Efficient solution of Noye–Hayman implicit finite-difference method for modelling wave propagation in tunnels

• Published in: Electronics letters 2020-10, Vol.56 (22), p.1167-1169
• Main Authors: Rasool, H.F, Qureshi, M.A, Aziz, A, Malik, F.H
• Format: Article
• Language: English
• Subjects: Antennas and propagation; CN method; computational requirements; conventional Crank–Nicolson method; efficient inversion; electromagnetic wave propagation; electromagnetic wave propagation characteristics; electromagnetic wave propagation problems; finite difference methods; NH2 implicit method; Noye–Hayman implicit finite‐difference method; parabolic equation models; parabolic equations; three‐dimensional parabolic equation; two‐level Noye–Hayman implicit method; wave propagation
• ISSN: 0013-5194; 1350-911X; 1350-911X
• DOI: 10.1049/el.2020.1978

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.