Fast Computation of Layered Media Green's Function via Recursive Taylor Expansion

The layered media Green's function (LMGF) is useful as a kernel of the method of moments (MoM) for a thin stratified medium. The self/mutual impedance expression of the MoM in conjunction with the LMGF includes a semi-infinite spectral integral inside the multiple integrals over spatial variables. As a result, computation of impedance matrix entries is quite costly. In this letter, an interpolation method by using the Taylor expansion is proposed. The method precomputes the spectral integral for a single spatial variable. The derivatives in the expansion are found in closed form using the recursive property of the Bessel functions. After that, the precomputed results of the spectral integral are interpolated via the Taylor expansion when the multiple integrals over spatial variables are performed. Due to the proposed method, the spectral integral and multiple integrals over spatial variables are separated from each other, and the resultant CPU time becomes quite manageable for very large problems.