We use the time-harmonic Maxwell partial differential equations (PDEs) to model the wave propagation in 3-D space, which comprises a closed penetrable scatterer and its unbounded free-space complement. Surface integral equations (SIEs) that are equivalent to the time-harmonic Maxwell PDEs provide an efficient framework to directly model the surface electromagnetic fields and hence the RCS.The equivalent SIE system on the interface has the advantages that: (a) it avoids truncation of the unbounded region and the solution exactly satisfies the radiation condition; and (b) the surface-fields solution yields the unknowns in the Maxwell PDEs through surface potential representations of the interior and exterior fields. The Maxwell PDE system has been proven (several decades ago) to be stable for all frequencies, that is, (i) it does not possess eigenfrequencies (it is well-posed); and (ii) it does not suffer from low-frequency. However, weakly-singular SIE reformulations of the PDE satisfying these two properties, subject to a stabilization constraint, were derived and mathematically proven only about a decade ago (see {J. Math. Anal. Appl. 412 (2014) 277-300}). The aim of this article is two-fold: (I) To effect a robust coupling of the stabilization constraint to the weakly singular SIE and use mathematical analysis to establish that the resulting continuous weakly-singular second-kind self-adjoint SIE system (without constraints) retains all-frequency stability; and (II) To apply a fully-discrete spectral algorithm for the all-frequency-stable weakly-singular second-kind SIE, and prove spectral accuracy of the algorithm. We numerically demonstrate the high-order accuracy of the algorithm using several dielectric and absorbing benchmark scatterers with curved surfaces.

翻译：我们使用时谐麦克斯韦偏微分方程对三维空间中的波传播进行建模，该空间包含一个封闭的可穿透散射体及其无界自由空间补集。等效于时谐麦克斯韦偏微分方程的表面积分方程提供了一种高效框架，可直接建模表面电磁场，从而计算雷达散射截面。界面上的等效表面积分系统具有以下优势：(a) 避免了对无界区域的截断，且解精确满足辐射条件；(b) 通过内外部场的表面势表示，表面场解给出了麦克斯韦偏微分方程中的未知量。麦克斯韦偏微分方程系统在数十年前已被证明对所有频率稳定，即：(i) 不存在本征频率（适定性）；(ii) 不受低频问题困扰。然而，满足这两个性质的弱奇异表面积分方程重构，在稳定约束条件下，直到大约十年前才被推导并数学证明（见《J. Math. Anal. Appl. 412 (2014) 277-300》）。本文目标有二：其一，将稳定约束与弱奇异表面积分方程稳健耦合，并通过数学分析证明所得连续弱奇异第二类自伴表面积分方程系统（无约束）保持全频稳定性；其二，对全频稳定的弱奇异第二类表面积分方程应用全离散谱算法，并证明该算法的谱精度。我们使用多个具有曲面的介质与吸收性基准散射体，通过数值实验展示了算法的高阶精度。