Efficient numerical computation of singular integrals with applications to electromagnetics

Efficient schemes to accurately compute singular integrals are presented. The singularity is removed prior to numerical integration, using a change of variables, integration by parts, or a combination of both. A change of variables eliminates power-law singularities of the type x^-α, α<1 and renders the integrand well behaved. Similarly, a logarithmic singularity of the form ln x is eliminated either by direct integration by parts or by multiplying and dividing the integrand by ln x followed by integration by parts. Cauchy-type singularities are also removed by integrating the singular term by parts twice. In all cases, the remaining integrand is well behaved and lends itself to straightforward numerical integration. The technique is applied to scattering from a perfectly conducting cylinder. Comparison of the numerical and exact solutions show the stability of the technique