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The purpose of this paper is to conduct the accurate analysis and systematic characterisation of realistic generalised bi‐isotropic and lossy chiral metamaterial 3D applications at microwave frequencies.

An accuracy‐adjustable time‐domain methodology is developed. The technique uses a convex combination of optimal stencils along with an advanced wavefield decomposition to precisely model the highly dispersive, double negative nature of chirality and constitutive parameters. Furthermore, open‐region radiation or scattering problems are terminated through a pertinently modified perfectly matched layer (PML) of variable depth.

The paper reveals that the proposed algorithm is versatile in the generation of adaptive stencils that attain a very natural way of manipulating continuity conditions at material interfaces. Thus, when periodic structures with split‐ring resonators are to be modelled, the resulting schemes attain optimal precision and minimised dispersion errors. Numerical validation proves these merits via diverse demanding structures of curved shape and multiple layers.

The new technique introduces a family of piecewise polynomials and spatial discretization criteria which lead to additional degrees of freedom for the discrete vectors of the application. In this manner, grid dual is intrinsically embedded in the physical profile of the problem, without resorting to the simplified conventions of other approaches. Moreover, singularity points or demanding geometric discontinuities are properly manipulated, even via coarse lattice resolutions. Thus, the overall accuracy is significantly improved and the computational requirements remain in very logical and affordable levels.