Finite element solution of the vector wave equation using divergenceless basis functions

In order to treat three-dimensional or two-dimensional scatterers that are anisotropic or illuminated by an obliquely incident excitation, the vector wave equation is required. The author describes a finite-element solution of the vector wave equation for scattering from two-dimensional bodies, in order to explore differences in the numerical treatment of scalar and vector equations. A novel feature of the method presented is the use of divergenceless basis functions to represent the transverse electromagnetic fields. To illustrate the accuracy of the approach, a homogeneous, circular cylinder illuminated by a TE plane wave is considered. Numerical results from two scatterer models are compared to the exact solutions.<>