On some Operator Filtering Strategies Based on Suitably Modified Green's Functions

TL;DR

This paper introduces a novel operator filtering method based on spectral truncation of Green's functions, applied to 2D electromagnetic integral equations, demonstrating improved effectiveness through numerical validation.

Contribution

It presents a new spectral filtering approach for EFIE operators, expanding beyond Laplacian-based filters and showing its benefits in electromagnetic problem solving.

Findings

Spectral filtering improves EFIE operator conditioning.

Two spectral representations yield effective filtering strategies.

Numerical results confirm enhanced solution efficiency.

Abstract

Recent contributions showed the benefits of operator filtering for both preconditioning and fast solution strategies. While previous contributions leveraged laplacian-based filters, in this work we introduce and study a different approach leveraging the truncation of appropriately chosen spectral representations of operators' kernels. In this contribution, the technique is applied to the operators of the 2D TE- and TM-electric field integral equations (EFIE). We explore two different spectral representations for the 2D Green's function that lead to two distinct types of filtering of the EFIE operators. Numerical results corroborate the effectiveness of the newly proposed approaches, also in the Calder\'on preconditioned EFIE