# Finite element based Green's function integral equation for modelling light scattering

## TL;DR

This paper introduces a finite element based Green's function integral equation method for light scattering, improving geometric approximation and numerical accuracy over traditional methods, demonstrated through complex scatter examples.

## Contribution

The paper integrates finite element techniques into Green's function integral equations, enhancing geometric modeling and numerical integration accuracy for light scattering simulations.

## Key findings

- Improved geometric approximation of scatterers.
- Enhanced numerical integration accuracy.
- Effective modeling of complex, large-scale scatterers.

## Abstract

We revisit the volume Green's function integral equation for modelling light scattering with discretization strategies as well as numerical integration recipes borrowed from finite element method. The merits of introducing finite element techniques into Green's function integral equation are apparent. Firstly, the finite element discretization provides a much better geometric approximation of the scatters, compared with that of the conventional discretization method using staircase approximation. Secondly, the accuracy of numerical integral inside one element associated with all different types of Green's function integral equations can be greatly improved by introducing quadrature rules. Within the standard framework of Green's function integral equation, we seamlessly introduce finite element techniques into the Green's function integral equation by introducing the auxiliary variables that confines the singular integrand inside each element, leading to a better and more flexible approximation of the geometry of the scatters and a more accurate numerical integral. We then illustrate the advantages of our finite element based Green's function integral equation method via a few concrete examples in modelling light scattering by optically large and complex scatters.