Hybrid Integration Scheme for the Evaluation of Strongly Singular and Near-Singular Integrals in Surface Integral Equations

The accurate and efficient evaluation of surface source integrals is a key step in obtaining reliable solutions of electromagnetic problems using integral equation formulations. In this paper, we propose to combine two of the most extensively used schemes to efficiently evaluate strongly singular and nearsingular source integrals, such as those arising in the K operator. In the proposed approach, singularity subtraction is first applied to remove the most dominant singular part; singularity cancellation, using the radial-angular variable transformation, is then employed to treat the remaining integrand. The method is compared to other common numerical schemes to demonstrate its effectiveness.