Machine Precision Numerical Evaluation of Reaction Integrals in the Method of Moments

One of the elements that affects the overall accuracy of the solution of Surface Integral Equations (SIEs) via the Method of Moments (MoM) is the accuracy in the numerical evaluation of the double surface reaction integrals that constitute the system matrix, especially for its near-field part (present in any applied fast solution method). Each reaction integral is formed by a source (inner) integral, that can be singular, and a test (outer) integral. The source integral singularity is due to its kernel that is the background Green’s function for the Electric Field Integral Equation (EFIE) or the gradient of the background Green’s function for the Magnetic Field Integral Equation (MFIE).