Near-singular and near-hypersingular surface integral evaluation by an adaptive singularity cancellation technique

Singular integrals encountered in surface integral equation formulation of electromagnetics need special treatment for their evaluation. Previously singularity extraction and Duffy transformations were very popular. However, recently proposed singularity cancellation transformations are the fully numerical methods which exactly cancel out the singularities of 1/R -and R/R³ -type integrals. However, these transformations become less efficient for near singularities. Also the convergence behaviour of these transformations is highly sensitive to variations in the height of observation point above the plane of source domain. We present adaptive singularity cancellation transformations which remove the drawbacks in the existing schemes resulting in dramatic enhancement in their efficiency by keeping the quadrature points always inside the original source domain. Further improvement in efficiency is acquired by adaptive choice of sample points proportional to the instantaneous dimensions in different directions. Theoretical analysis and numerical results are presented for triangular domains.