An Efficient Time-Domain Integral Solution for a Loaded Rectangular Metallic Enclosure With Apertures

This paper proposes an efficient time-domain mixed potential integral equation (TD-MPIE) technique to analyze the penetrated transient electromagnetic field into a perforated rectangular metallic enclosure loaded with conducting objects. To this end, the surface equivalent principle is applied, and the fields in the interior and the exterior regions of the enclosure are formulated by using the time-domain cavity and free space Green's functions, respectively. Then, the governing TD-MPIE is derived by enforcing the continuity of the tangential magnetic and electric fields on the surface of the apertures and conducting loads inside the shield, respectively. The resultant time-domain equation is then solved by using the marching-on-in time scheme. Here, the spatial integrations and temporal convolutions are carried out analytically which eliminates the need to complicated numerical integration routines and remove the late time instability. In addition, an accelerated algorithm is proposed to scale down the computational complexity from
$O(N_{\rm mod } N_t^2 N_s^2)$
down to
$O(N_{{\rm mod}} N_t (\log ^2 N_t + 2N_s))$
where
$N_{{\rm mod}}$
,
$N_{t}$
and
$N_{s}$
denote the total number of necessary modes inside the cavity, the number of time steps, and the spatial unknowns, respectively. The accuracy of the proposed technique is validated by comparing the simulated results with the well-known CST Microwave Studio time-domain solver, as well as the frequency-domain solution, and the measurements.