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

该提案旨在满足日益增长的工程需求：开发强大的计算效率高的方法来分析电大多尺度物体的瞬态辐射和散射。所提出的工作可以分为两个相互关联的领域：（i）建立并行瞬态电位评估器，用于计算随机非均匀源/观测器对之间的相互作用，其中两点之间的间隔范围从最小波长的百万分之一到一千分之一;（ii）开发并行时域高阶积分方程求解器，包括这些潜在的积分器。这一建议的四重目标如下：（一）严格的方法，可以与平面波时域（PWTD）算法集成，以扩展其适用性的准静态制度;（二）窗口运营商，将变形PWTD与梁;（三）并行，多尺度，快速潜在的评估，包括上述发展;和（四）这些集成到时域积分方程求解器。为了实现这些目标，将在两个方面取得进展：（一）数值方法，以实现这些操作与正确的理解错误的界限和手段来控制它们;（二）并行算法，可证明可扩展。 现实设备的设计和分析是任何计算奋进的圣杯。麦克斯韦求解器也是如此。由于麦克斯韦方程组形成了广泛的现代技术的基础，因此开发出的有效且准确地求解这些方程组的方法可以具有广泛的影响。迄今为止，模拟工具一直是实验的补充，但并没有取代实验。主要的挑战一直是由复杂的结构拓扑与精细功能，嵌入在电气大结构的瓶颈。 我们的目标，使现场可部署系统的分析，将实现的基础数值和并行算法的进步。反过来，这些将使这项技术从数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强大的，准确的，适应性强的代码，可以广泛采用在多个领域的电磁学，声学，等离子体动力学等，以确保传播，PI将与从业者在工业以及与密歇根中心工业和应用数学。 将利用管理支助股和执行支助股现有的招聘渠道，鼓励妇女和少数民族参与。本科生将参与高级设计项目，并可能通过REU补充。此外，博士后学者将在成为一名成功的学者所需的各个方面得到指导。

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.