Effects of higher order analytical evaluation of integrals on the accuracy of the on-surface discretized boundary equation method for two-dimensional scattering problems

The on-surface discretized boundary equation (OS-DBE) method for two-dimensional scattering problems achieves high accuracy for the current solution, primarily due to the features of the method itself, but also due to higher order analytical evaluation of the integrals concerned. In this paper, we provide detailed formulation of higher order analytical integral evaluation and show its effects on the solution accuracy. In view of the fast multiple method (FMM) applied to the solution of the OS-DBE matrices, the higher order approximations to far interactions are also derived. The method of moments without or with FMM implementation is incidentally addressed regarding this subject. Abnormal phenomena associated with higher order evaluation that may appear in the magnetic field expressions or magnetic field integral equations are discussed.