  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.
