一种耦合混合不连续伽辽金与边界积分方法用于电磁散射分析
A Coupled Hybridizable Discontinuous Galerkin and Boundary Integral Method for Analyzing Electromagnetic Scattering
AI总结：
本文提出一种混合HDG与BI方法，通过稀疏直接求解器和多级快速多重法提升电磁散射分析的效率与精度。
摘要：
本文提出了一种耦合混合不连续伽辽金（HDG）和边界积分（BI）方法，以高效分析非均匀/复合物体的电磁散射。HDG与BI方程的耦合通过在等效电流和HDG的全局未知数上操作数值通量来实现。这种方法在离散化后产生稀疏耦合矩阵。包含BI方程可确保唯一误差是在强制辐射条件时的离散化误差。然而，该方程的离散化会产生一个密集矩阵，这禁止了传统HDG方案中常用的直接矩阵求解器在整体耦合系统中的使用。为克服这一瓶颈，开发了一种
英文摘要：
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.
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