Regularization effect of a multi-resolution basis on the EFIE-MoM matrix

We investigate the spectral property of the method of moments (MoM) matrix of the electric field integral equation (EFIE) for antenna problems; the eigenvalue spectrum of the matrix determines the convergence of iterative solutions of the associated linear system, and is of crucial importance both in standard MoM approaches as well as in fast approaches like the fast-multipole method. We show that using the multi-resolution (MR) basis (Vipiana, F. et al., 2004 AP-S Digests, vol.2, p.1471-4, 2004) the diagonal entries of the MoM matrix are related to the "spatial filtering" effect of the Green\´s function. This property allows the distribution of the eigenvalues of the matrix to be improved upon a mere diagonal preconditioning, removing the clustering at zero of the EFIE; it results in a significantly improved convergence of iterative schemes, and robustness with respect to matrix clipping. The behavior of the MR basis is compared with the standard Rao-Wilton-Glisson (RWG) and the star-loop (SL) basis (Vecchi, G., IEEE Trans. Ant. Propag., vol.47, p.339-46, 1999).