A fast finite difference method for propagation predictions over irregular, inhomogeneous terrain

Propagation of electromagnetic waves over irregular, inhomogeneous terrain is solved by a finite difference scheme. The method is fast and requires considerably less memory than the integral equation methods. The method requires a storage space of order O(N) and an execution time of order O(N²). Fields generated by a TE₂ line source are represented in an integral form in terms of the field over a flat, constant impedance plane (the incident field), and the field scattered by the terrain irregularities and inhomogeneities. Accurate expressions are provided for the incident field and the Green´s function, whose evaluation is otherwise accomplished by the rather time-consuming Sommerfeld´s integrals. Measured equation of invariance is used to terminate the computational domain. The sparse matrix generated by the method is inverted by the Ricatti transform. Numerical results are presented for the ground wave as well as for the sky wave. Comparison is made for known geometries to establish the validity and limitations of the method