Code-Verification Techniques for an Arbitrary-Depth Electromagnetic Slot Model

TL;DR

This work develops a code-verification framework for an EFIE-based arbitrary-depth slot model that captures electromagnetic penetration through openings. It employs manufactured solutions to separate and quantify discretization, numerical-integration, and sine-series truncation errors, using exact residual evaluations and an exact slot solution derived from a manufactured current. A key innovation is prescribing a manufactured surface current $\mathbf{J}_{\mathrm{MS}}$ and computing a consistent magnetic current $I_m(s)$ via a sine-series representation so the slot equations are satisfied without explicit source terms, enabling precise convergence studies. The results demonstrate expected rates across depths and Green’s-function choices, guiding robust verification in electromagnetic scattering simulations and clarifying how truncation and discretization interact in complex slot models.

Abstract

Electromagnetic slot models are employed to efficiently simulate electromagnetic penetration through openings in an otherwise closed electromagnetic scatterer. Such models, which incorporate varying assumptions about the geometry of the openings, are typically coupled with electromagnetic surface integral equations that model electromagnetic scattering. In this paper, we introduce novel code-verification approaches and build upon our previously developed methodologies to assess the correctness of the numerical implementation of an arbitrary-depth slot model. Through these approaches, we measure the convergence rates of the different interacting sources of numerical error and demonstrate the impact of various factors on these rates for several cases.

Figures (14)

• Figure 1: The exterior of the electromagnetic scatterer is connected to the interior of the cavity by a slot (left), which is modeled by a pair of wires positioned along the slot openings (right) freno_efie_slot_2024.
• Figure 2: Discretized domain using $n_t=2240$ triangles for 3 depths.
• Figure 3: Dimensions of the domain, which are specified in freno_efie_slot_2024.
• Figure 4: Components of $\mathbf{J}_\text{MS}$: $J_{\xi_\theta}$\ref{['eq:j_xi_theta']} for the scatterer (top) and cavity (middle), and $J_{\xi_\phi}$\ref{['eq:j_xi_phi']} for the scatterer (bottom).
• Figure 5: Components of $\mathbf{J}_\text{MS}$: $J_{\xi_\theta}$\ref{['eq:j_xi_theta']} (top), $J_{\xi_\phi}$\ref{['eq:j_xi_phi']} (middle), and $J=|\mathbf{J}_\text{MS}|$\ref{['eq:J_MS_cube']} and \ref{['eq:J_MS_triangular_prism']} (bottom).