On the rigorous approximation methods for electromagnetic-wave scattering by fixed obstacles

Rigorous approximation techniques for the scattering of a classical electromagnetic wave by fixed obstacles are studied. For that purpose, a new Green's function G^T is introduced, which is divergenceless throughout all space and, hence, less singular at short distances than the one commonly used Γ. The two scattering integral equations for the total electric field with G^T and Γ respectively, as well as their iterations, are studied comparatively. It is concluded that the iterations of the integral equation containing G^T converge under more general conditions than those for the one containing Γ, so that G^T is, for rigorous studies, more suitable than Γ