# Efficient Field-Only Surface Integral Equations for Electromagnetics

## TL;DR

This paper introduces an improved surface integral method for electromagnetics that reduces problem size and provides the normal derivative of the electric field, beneficial for micro-photonics applications.

## Contribution

It advances a formulation that solves for electric field and its normal derivative, reducing problem size by 25% and enhancing applicability in micro-photonics.

## Key findings

- 25% reduction in problem size
- Provides normal derivative of electric field
- Applicable to micro-photonics

## Abstract

In a recent paper, Klaseboer et al. (IEEE Trans. Antennas Propag., vol. 65, no. 2, pp. 972-977, Feb. 2017) developed a surface integral formulation of electromagnetics that does not require working with integral equations that have singular kernels. Instead of solving for the induced surface currents, the method involves surface integral solutions for 4 coupled Helmholtz equations: 3 for each Cartesian component of the electric E field plus 1 for the scalar function r*E on the surface of scatterers. Here we improve on this approach by advancing a formulation due to Yuffa et al. (IEEE Trans.Antennas Propag., vol. 66, no. 10, pp. 5274-5281, Oct. 2018) that solves for E and its normal derivative. Apart from a 25% reduction in problem size, the normal derivative of the field is often of interest in micro-photonic applications.

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Source: https://tomesphere.com/paper/1901.01602