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Parabolic equation models discretised with the finite‐difference method have been a research topic for a long time. Through the simulation of electromagnetic wave propagation characteristics in typical scenarios, it is pointed out that the fast algorithm needs to be developed for the solution of two‐level Noye–Hayman (NH2) implicit method to meet the accuracy and computational requirements of electromagnetic wave propagation problems in three‐dimensional environments. In this Letter, hierarchical skeletonisation is used for an efficient inversion of three‐dimensional parabolic equation discretised by the NH2 implicit method which is the modification of conventional Crank–Nicolson (CN) method. Numerical results show that the NH2 implicit method is more accurate than the CN method at no additional cost for a given numerical example.

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Parabolic equation models discretized with the finite difference method have been extensively studied for a long time. However, several explicit and implicit schemes exist in the literature. The advantage in explicit schemes is its simplicity, while its disadvantage is conditional stability. On the other hand, implicit schemes are unconditionally stable but require special treatment for a fast and accurate solution such as the Crank-Nicolson (CN) method. This method becomes computationally intensive for problems with dense meshes. The resulting matrix from the CN in two and three-dimensional cases requires high computational resources. This paper applies hierarchical interpolative factorization (HIF) to reduce the computational cost of the CN method. Numerical experiments are conducted to validate the proposed HIF acceleration.

In this paper, a new single layer subwavelength unit cell is designed for reflective metasurface at 28 GHz suitable for 5G communication with linear phase response and wide bandwidth characteristics. The proposed unit cell is analyzed through Floquet mode analysis for two different sizes. The unit cell with conventional half-wavelength size (HWS) has achieved 590° phase range while the unit cell with a subwavelength size (SWS) of λ/3 has achieved exactly 360° phase range. It is observed that the unit cell with SWS provides linear phase response as compared to the unit cell with HWS. Since non-linear phase response may produce more phase errors on wide range of frequencies, so SWS unit cell with 360° phase range and linear phase response is more suitable option for wideband operation as compared to conventional HWS unit cell with more than 360° phase range.