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

摘要

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.