Operator filtering allows for the regularization and compression of dense integral operators, effectively mitigating the memory and computational costs associated with iterative solvers. Previous works introduced filters that leverage the analytical spectral truncation of kernels for operators of the 2D Electric Field Integral Equation (EFIE). In this contribution, we will demonstrate how to obtain filtered kernels in a discrete numerical form within the framework of an Adaptive Integral Method (AIM), yielding results entirely comparable to analytical filters. By operating directly on the discrete operator representations, the proposed strategy ensures a native and robust compatibility with fast solver schemes that analytical formulations often lack. The effectiveness of the proposed approach will be demonstrated through numerical results, including its application to the Calderón preconditioned EFIE.

翻译：算子滤波能够对稠密积分算子进行正则化与压缩处理，有效降低迭代求解器带来的内存开销与计算成本。已有研究针对二维电场积分方程（EFIE）算子引入了基于核函数解析谱截断的滤波技术。本文将在自适应积分方法（AIM）框架下，展示如何以离散数值形式获取滤波核，所得结果与解析滤波器完全可比。通过直接作用于离散算子表示，该策略确保了与快速求解器方案的原生鲁棒兼容性，而这正是解析公式通常难以实现的。数值结果验证了所提方法的有效性，包括其在Calderón预条件EFIE中的应用。