Using B-Splines to Entirely Model the Scattering of Thin Wires

Abstract:
This paper investigates if the Mixed Potential Integral Equation (MPIE) with the Method of Moments technique can be used to calculate the surface currents on a thin wire entirely using B-Splines when treated as a scatterer. This technique eliminates the use of conventional numerical Gauss- Quadrature integration. The singularity of the potentials in the MPIE are of lower order than those of the EFIE (r-1 compared to r-3) making the numerical computations of the integrals more accurate. By using second-degree B-Spline basis functions, fewer wire segments are needed therefore reducing the size of the impedance matrix and increasing the overall speed of the numerical calculations. The difficulty with this approach is developing an alternative method for the integration of the thin-wire approximation of the Green’s function when it becomes singular. Integrating over the complete basis function also gave this approach a significant increase in computational speed. As an example, excellent results are obtained for the surface currents of a straight 2lambda thin wire dipole when compared with those results obtained in "R. Harrington, Field Computation by Moment Method". This technique can also be modified for an arbitrary shaped wire positioned anywhere in 3D space.