Solution box: SOLBOX-12

In three-dimensional electromagnetic solvers, extreme values for electrical parameters typically lead to instability, inaccuracy, and/or inefficiency issues. Despite using the term “extreme,” such relatively large or small values of conductivity, permittivity, permeability, wavenumber, intrinsic impedance, and other electrical parameters are commonly observed in natural cases. Computational electromagnetic solvers adapt themselves to handle challenging cases by replacing exact models with approximate models, while minimizing the modeling error due to these transformations. For example, most metals with high conductivity values are assumed to be perfectly conducting, especially if the considered structure is comparable to the wavelength. This is very common for practical devices, such as antennas, metamaterials, filters, etc., at radio and microwave frequencies. In some cases — e.g., when the overall structure is small in terms of a wavelength — even a full-wave solver may not be required to analyze the underlying phenomena. Examples are circuit theory based on lumped elements and transmission-line modeling. On the other side, penetrable models are commonly used to represent dielectric and magnetic materials, when their electrical parameters (specifically, permittivity and permeability) have numerically “reasonable” values that facilitate their full-wave solutions without a fundamental issue. As the electrical parameters become extreme and other conditions (sizes, excitations, geometric properties) are satisfied, numerical approximations may again become useful, leading to the well-known implementations such as those based on impedance boundary conditions and physical optics.