Method for improving convergence of the reflected Sommerfeld integrals for a multilayered media

Reflected Sommerfeld integrals over a half-space or over a multilayered media are semi-infinite and for small heights of source and field points tend to converge slow. For improving the convergence, slowly converging terms can be asymptotically extracted, and analytically integrated. In this paper, by the use of one of the analytically solvable Bessel function integrals, a new integrand term is extracted. The results is that the convergence is improved and the numerical effort (and, thus, the computational time) reduced by the factor of ten.