Several recent contributions have analyzed and illustrated the effectiveness of operator filtering, both in terms of regularization and compression, when handling dense matrices arising from the discretization of integral operators, e.g. the single-layer operator. Previous works have introduced different filtering strategies, ranging from Laplacian-based filters to analytically derived ones, with the goal of improving the computational efficiency of iterative and direct solvers for integral equations in the two-dimensional space, like the 2D Electric Field Integral Equation (EFIE). In this work, we propose a filtering strategy based on the spectral truncation of the kernels of integral operators associated with the 3D EFIE. The approach relies on an appropriate spectral representation of the Green's function obtained via the spherical Hankel transform, which provides an analytical foundation for the proposed approach. Finally, we provide semi-analytical and numerical evidence of the impact of this filtering technique on the spectral properties of continuous integral operators and of their discretization through boundary elements, both for the static and dynamic cases.

翻译：近期多项研究分析并展示了算子滤波在处理积分算子离散化（如单层算子）产生的稠密矩阵时，在正则化与压缩方面的有效性。已有工作提出了从拉普拉斯滤波到解析推导滤波的不同策略，旨在提升二维空间积分方程（如二维电场积分方程）迭代求解器与直接求解器的计算效率。本文提出一种基于三维电场积分方程积分算子核谱截断的滤波策略。该方法通过球面汉克尔变换获得格林函数的合适谱表示，为所提方法提供了解析基础。最后，我们通过半解析与数值实验，从静态与动态两方面论证了该滤波技术对连续积分算子及其边界元离散化谱特性的影响。