Mixed element formulation for the efficient solution of electromagnetic scattering problems

The use of a mixed element formulation for the solution of the scattering of an electromagnetic wave by an infinite cylinder of arbitrary cross section and material composition is examined. A method that combines the conventional finite-element method (FEM) with the generalized scattering amplitude formulation is presented. In the immediate region of the scatterer, the conventional FEM is used to represent the scattered fields. In the exterior region, finite elements are used to model the generalized scattering amplitude, and a weak-form equation based on the transformed Helmholtz equation is derived. The exterior region is then truncated via a local absorbing boundary condition. The two regions are then coupled via a natural boundary condition. It is found that the mesh density can be reduced on the exterior region, and a significant savings in computational time and memory can be realized