Uni-directional basis functions based on endfire virtual sources for sparse matrix generation

Sparse impedance matrices can be generated approximately by using directive basis functions as in Canning´s (1990) impedance matrix localization (IML). These basis functions, defined over the surface of the scatterer, radiate collimated beams both outward and inward relative to the surface. In order to further reduce interactions within the body, uni-directional basis functions, i.e., ones that radiate primarily outward, have been recently proposed. The combined source integral equation (CSIE), used in conjunction with the combined field integral equation (CFIE), involves a dual source representation, whereby both electric and magnetic equivalent currents are employed in order to generate radiation in the preferred direction. Alternatively, the complex multipole beam approach makes use of virtual sources in complex coordinates in order to generate beams which propagate outward. We