On the Volume-Surface Integral Equations for Low-Frequency Problems

Electromagnetic problems with both conducting media and penetrable media are formulated by volume-surface integral equations (VSIEs) in the integral equation approach. Conventionally, the electric field integral equation (EFIE) is used to describe the conducting part, but it has a serious low-frequency breakdown problem. In this work, we use the magnetic field integral equation to replace the EFIE for the conducting part and combine the volume integral equations of the penetrable part to form the VSIEs. The resulting VSIEs belong to a second kind of integral equations and can remove the low-frequency breakdown problem. A numerical example is presented to demonstrate the approach and good results have been obtained.