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

2026-06-09

AI Summary

This work addresses the high memory and computational costs arising from dense operators in iterative solutions of electromagnetic integral equations. Within the adaptive integral method (AIM) framework, the authors propose a fully numerical discrete operator filtering strategy that eliminates the need for analytical spectral truncation. By directly applying numerical filtering to the discretized operator, the approach achieves regularization and compression comparable to analytical filtering, while naturally integrating with fast algorithms and enhancing robustness and applicability. Combined with Calderón preconditioning, numerical experiments demonstrate that the method substantially reduces computational resource requirements for the electric field integral equation (EFIE) without compromising solution accuracy.

Abstract

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.

Problem

• operator filtering
• Adaptive Integral Method
• EFIE
• numerical approach
• integral equations

Innovation

• operator filtering
• Adaptive Integral Method
• numerical discretization
• EFIE
• fast solvers