Evaluation of reaction integrals in the Galerkin's Method of Moments

The importance of guaranteeing the triangle-wise balance in the evaluation of the 4-D reaction integral for the scalar potential is evaluated in this paper. We will show that the div-conforming character of the RWG basis functions must be numerically preserved to machine precision. This is done naturally when the integration is performed by triangle pairs. However, a very small imbalance (even at high accuracy) in the evaluation of this integral for different basis and/or testing functions supported by a given triangle results in the accumulation of fictitious charges over the triangle's surface, artificially extending the frequency range over which the low-frequency breakdown should be a problem.