Rigorous grid truncation for the finite element solution of electromagnetic scattering problems.

Abstract

The bymoment method is presented for the analysis of electromagnetic wave scattering from cylinders in an unbounded region. The method introduces a conforming surface to geometrically decouple the interior region containing the scatterer from the exterior region extending to infinity. The solution in the interior is generated from the standard finite element solution of an interior Dirichlet boundary-value problem. The interior solution is then coupled to the exterior by applying Green's theorem to the scattered field and each one of the members in a set of properly chosen testing functions. Because the finite element method is used for the solution in the interior region, the cylinder may be of arbitrary shape, and its material properties may, in general, be inhomogeneous. To demonstrate the capabilities of the method several problems involving cylindrical geometries are considered. The first is the problem of electromagnetic scattering from a single infinitely long cylinder in free space. The wave vector of the incident field is assumed to be normal to the axis of the cylinder so that the problem becomes two dimensional. The second is the case where there are a multiple number of parallel, infinitely long cylinders in free space. In this instance, an individual finite element grid is generated for each cylinder, and the coupling between the cylinders results from the application of Green's theorem. Next, the cylinder is placed in the presence of two semi-infinite half-spaces. This requires the evaluation of Sommerfeld-type integrals for the testing functions. Finally, the wave vector of the incident field is allowed to be obliquely incident on the cylinder. Numerical results are presented and compared to eigenfunction series and integral equation solutions in order to validate the method.