Evaluation of hypersingular integrals on non-planar surfaces

Abstract

Solving electric field integral equation (EFIE) with Nyström method requires accurate evaluation of hypersingular surface integrals since this method does not use divergence conforming basis and testing functions. The success of the method also depends on accurate representation of non-planar characteristics of the scattering object. In this study Hadamard finite part interpretation is used to evaluate hypersingular integrals over non-planar surfaces, which are represented by their Taylor series expansions. Numerical tests are conducted to show the effectiveness of the formulas. Also a scattering problem is solved which confirms the accuracy.