Efficient Evaluation of Test Integrals for Surface Method of Moments Based on Vertex Functions

The performance of any surface integral equations (SIE) code developed using the method of moments (MoM) is based on the efficient evaluation of a double surface integral. Much effort has been focused on the efficient solution of the interior (source) integral [1–2]. However, improving the exterior (test) integral is usually ignored, it often being assumed that once the inner integral has been evaluated, the integrand of the outer integral is sufficiently smooth that it may be evaluated numerically using standard numerical integration. However, this assumption is not always valid. As shown in [3], the evaluation of the outer integrals can be inefficient and surprisingly inaccurate, especially for dominant reactions such as between edge-and vertex-adjacent test and source triangles or for poorly-shaped triangles.