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

在飞机天线设计中，对具有多个部件或复杂几何形状的物体的电磁特性进行仿真是非常重要的。 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新数学的算法。 该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：通过生成适合分析的模型，并独立分析单个组件，可以自动组装组件以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，从而产生高保真仿真软件，可以推进计算机辅助设计和工程（CAD/CAE）。该提案旨在研究时谐麦克斯韦方程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增长而扩展。这一目标将通过三个主要的研究工作来实现：1。研究了一种几何自适应多分辨率间断伽辽金边界元方法，该方法允许使用非共形表面离散，允许混合不同类型的单元，并有利于高清晰度物体的网格生成任务.研究一个条件良好的多轨迹IE制定复杂的复合对象，以解决复杂的复合结构中的材料。3.）第三章开发一种几何感知的区域分解（DD）方法来克服物理区域的几何复杂性。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。所开发的算法的能力将在从高清喷气式飞机到雷达隐身物体到纳米粒子和等离子体纳米天线的应用中得到说明。 模块化软件库将实现所开发的算法，并提供详细文档以允许广泛重用。 在教育方面，该项目将培训学生（从本科生到研究生）计算数学，电磁学，微波工程和计算机辅助工程，并将通过UNM本科研究和教育计划（PROFOUND，PREP）和少数民族推广计划（新墨西哥州AMP和HESO）扩大参与。这将促进对计算科学和工程的更大认识和兴趣，并加强学生面对未来挑战的准备。

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.