On the Use of Continuity Condition in the Fast Solution of Volume-Surface Integral Equation

The validity of the use of continuity condition (CC) is studied when it is combined with the volume-surface integral equation (VSIE) to solve the electromagnetic scattering/radiation of composite conductor-dielectric objects. It is found that the explicit enforcement of CC in VSIE may be inaccurate if the involved conductor is infinitesimally thin, but it works well for the composite structures that only contain conductors with closed surfaces. Anew combined field integral equation-volume integral equation with enforced CC (CC-CFIE-VIE) is then proposed, and a convenient way to embed it into the context of the multilevel fast multipole algorithm is also provided. Numerical results show that CC-CFIE-VIE not only reduces the overall memory usage and the CPU time of a single iteration, but also decreases the number of iterations to reach desired accuracy.