Simulation of fields in an axially symmetric medium (Q2746901)

The authors develop numerical methods for calculating three-dimensional electric fields in unbounded media with an axial symmetry which are generated by dipole sources. Using the Fourier expansion, the authors reduce the initial-boundary value problem to a sequence of two-dimensional problems for harmonics. Finite-volume methods are described which approximate the initial problem on a rectangular grid. The system of difference equations is solved by an iterative method of incomplete factorization. In order to accelerate convergence, the solution is considered on three enclosed grids; intermediate interpolation, discrepancy correction, and inter-grid interpolation are used. Efficiency of the methods proposed is shown by a series of numerical experiments.