# Magnetic and Combined Field Integral Equations Based on the Quasi-Helmholtz Projectors

## TL;DR

This paper introduces new electromagnetic boundary integral equations based on quasi-Helmholtz projectors that address common numerical issues like ill-conditioning and spurious resonances, improving solution stability across frequencies.

## Contribution

The paper develops a novel quasi-Helmholtz projector-based formulation for magnetic and combined field integral equations that are immune to multiple numerical drawbacks.

## Key findings

- The new formulations are immune to low-frequency ill-conditioning.
- They effectively eliminate spurious resonances.
- Numerical results demonstrate improved stability and accuracy.

## Abstract

Boundary integral equation methods for analyzing electromagnetic scattering phenomena typically suffer from several of the following problems: (i) ill-conditioning when the frequency is low; (ii) ill-conditioning when the discretization density is high; (iii) ill-conditioning when the structure contains global loops (which are computationally expensive to detect); (iv) incorrect solution at low frequencies due to current cancellations; (v) presence of spurious resonances. In this paper, quasi-Helmholtz projectors are leveraged to obtain a magnetic field integral equation (MFIE) formulation that is immune to drawbacks (i)-(iv). Moreover, when this new MFIE is combined with a regularized electric field integral equation, a new quasi-Helmholtz projector combined field integral equation is obtained that also is immune to (v). Numerical results corroborate the theory and show the practical impact of the newly proposed formulations.