Splines and their reciprocal-bases in volume-integral equations

The author outlines the use of higher-order splines and their reciprocal bases in discretizing the volume-integral equations of electromagnetics. The discussion of higher-order splines and the computation of their reciprocal bases are based on the theory presented by J. Aubin (1972). 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. Thus, the method is not Galerkin, but the structure of the resulting equations is quite regular, nevertheless