Fast Fourier Transform Accelerated Multiscale Algorithms for Computational Electromagnetics

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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.