Singularity extraction for periodic layered medium green's function under matrix-friendly formulation

A singularity extraction technique is proposed to calculate the doubly periodic dyadic layered medium Green's function (P-DLMGF). Contrast from the conventional singularity subtraction method, the proposed approach starts from the matrix-friendly formulation of P-DLMGF. By first transferring the spatial derivatives from the P-DLMGF to the testing and basis function, the singularity of the dual summation kernel can be reduced by up to two order. Asymptotic and add-back terms are then derived with considerably improved feasibility.