# A Surface Integral Formulation for Scattering Modeling by 2D Penetrable Objects

## TL;DR

This paper introduces a novel single-source surface integral method for accurately modeling electromagnetic scattering by 2D penetrable objects, simplifying computations and improving stability over existing techniques.

## Contribution

It presents a new surface integral formulation using a single electric current source to model penetrable objects, enhancing accuracy and computational efficiency.

## Key findings

- Validated through numerical experiments showing high accuracy
- Demonstrated stability and robustness for complex shapes
- Capable of handling non-smooth objects effectively

## Abstract

In this paper, we proposed a single-source surface integral formulation to accurately solve the scattering problems by 2D penetrable objects. In this method, the objects are replaced by their surrounding medium through enforcing a surface equivalent electric current to ensure fields exactly the same as those in the original scattering problem. The equivalent electric current is obtained through emitting the equivalent magnetic current by enforcing that the electric fields in the original and equivalent problems equal to each other. Through solving the Helmholtz equation inside objects by the scalar second Green theorem, we could accurately model arbitrarily shaped objects. Then, we solve the exterior scattering problems through the combined integral equation (CFIE) with the equivalent electric current. The proposed formulation only requires a single electric current source to model penetrable objects. At last, two numerical experiments are carried out to validate its accuracy, stability and capability of handling non-smoothing objects.