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

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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.