Volume Integral Equation Methods for Axisymmetric Problems With Conductive and Magnetic Media

Two new different integral equation methods for the study of axisymmetric harmonic electromagnetic problems are presented. Both proposed formulations allow the modeling of conductive and magnetic media, and inhomogeneous media can be considered as well. Thanks to the use of low-rank approximation techniques, a drastic reduction in the required memory and computational cost is achieved with a truly negligible loss of accuracy. The numerical features of the two proposed integral methods are widely discussed and compared. Moreover, most of the considerations hold for the case of 3-D integral methods. Sample implementations of the two formulations are made publicly available.