A Singularity Cancellation Technique for Weakly Singular Integrals on Higher Order Surface Descriptions

Accurate integration of singular and near-singular functions is critical to the accuracy of the method of moments solution to surface integral equations. While this problem has been widely addressed for flat geometries, its extensions to higher order surface descriptions have been limited. This letter provides a systematic prescription for the application of the rules for weakly singular integrals on higher order surfaces. Here, we present implementation details and several demonstrative results that compare the accuracy and convergence of the integration rules.