The construction of effective methods for electromagnetic modelling

Summary. This paper deals with the further development of finite-difference methods for electromagnetic field modelling in two-and three-dimensional cases. The main feature of the approach suggested here is the application of generalized asymptotic boundary conditions valid with the accuracy (1/ρ^N), where ρ is the distance from the heterogeneities. The finite-difference approximation of problems under solution is made using the balance method, which results in 5-point difference schemes in the 2-D case and 7-point difference schemes in the 3-D case. To solve the linear system of difference equations the successive over-relaxation (SOR) method is used, the relaxation factor being chosen during the iteration procedure. In view of the vectorial character of the problem for the 3-D case, a successive blocked over-relaxation method (SBOR) is applied.
The model's validity is based on the comparison of the fields accounted at the ground surface with those computed by the integral transformation of excessive currents, determined in the heterogeneity region using the finite-difference scheme.