A new fast matrix-vector multiplication scheme for the solution of the electric field integral equation is presented in this work. Similarly to other fast methods, our approach reduces the matrix-vector multiplication cost from $O(N^2)$ to $O(Nlog N)$. Differently from other fast solvers, however, the effectiveness of EFIE preconditioning techniques such as quasi-Helmholtz decompositions or Calderón approaches is maintained by our method even for very high matrix compression rates. This is thanks to the fact that, in the scheme we are proposing, the contribution from the scalar potential when applied to or tested with solenoidal functions is always zero independent of the compression error. In addition, the new method will take advantage of the redundancies of the EFIE matrix in the low-frequency/dense discretization regime, and it will further decrease both the memory storage and the multiplication cost with respect to currently available fast solvers. Numerical results will show the effectiveness of our approach and its impact on the solution of realistic problems.

A stable discretization scheme is presented for the combined source integral equation (CSIE) of electromagnetic scattering from three-dimensional arbitrarily shaped homogeneous dielectric objects. The discretization scheme uses both the primary (Rao-Wilton-Glisson, RWG) and the dual (Buffa-Christiansen, BC) functions and avoids numerical problems that would appear if the equations were discretized with the RWG functions only.

A new analysis of the spectral properties of Loop-Star and Loop-Tree decompositions is presented in this work. The analysis will shed light on the behavior of these decompositions when used with regular operators such as the magnetic field and the Calderón preconditioned electric field integral operators. This work will explain the ill-conditioning problems reported in literature and will provide a family of efficient algorithms to solve the ill-conditioning and regularizing several Loop-Star/Tree decomposed equations of interest for applications. The theory will be corroborated by numerical results that will show the practical impact of the theoretical development.

This article aims to provide readers with a physical understanding of the propagation channel that is complementary to mathematical channel modeling. It presents an analysis of the directional propagation channel based on radiophotos. Radiophotos are graphical objects where directions of arrival are superimposed on three-dimensional (3D) panoramic photographs. The interaction between electro magnetic waves and the environment is immediately identified with these representations. This paper focuses on the direction of arrival at mobile in an urban macrocell environment. The first radiophoto collection illustrates the major propagation phenomena such as reflection, diffraction, or street canyoning. The second collection illustrates typical propagation channel profiles that are classified according to delay, azimuth, and elevation spread values. The paper also describes an original panorama-based method for estimating noise level in the azimuth–elevation domain.