The condition number issue for EFIE-MoM: spectral and MR considerations

The possibility of sparsifying the (fully populated) MoM matrix, as well as the speed of convergence of iterative solvers bear on the condition number of the MoM matrix itself. We discuss how the spectral properties of the employed basis functions determine the condition number of the associated MoM matrix, and the possibility of reducing it through a very low-cost diagonal preconditioner. We analyze the multiresolution (MR) basis functions from this standpoint, considering a previously proposed scheme for printed antennas and circuits, and proposing all extension. In it, the structure is hyerarchically decomposed in simple sub-domains, in which MR functions are employed; at the coarsest level a novel, structure-fitting spectral set of basis function is generated. An example of application concludes the work.