Finite element-based Green’s function integral equation for modelling light scattering

We revisit the Green’s function integral equation for modelling light scattering with discretization strategies as well as numerical integration recipes borrowed from the finite element method. The finite element-based Green’s function integral equation is implemented by introducing auxiliary variables, which are used to discretize the Green’s function integral equation. The merits of introducing finite element techniques into Green’s function integral equation are apparent. Firstly, the finite element discretization provides a better geometric approximation of the scatterers, compared with that of the conventional discretization method using staircase approximation. Secondly, the accuracy of a numerical integral inside one element associated with Green’s function integral equations can be improved by using more quadrature points, where the singular terms confined inside each triangle can be approximated analytically. 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 scatterers in 2-dimensional scenarios.