杂工程系统的理解和设计。通过这个项目，研究人员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，将多尺度算法概念引入研究生和本科生课程，并为研究提供先进的计算工具。该研究的结果正在通过在得克萨斯州附近的大学，包括少数民族人口代表性严重不足的大学举行的研究研讨会，以及通过具有图形用户界面的互动网站进行传播。