AF: :Small: Parallel Transient Solvers for Multiscale Electromagnetics Simulation

这一建议旨在满足日益增长的工程需求：开发强大的计算效率方法来分析电大尺寸多尺度目标的瞬变辐射和散射。建议的工作可分为两个相互关联的领域：(I)构建用于计算随机非均匀源/观察者对之间相互作用的并行瞬变势估值器，其中两点之间的间隔从最小波长的百万分之一到千分之一；(Ii)包括这些势积分器的并行时间域高阶积分方程解的开发。这个提议的四个目标如下：(I)可以与平面波时间域(PWTD)算法集成的严格方法，以将其适用范围扩展到准静态区域；(Ii)将波束变形PWTD的加窗算子；(Iii)包括上述发展的并行、多尺度、快速位势评估器；以及(Iv)将这些方法集成到时间域积分方程解中。为了实现这些目标，将在两个方面取得进展：(I)在正确理解误差界和控制误差界的情况下实现这些运算的数值方法；(Ii)可证明可扩展的并行算法。现实设备的设计和分析是任何计算努力的圣杯。麦克斯韦解算器也是如此。由于麦克斯韦方程构成了一系列现代技术的基础，开发出高效而准确地求解这些方程的方法可能会产生广泛的影响。到目前为止，模拟工具一直是对实验的补充，但还没有取代实验。主要的挑战是嵌入在电大结构中的具有良好特征的复杂结构拓扑所带来的瓶颈。我们的目标--能够分析现场可部署的系统--将通过在基础数值和并行算法方面取得进展来实现。这些反过来将使这项技术从几十个处理器过渡到数千个和数万个处理器。开发的方法将产生一个健壮、准确和适应性强的代码，可以在电磁学、声学、等离子体动力学等多个领域广泛采用。为了确保传播，PI将与工业从业者以及密歇根工业和应用数学中心合作。将利用密歇根州立大学和执行支助股现有的招聘渠道，鼓励妇女和少数群体参与。本科生将参与高级设计项目，并可能通过REU补充材料参与。此外，博士后学者将在成为一名成功学者所需的所有方面得到指导。

This proposal seeks to answer a growing engineering need: the development of robust computationally efficient methods to analyze transient radiation and scattering from electrically large multiscale objects. The proposed work can be categorized into two interrelated areas: (i) building parallel transient potential evaluators for computing interactions between random non-uniform source/observer pairs wherein separation between two points ranges from a millionth to a thousand of the minimum wavelength; (ii) development of parallel time domain higher-order integral equation solvers that include these potential integrators. The four-fold objectives of this proposal are as follows: (i) rigorous methods that can be integrated with the plane wave time domain (PWTD) algorithm to extend its applicability to the quasi-static regime; (ii) windowed operators that will morph PWTD with beams; (iii) parallel, multiscale, fast potential evaluators that include the above developments; and (iv) integration of these into time domain integral equation solvers. To realize these objectives, advances will be made on two fronts: (i) numerical methods to effect these operations with a proper understanding of error bounds and the means to control them; and (ii) parallel algorithms that are provably scalable. The design and analysis of realistic devices is the holy grail of any computational endeavor. The same is true of Maxwell solvers. As Maxwell's equations form the foundation to a wide array of modern technology, methods developed to efficiently and accurately solve these equations can have wide ranging impact. To date, simulation tools have been complementary to, but have not supplanted experiments. The principal challenge has been bottlenecks posed by complex structural topologies with fine features, embedded in electrically large structures. Our goal-to enable the analysis of field deployable systems-will be realized by making advances in both the underlying numerics and parallel algorithms. These, in turn, will enable transition of this technology from tens of processors to thousands and tens of thousands of processors. Methods developed will yield a robust, accurate, and adaptable code that can be widely adopted in multiple domains in electromagnetics, acoustics, plasma dynamics, etc. To ensure dissemination, the PIs will work with practitioners in industry as well as with the Michigan Center for Industrial and Applied Mathematics. Existing channels in recruitment at MSU and ISU will be utilized to encourage participation by women and minorities. Undergraduate students will be involved through senior design projects and potentially through REU supplements. Additionally, a post-doctoral scholar will be mentored in all aspects necessary to be a successful academic.