Solution of Volume Integral Equations with Novel Treatment to Strongly Singular Integrals

Locally corrected Nystrom (LCN) method is applied for the solution of volume integral equations (VIEs). Unlike the conventional method of moments (MoM) procedure, LCN method does not use divergence conforming basis and testing functions to reduce the order of singularity of the integrand. Therefore LCN method needs to handle kernels with higher order singularities. For VIEs, worst singularity is due to the double derivative operator acting on free space Green's function and resulting integrals are referred to strongly singular integrals. Using finite part interpretation, we converted strongly singular integrals to regular integrals, for the solution of which conventional numerical methods can be applied. We have solved a three-dimensional scattering problem from a dielectric cube and showed the validity of the method.