AF: Small: Geometry-aware Integral Equation Solvers for High-fidelity Electromagnetic Modeling and Simulation

对于飞机天线的设计，模拟具有许多部件或复杂几何形状的物体的电磁行为非常重要。 该项目研究几何感知的高性能积分方程 (IE) 求解器：分解几何并创建适合几何的新数学算法。 这项研究通过可重构建模和可重用仿真，实现了工程应用中的集成设计和仿真：通过为每个组件生成适合分析的模型并独立分析各个组件，人们可以希望自动组装组件来模拟整个产品的虚拟原型。这将克服基于仿真的工程和科学（SBES）中的关键挑战，从而产生能够推进计算机辅助设计和工程（CAD/CAE）的高保真仿真软件。该提案旨在研究时谐麦克斯韦方程组的高分辨率和高性能IE求解器，其仿真能力和建模保真度随着计算能力的指数级增长而提高。这一目标将通过三项主要研究工作来实现：1.) 研究几何自适应多分辨率不连续伽辽金 (DG) 边界元方法，该方法允许使用非共形表面离散化，允许混合不同类型的元素，并促进高清对象的网格生成任务。2.) 研究复杂复合对象的条件良好的多迹 IE 公式，以解决复合结构中材料的复杂性。 3.) 开发一种几何感知域分解（DD）方法来克服物理域的几何复杂性。这项工作将影响先进天线、光学集成电路、纳米材料和其他工程应用的设计。所开发算法的能力将在高清喷气式飞机、雷达隐形物体、纳米粒子和等离子体纳米天线等应用中得到体现。 模块化软件库将实现所开发的算法，并提供详细的文档以允许广泛重复使用。 在教育方面，该项目将对学生（从本科生到研究生）进行计算数学、电磁学、微波工程和计算机辅助工程方面的培训，并将通过新墨西哥大学本科生研究和教育计划（PROFOUND、PREP）和少数族裔外展计划（新墨西哥州 AMP 和 HESO）扩大参与范围。这将增强学生对计算科学和工程的认识和兴趣，并加强学生应对未来挑战的准备。

For the design of antennas to aircraft, it is important to simulate the electromagnetic behavior of objects with many parts or complex geometry. This project investigates geometry-aware, high-performance integral equation (IE) solvers: decomposing the geometry and creating algorithms that fit new mathematics to the geometry. This research enables integrated design and simulation in engineering applications via reconfigurable modeling and reusable simulation: by generating analysis-suitable models per-component and independently analyzing individual components, one can hope to automatically assemble components to simulate a virtual prototype of an entire product. This will overcome key challenges in simulation-based engineering and science (SBES), resulting in high-fidelity simulation software that can advance computer-aided design and engineering (CAD/CAE).This proposal aims to investigate high-resolution and high-performance IE solvers for time-harmonic Maxwell Equations, whose simulation capability and modeling fidelity scale with the exponential growth in computing power. This objective will be attained through three major research efforts: 1.) investigate a geometry-adaptive multi-resolution discontinuous Galerkin (DG) boundary element method, which permits the use of non-conformal surface discretizations, allows mixing different types of elements, and facilitates the mesh generation task for high-definition objects.2.) investigate a well-conditioned multi-trace IE formulation for complex composite objects to resolve the intricacies of materials in composite structures. 3.) develop a geometry-aware domain decomposition (DD) method to conquer the geometric complexity of physical domains.The work will impact design of advanced antennas, optical integrated circuits, nanomaterials and other engineering applications.The capability of the developed algorithms will be illustrated in applications ranging from high-definition jet aircraft to radar stealth objects to nanoparticles and plasmonic nanoantennas. A modular software library will implement the algorithms developed, with detailed documentation to allow wide reuse. On the educational side, this project will train students (from undergraduates to graduates) in computational mathematics, electromagnetics, microwave engineering and computer-aided engineering, and will broaden participation via UNM undergraduate research and education programs (PROFOUND, PREP) and minority outreach programs (New Mexico AMP and HESO). This will foster greater awareness and interest in computational science and engineering, and reinforce student preparation to face future challenges.