Rectangular cells offer a major advantage over triangular cells for numerical MoM simulation of planar structures. This is due to the fact that the dyadic Green's functions of planar layered background structures are space-invariant on the transverse plane. Recall that the elements of the moment matrix are given by the following equation:
:<math> Z_{ij}^{(\mu v)} = \iiint_{V_i} dv f_i^{(\mu)}(r) \cdot \iiint_{V_j}dv' \overline{\overline{G}}_{\mu v}(r|r') \cdot f_j^{(v)}(r') </math><!--[[File:PMOM24(1).png]]-->
where the spatial-domain dyadic Green's functions are a function of the observation and source coordinates, '''r'''and '''r' '''. The MoM matrix elements can indeed be interpreted as interactions between two elementary basis functions '''f<sub>i</sub>(r)''' and '''f<sub>j</sub>(r')''' on that particular background structure. The spatial-domain dyadic Green's functions can themselves be expressed in terms of the spectral-domain dyadic Green's functions as follows:
:<math>\overline{\overline{G}}_{\mu v}(r|r') = \frac{1}{(2\pi)^2} \int\limits_{-\infty}^{\infty} \int\limits_{-\infty}^{\infty} \tilde{\overline{\overline{G}}}_{\mu v} (k_p, z|z') e^{-j[k_x(x-x')+k_y(y-y')]} \, dk_x \, dk_y ,\quad {k_p}^2 = {k_x}^2 + {k_y}^2</math><!--[[File:PMOM26.png]]-->
where the doubly infinite integration is performed with respect to the spectral [[variables]] k<sub>x</sub> and k<sub>y</sub>. As can be seen from the above expression, the spatial-domain dyadic Green's functions are functions of z, z', as well as (x-x') and (y-y'). The MoM matrix elements can now be transformed into the spectral domain as