Stochastic Computational Electromagnetics: Fundamental Aspects and Advanced Applications

计算电磁学的研究一直致力于模拟任意复杂但定义良好的结构。然而，一些前沿研究领域，特别是等离子体和纳米技术，所使用的设备越来越受到制造工艺变化的影响。此外，虽然电磁模拟器现在能够模拟大规模的无线传播问题，但它们仍然受到室内和城市环境固有的统计变异性的限制。总的来说，强大的电磁模拟工具的发展，有效地结合了统计不确定性，必然会对技术进步的步伐产生深远的影响，涉及重大的研究挑战，如设计低成本而高效的太阳能电池，开发用于癌症检测和治疗的生物医学仪器，以及无线服务规划。目前，随机不确定性下的科学计算是基于重复模拟的后处理数据。毫不奇怪，这种方法已经存在多年了，而且在典型的工程设计周期中，它太耗时了。换句话说，虽然建模不确定性的复杂性和重要性不断上升，但相关的建模工具基本保持不变。目前的建议旨在缩小这一差距，以应对在等离子体、生物医学热疗和无线通信中应用的统计可变电磁结构和场建模的挑战。我们的方法是集中在领域求解的基本重新制定嵌入统计不确定性在计算有效的方式。时域有限差分法将作为一个平台来演示这些思想。

Research on computational electromagnetics has been dedicated to the simulation of arbitrarily complex yet well-defined structures. However, several cutting-edge research areas, notably plasmonics and nanotechnology, employ devices that are increasingly subject to fabrication process variability. Moreover, while electromagnetic simulators are now able to model large-scale wireless propagation problems, they are still limited by the inherent statistical variability of indoor and urban environments. In general, the development of powerful electromagnetic simulation tools that effectively incorporate statistical uncertainty is bound to have a far-reaching impact on the pace of technology advancement with respect to grand research challenges such as the design of low-cost yet efficient solar cells, the development of biomedical instrumentation for cancer detection and treatment, and wireless service planning.Current state of the art in scientific computing under stochastic uncertainty is based on post-processing data from repetitive simulations. Not surprisingly, this approach has existed for years and it is too time consuming to incorporate in a typical engineering design cycle. In other words, while the level of complexity and significance of modeling uncertainty is constantly rising, the relevant modelling tools have remained fundamentally the same. The present proposal is aimed at closing this gap, in order to meet the challenge of modeling statistically variable electromagnetic structures and fields with applications in plasmonics, biomedical hyperthermia and wireless communications. Our approach is focused on the fundamental reformulation of field solvers to embed statistical uncertainty in a computationally efficient manner. The Finite-Difference Time-Domain method will be used as a platform to demonstrate these ideas.