Mirco Raffetto

On the Convergence of Galerkin Finite Element Approximations of Electromagnetic Eigenproblems

The convergence of Galerkin finite element approximations of electromagnetic eigenproblems modelling cavity resonators is studied. Since the operator involved is noncompact, the first part of the analysis is carried out in terms of the specific definition of convergence that is known to be appropriate for this case. Then, a slightly stronger definition of convergence is proposed, which is tuned to the features a practitioner of the numerical simulation of electromagnetic devices requires for a good computational model of a resonant cavity. For both definitions, necessary and sufficient conditions are introduced and discussed. Moreover, it is proved that the convergence of an approximation in the stronger sense is unaffected by the presence of different materials filling the cavity resonator. Exploiting this basic feature of the newly defined convergence, the previously developed theory is applied to generalize the convergence proof for the lowest order edge element approximations to the case of anisotropic, inhomogeneous and discontinuous material properties. Results clarifying the relationships among the various conditions occurring in our analysis and examples showing what may happen when not all the conditions for convergence hold true are also reported and contribute to a clear picture about the origin and the behavior of spurious modes.

Electromagnetic scattering by a multilayer elliptic cylinder under transverse-magnetic illumination: series solution in terms of Mathieu functions

An exact solution to the electromagnetic scattering by a dielectric multilayer infinite cylinder of elliptic cross section is proposed. The interfaces between different media, which are assumed to be lossless and nonmagnetic, are confocal elliptic cylinders. Starting from the series expansions in terms of Mathieu functions, an efficient recursive procedure for the computation of fields and radar cross sections per unit length under a transverse-magnetic illumination is developed. The mathematical formulation is detailed and some numerical results are provided.

Parallel GA-based approach for microwave imaging applications

Genetic algorithms (GAs) are well-known optimization strategies able to deal with nonlinear functions as those arising in inverse scattering problems. However, they are computationally expensive, thus offering poor performances in terms of general efficiency when compared with inversion techniques based on deterministic optimization methods. In this paper, a parallel implementation of an inverse scattering procedure based on a suitable hybrid genetic algorithm is presented. The proposed strategy is aimed at reducing the overall clock time in order to make the approach competitive with gradient-based methods in terms of runtime, but preserving the capabilities of escaping from local minima. This result is achieved by exploiting the natural parallelism of evolutionary techniques and the searching capabilities of the hybrid approach . The effectiveness of the proposed implementation is demonstrated by considering a selected numerical benchmark related to two-dimensional scattering geometries.

Cognitive Radios With Multiple Antennas Exploiting Spatial Opportunities

In this correspondence, the achievable rates of the so called “multiple-input multiple-output interference channel,” exploited by a couple of single antenna primary terminals and two antenna cognitive radios under specific interference constraints, are analyzed. In particular, by assuming perfect channel state information at the cognitive terminals, a closed form expression for a linear precoding and linear reception scheme, which guarantees to meet the achievable rates and no mutual interference between primary and cognitive terminals, is obtained. Numerical results regarding the effects of different fading channels and of an imperfect knowledge of the channel are provided to evaluate the performances of the proposed scheme in real environments.

Detection of buried inhomogeneous elliptic cylinders by a memetic algorithm

The paper studies the application of a global optimization procedure to the detection of buried inhomogeneities. The object inhomogeneities are schematized as multilayer infinite dielectric cylinders with elliptic cross sections. An efficient recursive analytical procedure is used for the forward scattering computation. A functional is constructed in which the field is expressed in a series solution of Mathieu functions. Starting with the input scattered data, the iterative minimization of the functional is performed by a new optimization method called memetic algorithm.

Existence, uniqueness and finite element approximation of the solution of time‐harmonic electromagnetic boundary value problems involving metamaterials

Purpose – To provide sufficient conditions for existence, uniqueness and finite element approximability of the solution of time‐harmonic electromagnetic boundary value problems involving metamaterials.Design/methodology/approach – The objectives are achieved by analysing the most simple conditions under which radiation, scattering and cavity problems are well posed and can be reliably solved by the finite element method. The above “most simple conditions” refer to the hypotheses allowing the exploitation of the simplest mathematical tools dealing with the well posedness of variationally formulated problems, i.e. Lax‐Milgram and first Strang lemmas.Findings – The results of interest are found to hold true whenever the effective dielectric permittivity is uniformly positive definite on the regions where no losses are modelled in it and, moreover, the effective magnetic permeability is uniformly negative definite on the regions where no losses are modelled in it. The same good features hold true if “positive...

WELL-POSEDNESS AND FINITE ELEMENT APPROXIMABILITY OF TIME-HARMONIC ELECTROMAGNETIC BOUNDARY VALUE PROBLEMS INVOLVING BIANISOTROPIC MATERIALS AND METAMATERIALS

A boundary value problem for the time harmonic Maxwell system is investigated through a variational formulation which is shown to be equivalent to it and well-posed if and only if the original problem is. Different bianisotropic materials and metamaterials filling subregions of the problem domain with Lipschitz continuous boundaries are allowed. Well-posedness and finite element approximability of the variational problem are proved by Lax–Milgram and Strang lemmas for a class of material configurations involving bianisotropic materials and metamaterials. Belonging to this class is not necessary, yet, for well-posedness and finite element approximability. Nevertheless, the material configurations of many radiation or scattering problems and many models of microwave components involving bianisotropic materials or metamaterials belong to the above class. Moreover, none of the other available tools commonly used to prove well-posedness seems to be able to cope with the material configurations left out by our treatment.

Microwave detection and dielectric characterization of cylindrical objects from amplitude-only data by means of neural networks

In this paper, we propose a new microwave technique for the localization and the dielectric characterization of physically inaccessible cylindrical objects from amplitude-only data. By means of a neural network used to solve the inverse scattering problem; this technique allows to directly achieve the object retrieval, avoiding the drawbacks related to the measurement of the phase distribution of the field that generally represent a critical point, especially at high frequency. The efficiency of the proposed technique in the reconstruction of both the position and the dielectric properties of a circular cylindrical body from amplitude-only information is illustrated and compared with the reconstruction performances of a neural network imaging technique that makes use of both amplitude and phase of the scattered field. The presence of noisy data is also taken into account, showing the dependence of the reconstruction accuracy on the signal-to-noise-ratio.

An Inverse Scattering Approach Based On a Neural Network Technique for the Detection of Dielectric Cylinders Buried in a Lossy Half-Space - Abstract

In this paper, we present an inverse scattering approach based on a neural network technique for the detection of dielectric targets buried in a lossy half-space. In particular, we focus the attention on the analysis of the neural network capability to localize a given cylinder starting from the known values of the electromagnetic scattered field evaluated at a number of points near the half-space interface. The robustness of the developed technique is firstly tested by considering a target and/or an electromagnetic scenario characterized by dielectric parameters different from those used during the training phase and secondly by using noisy input data.

A SVM-based approach to microwave breast cancer detection

Early breast cancer detection is of crucial importance: this form of cancer is the second most common cause of death among women due to malignant tumors, whereas early detection leads to longest survival or even full recovery. Conventional X-ray mammography possesses a range of shortcomings and new techniques must be developed. Features of microwave breast imaging make it an attractive alternative. The aim of the present work is to propose a 3-D approach based on support vector machine classifier whose output is transformed to a posteriori probability of tumor presence. Like confocal microwave imaging introduced by S.C. Hagness et al., the present approach is aimed at detecting tumor locations directly, avoiding solving computationally extensive inverse scattering problem. Microwave data have been generated using finite element method with impedance boundary conditions. Noisy environments have been considered as well. The obtained probability maps demonstrate that the region around the tumor location usually clearly stands out against the background of overall probability values.