Acceleration of the Surface Test Integral Using Vertex Functions

In recent years, many papers have reported on the efficient and accurate evaluation of the double surface integrals that arise in the Method of Moments. Most have focused on the careful evaluation of the inner integral and assumed that the outer integral is sufficiently smooth to be easily evaluated numerically. More recently, several papers have appeared where the double integral is treated as a whole using the divergence theorem. These papers show promising results, though their implementation may imply changes to the integration paradigm for the associated codes. Here, instead, we investigate a technique that improves the numerical evaluation of the test integral without affecting the treatment of the source integral. From the integrand of the outer integral, we subtract pairs of quasi-static, so-called vertex functions defined on the source triangle. The approach is compared to standard Gauss-triangle schemes to demonstrate its effectiveness.