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明确的结构。然而，几个尖端研究领域，特别是等离子激元和纳米技术，使用的设备越来越容易受到制造工艺变异性的影响。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。总体而言，有效纳入统计不确定性的强大电磁模拟工具的开发必然会对重大研究挑战的技术进步速度产生深远影响，例如设计低成本但高效的太阳能电池，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。 在随机不确定性下的科学计算的当前技术状态是基于来自重复模拟的后处理数据。不足为奇的是，这种方法已经存在多年，而且它太耗时了，无法融入到典型的工程设计周期中。换句话说，虽然建模不确定性的复杂程度和重要性在不断上升，但相关的建模工具基本上保持不变。本提案旨在缩小这一差距，以应对在等离子体、生物医学热疗和无线通信中应用对统计可变的电磁结构和场进行建模的挑战。我们的方法集中在场解算器的基本重新表述上，以一种计算高效的方式嵌入统计不确定性。本文将以时域有限差分方法为平台，对这些思想进行论证。

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.