Application of higher-order splines and reciprocal-bases to the moment method solution of the electromagnetic scattering of three-dimensional flaw in anisotropic slab

The authors outline the scattering problem of the anomalous conductivity within an anisotropic slab. They use the higher-order splines and their reciprocal bases in discretizing the E-field volume integral equation. The discretization is carried out by means of the moment method, in which the expansion functions are the higher-order splines and the testing functions are the corresponding reciprocal-basis functions. Hence, the method is not Galerkin, but the resulting matrix equation is quite regular. The significance of the new procedure is to introduce smooth volumetric currents within the anomaly region. The authors first present the theory of the higher-order splines and their associated reciprocal bases, and then show how it can be applied to discretize the E-field volume integral equation for a flaw in an anisotropic slab.<>