A Numerical Approach to Operator Filtering within the Adaptive Integral Method for Electromagnetic Integral Equations

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 Calder\'on preconditioned EFIE.