A method for calculating closed form integration of 2-D PMM impedance matrix

Abstract

Periodic moment method (PMM) is a useful tool to solve electromagnetic (EM) scattering problems for periodic structures. Double integrals over the cross section of the reference element are performed in the spectral domain formulation. Cross section of reference element of two-dimensional periodic structures; such as wedge absorber, is divided into different shape of cells to obtain scattering behavior. Cells are divided right-angled triangles and rectangles for PMM impedance matrix calculation. Integrating over multiple regions and summing results is needed more CPU time. In this paper, a square region based calculation technique instead of multiple regions technique is introduced for efficiently interpolating of two-dimensional PMM impedance matrices. Using this technique, arbitrary-shaped cells are transformed square cells, which have same area and centroid with existing cells. Thus, calculation of double integrals over cells are obtained easily. Contribution of the study is obtaining integration values by using a new and simple technique.