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Like all branches of physics and engineering, electromagnetics relies on mathematical methods for modeling, simulation, and design procedures in all of its aspects (radiation, propagation, scattering, imaging, etc.). Originally, rigorous analytical techniques were the only machinery available to produce any useful results. In the 1960s and 1970s, emphasis was placed on asymptotic techniques, which produced approximations of the fields for very high frequencies when closed-form solutions were not feasible. Later, when computers demonstrated explosive progress, numerical techniques were utilized to develop approximate results of controllable accuracy for arbitrary geometries. In this Special Issue, the most recent advances in the aforementioned approaches are presented to illustrate the state-of-the-art mathematical techniques in electromagnetics.

History of engineering & technology --- cubic-quartic Schrödinger equation --- cubic-quartic resonant Schrödinger equation --- parabolic law --- wave field transformation --- finite difference method --- Cole–Cole model --- Monte Carlo simulations --- percolation --- conductivity --- carbon nanotubes composite --- optical parametric amplification --- non-linear wave mixing --- micro-resonator --- optimization --- MRI system --- birdcage coil --- birdcage configurations --- coil capacitance --- analytical solution --- equivalent circuit modelling --- T-matrix theory --- 3D-EM simulation --- small volume RF coil --- method of auxiliary sources (MAS) --- electromagnetic scattering --- wedge --- numerical methods --- accuracy --- coil gun --- reluctance --- electromagnetic launcher --- mechatronics --- electronics --- mechanics --- simulation --- RoboCup --- magnetic field strength --- magnetic flux density --- magnetic potential --- current density --- power transmission line --- electromagnetic modelling --- integral formulation --- skin effect --- thin shell approach --- mutual inductance --- finite element method --- partial element equivalent circuit method --- magnetite nanoparticles --- Mie scattering theory --- near infrared laser --- photothermal therapy --- bioheat transfer --- diffusion approximation --- Arrhenius integral --- breast cancer --- air-core pulsed alternator --- electromagnetic rail launcher --- coupled analysis --- computational electromagnetics --- integral formulations --- n/a --- cubic-quartic Schrödinger equation --- cubic-quartic resonant Schrödinger equation --- Cole-Cole model