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

在飞行器天线设计中，对具有多个部件或复杂几何形状的目标的电磁行为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式(IE)解算器：分解几何并创建适合于几何的新数学的算法。这项研究通过可重构的建模和可重用的仿真，使工程应用中的集成设计和仿真成为可能：通过对每个部件生成适合分析的模型并独立分析单个部件，人们可以希望自动组装部件来模拟整个产品的虚拟原型。这将克服基于模拟的工程与科学(SBES)中的关键挑战，产生能够推进计算机辅助设计与工程(CAD/CAE)的高保真模拟软件。该方案旨在研究高分辨率、高性能的时间调和Maxwell方程的IE求解器，其模拟能力和建模保真度随着计算能力的指数增长而扩大。这一目标将通过三大研究努力来实现：1.)研究了一种几何自适应的多分辨率间断Galerkin(DG)边界元方法，该方法允许使用非保角曲面离散，允许混合不同类型的单元，并简化了高清晰度对象的网格生成任务。为解决复杂结构中复杂材料的复杂问题，研究了一种条件良好的多道IE公式。3.)开发了一种几何感知区域分解(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。所开发的算法的能力将在从高清晰度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展示。一个模块化的软件库将实现开发的算法，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，并将通过新墨西哥州大学本科生研究和教育方案(REPER，PREP)和少数民族外联方案(新墨西哥州AMP和HESO)扩大参与范围。这将培养学生对计算科学和工程的更大意识和兴趣，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.