Analysis of surface integral equations in electromagnetic scattering and radiation problems

Properties of various surface integral equations of the first and second kinds are studied in electromagnetic scattering and radiation problems. The second-kind equations are found to give better conditioned matrix equation and faster converging iterative solutions but poorer solution accuracy than the first-kind equations. The solution accuracy and matrix conditioning seem to be almost opposite properties associated with the singularity of the kernel of integral operators. The more singular/smoother the kernel, the more/less diagonally dominant and the better/poorer conditioned the matrix, but the poorer/better the solution accuracy. Accuracy of the integral equations of the second kind can be improved by increasing the order of the basis and testing functions. However, the required expansion order seems to be problem dependent. The more singular the unknown, the higher the expansion order and the finer the discretization needed in order to maintain the solution accuracy of the second-kind equations.