Applying divergence-free condition in solving the volume integral equation

Abstract

Applying divergence-free condition to volume integral equation solver will be discussed. Three schemes are available: basis reduction scheme, minimal complete volume loop basis set and expanded volume loop basis set. All of them will generate smaller matrix equations than the SWG basis. The first two schemes generate poorly-conditioned matrices that are hard to solve by iterative solvers. The expanded loop basis set is easier to solve iteratively in spite of the existence of a null space in the matrix. Moreover, the construction of the expanded loop basis set is much easier than the other two schemes.