This paper aims to improve the computational efficiency of higher-order accurate Noye–Hayman [NH (9,9)] implicit finite difference scheme for the solution of electromagnetic scattering problems in tunnel environments.
The proposed method consists of two major steps: First, the higher-order NH (9,9) scheme is numerically discretized using the finite-difference method. The second step is to use an algorithm based on hierarchical interpolative factorization (HIF) to accelerate the solution of this scheme.
It is observed that the simulation results obtained from the numerical tests illustrate very high accuracy of the NH (9,9) method in typical tunnel environments. HIF algorithm makes the NH (9,9) method computationally efficient for two-dimensional (2D) or three-dimensional (3D) problems. The proposed method could help in reducing the computational cost of the NH (9,9) method very close to O(n) usual O(n3) for a full matrix.
For simplicity, in this study, perfect electric conductor boundary conditions are considered. Future research may also include the utilization of meteorological techniques, including the effects of backward traveling waves, and make comparisons with the experimental data.
This study is directly applicable to typical problems in the field of tunnel propagation modeling for both national commercial and military applications.
