论文标题
单轴各向异性介质的高阶3D表面积分方程求解器
A High-Order-Accurate 3D Surface Integral Equation Solver for Uniaxial Anisotropic Media
论文作者
论文摘要
本文介绍了一种高阶精确表面积分方程方法，用于求解具有单次各向异性介电常数张量的介电物体的3D电磁散射。 N-müller配方具有杠杆作用，从而产生了第二种积分配方，并且使用有限差异的方法来处理由二元格林的功能引起的强烈奇异术语，同时维持了单轴性媒介媒体，同时维持了iScetization策略的高阶精度。通过NyStröm-Colocation方法将积分运算符离散，该方法代表了曲线四边形四边形表面斑块上Chebyshev多项式的未知表面密度。研究了各种几何形状的收敛性，包括球体，立方体，从3D CAD Modeler软件中进口的复杂NURBS几何形状和纳米硅硅波导，并将结果与商业有限元求解器进行了比较。据我们所知，这是使用表面积分方程单轴上各向异性材料的物体的高阶精度的首次演示。
This paper introduces a high-order accurate surface integral equation method for solving 3D electromagnetic scattering for dielectric objects with uniaxially anisotropic permittivity tensors. The N-Müller formulation is leveraged resulting in a second-kind integral formulation, and a finite-difference-based approach is used to deal with the strongly singular terms resulting from the dyadic Green's functions for uniaxially anisotropic media while maintaining the high-order accuracy of the discretization strategy. The integral operators are discretized via a Nyström-collocation approach, which represents the unknown surface densities in terms of Chebyshev polynomials on curvilinear quadrilateral surface patches. The convergence is investigated for various geometries, including a sphere, cube, a complicated NURBS geometry imported from a 3D CAD modeler software, and a nanophotonic silicon waveguide, and results are compared against a commercial finite element solver. To the best of our knowledge, this is the first demonstration of high-order accuracy for objects with uniaxially anisotropic materials using surface integral equations.
