Self-consistent impedance method for the solution of electromagnetic problems

A two-dimensional, self-consistent, impedance method for modelling electromagnetic problems has been derived from Faraday´s and Ampere´s Laws. The result is a single matrix equation for the magnetic field scaled by the constitutive electrical parameters of the media. From this a complete solution of the magnetic field is calculated for every cell in the solution space. The source field is introduced into the model as a fixed magnetic field value on the right hand side of this matrix equation. This extends previous formulations of the impedance method to cover a wider variety of electromagnetic problems across the complete electromagnetic spectrum, including all types of materials. An absorbing boundary consisting of a single cell backed by a PEC was optimised to give a reflection coefficient of less than -55 dB for normal incidence. The method has been applied to various models including CW scattering from a dielectric filament at 10 GHz to determine permittivity changes, waveguides containing lossy media, and VLF surface impedance calculations