This paper presents the construction, use, and properties of a multiresolution (wavelet) basis for the method of moments (MoM) analysis of metal antennas, scatterers, and microwave circuits discretized by triangular meshes. Several application examples show fast convergence of iterative solvers and accurate solutions with highly sparse MoM matrices. The proposed basis is organized in hierarchical levels, and keeps the different scales of the problem directly into the basis functions representation; the current is divided into a solenoidal and a quasi-irrotational part, which allows mapping these two vector parts onto fully scalar quantities, where the wavelets are defined. As a byproduct, this paper also presents a way to construct hierarchical sets of Rao-Wilton-Glisson (RWG) functions on a family of meshes obtained by subsequent refinement, i.e., with the RWG of coarser meshes expressed as linear combinations of those of finer meshes.

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The particle swarm optimization (PSO) method has been successfully applied to different electromagnetic optimization problems. Because of the complexity of this kind of problems, the associated cost function is in general computationally expensive. A fast convergence of the optimization algorithm is hence required to attain results in short time. Here few variations over the standard algorithm, referred to as differentiated meta-PSO, aimed to enhance the global search capability, and to improve the algorithm convergence, are introduced. In order to verify their effectiveness the different techniques have been first applied to benchmark test functions and then used for the optimization of a planar array

An efficient artificial neural network (ANN) approach for the modeling of reflectarray elementary components is introduced to improve the numerical efficiency of the different phases of the antenna design and optimization procedure, without loss in accuracy. The comparison between the results of the analysis of the entire reflectarray designed using the simplified ANN model or adopting a full-wave characterization of the unit cell finally proves the effectiveness of the proposed model.

We present a synthesis of the sparse matrix/adaptive integral method (SM/AIM) and the multiresolution (MR) approach for the analysis of electrically large finite arrays, with planar or 3-D radiating elements; the two methods were separately introduced previously. The use of the MR has the effect of a preconditioner and speeds up the convergence rate of the SM/AIM of almost two orders of magnitude, with a total reduction of the numerical complexity with respect to the standard MoM of almost three orders of magnitude.