Comparison of a class of subdomain and entire domain basis functions automatically satisfying KCL

Accuracy, number of unknowns, and CPU time are compared for piecewise linear subdomain basis functions and polynomial entire domain basis functions. Both types of functions automatically satisfy a continuity equation at wire ends and junctions, according to Kirchoff's current law (KCL). The relative root mean square (RMS) current deviation is chosen as the error metric. An electrically short scatterer, a crossed wire scatterer and an electrically long scatterer are used for comparison. Currents are obtained by solving the electric field integral equation (EFIE), by means of the Galerkin method. It was shown that in most cases, for the same accuracy required, the entire domain approximation uses three to five times less numbers of unknowns and 10-100 times less CPU time than the subdomain approximation. Generally, such efficiency is achieved by using entire domain expansions the order of which is up to n=5 and cannot be significantly improved by using higher order expansions.