利用准亥姆霍兹投影子的稳定时域组合场积分方程
A stabilized time-domain combined field integral equation using the quasi-Helmholtz projectors
AI总结：
本文提出一种基于准亥姆霍兹投影子的稳定时域组合场积分方程，通过分量重缩放和Calderon预处理解决精度与稳定性问题，数值实验验证了其有效性。
摘要：
本文针对完美电导体电磁散射问题，提出了一种时域组合场积分方程。该新方程通过利用准亥姆霍兹投影子获得，该投影子将未知场和源场分别分解为螺线管分量和无旋分量。随后对这两个分量进行适当重新缩放，以解决当时间步长较大时出现的精度损失问题。同时，采用具有纯虚波数的Yukawa型积分算子作为Calderon预处理器，以消除矩阵系统的病态性。稳定的时域电场和磁场积分方程以类似Calderon的方式线性组合，然后使用适当的试验函数对时间进行离散，从而得到一个时间步进线性系统。该新公式对虚假共振、密集离散化崩溃、大步长崩溃以及由非平凡核引起的直流不稳定性具有免疫性。针对单连通和多连通散射体的数值结果证实了理论分析。
英文摘要：
This paper introduces a time-domain combined field integral equation for electromagnetic scattering by a perfect electric conductor. The new equation is obtained by leveraging the quasi-Helmholtz projectors, which separate both the unknown and the source fields into solenoidal and irrotational components. These two components are then appropriately rescaled to cure the solution from a loss of accuracy occurring when the time step is large. Yukawa-type integral operators of a purely imaginary wave number are also used as a Calderon preconditioner to eliminate the ill-conditioning of matrix systems. The stabilized time-domain electric and magnetic field integral equations are linearly combined in a Calderon-like fashion, then temporally discretized using an appropriate pair of trial functions, resulting in a marching-on-in-time linear system. The novel formulation is immune to spurious resonances, dense discretization breakdown, large-time step breakdown and dc instabilities stemming from non-trivial kernels. Numerical results for both simply-connected and multiply-connected scatterers corroborate the theoretical analysis.
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