The interest in the electromagnetic behavior of periodic structures has significantly increased due to their crucial role in advancing cutting-edge applications in nanoscale and metasurface devices in scattering networks, plasmonic crystals, and nanophotonics. The rise of these technologies makes the improvement of the state-of-the-art methods in computational electromagnetics for the efficient solution of these kind of periodic structures even more crucial than ever. Traditional approaches predominantly centered on methods tailored for infinite periodic structures based on Floquet’s theorem and the Ewald transformation. However, although these methods have been demonstrated as powerful tools in the design process, they are not suitable for integration with other systems and sensors due to the limitation of infinite periodic structures or the accurate modeling of complex physical phenomena like edge effects and standing waves, vital phenomena for certain applications.

The electromagnetic behavior of periodic structures has gained great interest in recent years due to their fundamental role in the development of scattering networks, plasmonic crystals and many other fields related to nanophotonics, including nanoscale and metasurface devices. Linked to this interest is an increasing demand for the development of tools capable of modelling the electromagnetic behaviour of periodic structures as efficiently as possible. In the context of surface integral equation (SIE) methods based on the method of moments (MoM), most of the existing literature has focused on the development of techniques based on the Ewald method, which requires modelling the system with an infinite periodic structure or dealing with complex physical issues to correctly model the edge effects or the standing waves, whose accurate prediction can be critical in some applications.

This work proposes a domain decomposition method (DDM) based on Huygens' equivalence principle to efficiently perform an adaptive h-refinement technique for the electromagnetic analysis of multiscale structures via surface integral equations (SIEs). The procedure starts with the discretization of the structure under analysis via an initial coarse mesh, divided into domains. Then, each domain is treated independently, and the coupling to the rest of the object is obtained through the electric and magnetic current densities on the equivalent Huygens' surfaces (EHSs), surrounding each domain. From the initial solution, the error is estimated on the whole structure, and an adaptive h-refinement is applied accordingly. Both the error estimation and the adaptive h-refined solution are obtained through the defined EHSs, keeping the problem local. The adaptive h-refinement is obtained by a nonconformal submeshing, where multibranch Rao-Wilton-Glisson (MB-RWG) basis functions are defined. Numerical experiments of multiscale perfect-electric-conductor (PEC) structures in air, analyzed via the combined field integral equation, show the performance of the proposed approach.

In an Energy Harvesting system (EHS) the gamma process is used to model the electromagnetic energy received from radiofrequency (RF) radiation. The stochastic characterization of the harvested energy as a continuous-time stochastic process, namely, gamma process, is obtained from the Nakagami-m fading model, which describes the signal reception in a large amount of types of radiofrequency channels. Using the gamma process, some performance measures of the EHS system are obtained. Also, a transmission policy subject to different fading conditions is considered.

In recent years, invisibility has become a research area of increasing interest due to the advances in material engineering. It may be possible to achieve invisibility through cloaking devices by coating the body using one or more layers of materials with the proper electromagnetic properties. By using techniques associated to plasmonic cloaking it is maybe possible to obtain also invisibility for small objects with several layers of homogeneous materials working from inside the object. We demonstrate numerically that it is, therefore, possible to achieve invisibility through an inner system based on scattering cancellation techniques.

The solution of very large electromagnetic problems might be obtained using large computer facilities as singular High Performance Computers or Supercomputers. In these solutions, suitable numerical methods for large structures should be used, as fast methods e.g. Multilevel Fast Multipole Algorithms. The implementation of this kind of methods in a Computer capable to deal with the large amount of data and calculations is not simple; depending on the nature of the computer (shared memory based, distributed memory based, multi-core, many-core, etc.) you can obtain different performances, you can solve different applications, you must adapt the method to the machine-type, or you should reconsider the implementation strategies to achieve success when you lead with bigdata issues.

Electromagnetic applications of periodic materials have become popular in many modern optical and RF applications. The accurate computation of the electromagnetic response of large structures requires solving problems with high number of unknowns. Fast methods are useful to deal with such big problems, but, in general they do not take advantage of the periodicity properties. Based on the behaviour of impedance matrices involved in the solution of the surface integral equations with the Method of Moments, an accelerated solution based on the FFT is implemented. The presented approach slots the original impedance matrix and it applies the FFT to calculate the exact solution of the matrix vector product in an iterative process. The proposed solution achieves a linear memory cost proportional to 𝒪(N) and a computing time of 𝒪(N log N), where N is the problem number of unknowns. Also, in this paper, the advantages of this technique are shown in the developed applications.

Large periodic structures in computational electromagnetics need the management of large number of unknowns, implying high memory use and computation time. Apart from fast techniques such as the multilevel fast multipole algorithm, this kind of problems might be accelerated taking advantage of periodicity properties. We will present some techniques based on the application of the FFT to the method of moments for periodic structures (techniques that we called slotFFT) and some compression utilities based on macrobasis calculation, in order to further increase the sizes of the structures analyzed. The costs of these techniques are roughly O(N) in memory usage and O(N log N) or less in CPU time.

Large finite periodic problems are suitable for the application of methods to achieve high acceleration rates in the solution process. Applying distributed macrobasis decomposition to compress the method of moments impedance matrix combined to slotFFT algorithm allow to cover larger structures closer to real cases.