A hybrid FEM/MoM approach for analyzing inhomogeneous structures with fine features

The hybrid finite element method (HFEM) approach has been used to solve Maxwell´s equations in unbounded regions [Lynch et al., 1986], and to analyze electromagnetic scattering from objects located in free-space [Lin and Liepa, 1988]. In these hybrid FEM applications, a surface integral equation (SIE) for the fields in the exterior region is utilized as a boundary condition for the FEM solution of the fields in the interior region. The fields in the two regions are coupled by augmenting the FEM global system matrix, associated with the fields in the interior region, with submatrices pertaining to the exterior region fields. More recently, a hybrid method, in which the Green´s function is evaluated numerically through the use of FEM, has been introduced for the analysis of thin wires in the presence of inhomogeneous structures [Mahadevan et al., 1994]. In the present work, a new first-order hybrid approach, which combines the conventional FEM and MoM techniques, is presented. Instead of coupling the interior and exterior region fields and matrices directly, the initial FEM field solution generated by using a relatively-coarse mesh is employed, together with the original incident field, to obtain a modified incident field expression in the righthand-side vector of the subsequent MoM analysis. The combination of FEM and MoM leads to an improvement in the numerical accuracy, and enables the user to indirectly apply MoM to problem domains with extensive dielectric inhomogeneities and/or anisotropies, without having to generate a Green´s function, either analytically or numerically.