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The use of the Fast Multipole Method (FMM) in an equivalent current reconstruction technique, based on a dual-equation formulation, has been presented in the past for antenna design and diagnostics. The method was applied in design validation from measured data, demonstrating diagnostics feasibility of different large antennas up to an equivalent antenna volume of 2380 $\lambda^{\wedge}3$. Despite the computational advantages coming from the FMM, the memory request and the run time constraints could be still crucial in the processing of electrically large antennas. An enhancement of the equivalent current reconstruction technique based on a Nested Skeletonization Scheme is here presented. The new technique leads to a further reduction of memory requirements and computational time, applicable to diagnostic investigation of electrically larger problems in a wider frequency band. In this paper the nested skeletonization scheme enhancement of the equivalent current technique is applied and demonstrated for diagnostics on electrically large structures.

The equivalent source technique (EQC) has proved to be a useful aid in antenna processing, diagnostics and in the link with Computational ElectroMagnetic Tools (CEM). For broadband frequency antennas or in case of very large number of frequencies, reduction of the number of frequency points to be computed is a desirable feature, to significantly limit the global computational time. In recent applications this is a realistic need, since antennas are present in almost all commercial products, operating on a large set of frequency bands, and exhibiting a wide variety of pattern types. Therefore, they need to be analysed on a relevant number of frequency points, to finally check compliance with standards. For this purpose, in case of multifrequency processing, an interpolation technique based on radiation patterns and antenna S-parameters has been implemented in the EQC. In this paper the new implementation is applied and demonstrated on a large band antenna.

Near-field (NF) measurements with NF-to-far-field (FF) transformation are a powerful and standard approach to modern antenna measurements. This approach implies a relatively close distance between device under test (DUT) and probe and, since the latter is rarely an ideal probe, it will introduce effects that have to be removed to obtain a FF which is only expression of the DUT. In this study, the authors introduce a probe compensation technique applicable to a generic scan surface with non-uniform, possibly incomplete sampling. The procedure is based on a hybridisation between simulations and measurements of the DUT, originally devised to achieve a radical undersampling of the NF with respect to the Nyquist criteria, in order to perform fast and accurate measurements. They present results that prove the effectiveness of the proposed approach.

Entire-domain, spectral basis functions (BFs) have witnessed recent interest in the integral-equation analysis of large metasurface (MS) antennas modeled via homogenized impedance boundary conditions. We present a formulation employing classical Galerkin test via Rao–Wilton–Glisson functions yet assembled to represent entire-domain div-conforming BFs for the shape of interest (e.g., circular/coaxial waveguide modes). On the one hand, the rationale is that entire-domain, spectral BFs afford a significant economy in the number of necessary unknowns; on the other hand, being expressed as combination of Rao–Wilton–Glisson functions, reaction integrals are computed with optimum cost via fast methods. This is applied to reduce the cost of the optimization process used to design MS antennas based on spatially modulated reactance profiles. The authors support the method proposed, presenting criteria to define the entire-domain functions, considering the overall numerical complexity in an optimization framework, and providing a convergence analysis and the numerical results for holographic leaky-wave antennas, relevant in the MS context.

In this chapter the source reconstruction using equivalent currents is a mature technique with a number of interesting applications such as field transformation (NF-FF/NF-NF), electromagnetic diagnostics, design optimization, general source modeling, and antenna synthesis. Its formulation and numerical solution are based on the widely popular MoM and therefore inherits its well-known properties such as accuracy and flexibility and profits directly from advanced techniques developed around MoM such as low-frequency, large-scale, and multi-resolution solvers to mention some. It has been found that the DEqF provides robust results and the best accuracy in real-world situations both for diagnostics and for field transformations, while the simpler SEqFs could be of interest in order to reduce memory and time requirements when the loss in accuracy is acceptable, or when dealing with data from simulation.

The success and worldwide diffusion of microsatellites lies mainly in the time reduction for mission preparation and launch costs. Testing and validation of the installed antenna using conventional Near-field (NF) techniques can be prohibitive in terms of cost and duration in some cases. An advanced and innovative RF test methodology that allows to dramatically reduce time and costs associated with the microsatellites integration phase has been developed, consolidated and validated. The time reduction has been achieved by dramatically reducing the number of measurement points. This has been achieved by combining measurements and fast numerical modelling using Numerically Defined Basis Function Expansion (NDBFE). Considerably faster testing is accomplished, with a known level of confidence with respect to traditional measurements. In this paper, we present the methodology together with validation results on a microsatellite mock-up.

A hierarchical quasi-Helmholtz decomposition, originally developed to address the dense-discretization breakdowns for the electric field integral equation, is applied together with an algebraic preconditioner to improve the convergence of the combined field integral equation in multiscale problems. The effectiveness of the proposed method is studied first on some simple examples; next, tests on real-life cases up to several hundreds of wavelengths show its good performance.

This paper offers an efficient numerical approach to optimizing the design of large circular planar Metasurfaces (MTSs) antennas based on specially varying impedance profiles. Div-conforming spectral basis functions on the whole antenna are defined. The goal is to reduce the number of unknowns, to lead to a well-conditioned system, and to speed up the multiple solutions needed by an automatic optimization code. We consider the overall numerical complexity of the scheme and show its advantages in optimization applications.

Synchronization is deemed to play an important role in information processing in many neuronal systems. In this work, using a well known technique due to Pecora and Carroll, we investigate the existence of a synchronous state and the bifurcation diagram of a network of synaptically coupled neurons described by the Hindmarsh-Rose model. Through the analysis of the bifurcation diagram, the different dynamics of the possible synchronous states are evidenced. Furthermore, the influence of the topology on the synchronization properties of the network is shown through an example.

This paper proposes an innovative functional testing methodology suitable for RF end-to-end antenna testing. Any measurement point requires mechanical movement and signal integration time to produce a sample; thus, the most radical way to reduce testing time is to reduce the number of required measured samples to a minimum. The presented approach exploits existing measurement capabilities, and allows a radical under-sampling via insertion of a-priori information by way of suitable use of advanced numerical modeling tools. The methodology can be used also with non-canonical grids, and when only a limited number of measured points is available. Experimental results are provided to show the potentials of the method.

In this chapter, the subject of synchronization is introduced and discussed considering the effects due to network topology. The chapter is organized as follows: (a) after a brief recap of a method due to Pecora and Carroll for checking the conditions for identical synchronization, several of the most popular topologies are considered, showing their influence on network synchronizability; (b) a technique, useful to find out the onset of synchronization in network of periodic oscillators is described in detail; (c) some simulation examples are given; (d) the case of synchronization in networks of nearly identical oscillators is illustrated by examples.

This paper uses synchronization as a tool for further validating a circuit (HR-PWL circuit) recently proposed in the literature and based on a piecewise-linear (PWL) approxima- tion of the Hindmarsh-Rose (HR) neuron model. The accuracy of the single neuron hardware implementation has been already validated through bifurcation analysis tools. Here, the syn- chronization behavior of networks formed by HR neurons is simulated and compared to that of companion networks of PWL neurons, with the purpose of validating the HR-PWL circuit also from a collective behavior point of view. In the considered cases, the neurons are connected either by linear diffusive or by nonlinear sigmoidal coupling, with different topologies. The analysis is based on the Master Stability Function approach and is verified by extensive nu- merical time-domain simulations. The synchronization properties of the PWL neuron networks turn out to be qualitatively very similar to those of the companion HR networks, confirming the validity of the proposed hardware-implemented neuron.

Synchronization plays central role in processing of information in many systems. In this work we propose a method for both to predict the behavior of the synchronous state of a network of Hindmarsh-Rose neurons and to synthesize such a network with a prescribed time-domain evolution. This method combines the synchronization conditions of the network and the bifurcation diagram of the synchronous state.

Synchronization plays a central role in information processing in many systems. In this work, starting from a method for predicting the behavior of the synchronous state in a network of Hindmarsh-Rose neurons, the dependence of the synchronization properties of the network on the topology is shown.