Splines and their reciprocal-bases in volume-integral equations

The use of higher-order splines and their reciprocal-bases in discretizing the volume-integral equations of electromagnetics is outlined. The discretization is carried out by means of the method of moments, in which the expansion functions are the higher-order splines, and the testing functions are the corresponding reciprocal-basis functions. These functions satisfy an orthogonality condition with respect to the spline expansion functions. The method is not Galerkin, but the structure of the resulting equations is quite regular. The theory is applied to the volume-integral equations for the unknown current density, or unknown electric field, within a scattering body, and to the equations for eddy current nondestructive evaluation. Numerical techniques for computing the matrix elements are given