A coupled hybridizable discontinuous Galerkin (HDG) and boundary integral (BI) method is proposed to efficiently analyze electromagnetic scattering from inhomogeneous/composite objects. The coupling between the HDG and the BI equations is realized using the numerical flux operating on the equivalent current and the global unknown of the HDG. This approach yields sparse coupling matrices upon discretization. Inclusion of the BI equation ensures that the only error in enforcing the radiation conditions is the discretization. However, the discretization of this equation yields a dense matrix, which prohibits the use of a direct matrix solver on the overall coupled system as often done with traditional HDG schemes. To overcome this bottleneck, a "hybrid" method is developed. This method uses an iterative scheme to solve the overall coupled system but within the matrix-vector multiplication subroutine of the iterations, the inverse of the HDG matrix is efficiently accounted for using a sparse direct matrix solver. The same subroutine also uses the multilevel fast multipole algorithm to accelerate the multiplication of the guess vector with the dense BI matrix. The numerical results demonstrate the accuracy, the efficiency, and the applicability of the proposed HDG-BI solver.

翻译：提出了一种耦合混合化不连续伽辽金（HDG）与边界积分（BI）方法，以高效分析非均匀/复合目标的电磁散射问题。HDG与BI方程之间的耦合通过作用于等效电流和HDG全局未知量的数值通量实现，这使得离散化后的耦合矩阵具有稀疏性。引入BI方程可确保辐射条件误差仅源于离散化过程。然而，该方程离散化后生成的稠密矩阵阻碍了传统HDG方案中常采用的全局直接求解器。为突破这一瓶颈，本文发展了一种“混合”方法：采用迭代格式求解全局耦合系统，但在迭代的矩阵-向量乘法子程序中，利用稀疏直接求解器高效处理HDG矩阵的逆运算；同时，该子程序采用多层快速多极子算法加速猜测向量与稠密BI矩阵的乘法运算。数值结果验证了所提HDG-BI求解器的准确性、高效性与适用性。