Block Structure Preserving Model Order Reduction for A-EFIE Integral Equation Method

TL;DR

This work tackles efficient wide-frequency electromagnetic analysis using integral-equation methods by applying a block-structure preserving MOR to the A-EFIE, which augments the EFIE with charge-continuity to produce a PEEC-like formulation. The method projects currents $\mathbf{j}$ and potentials $\phi$ separately via two projection bases $\mathbf{V}_1$ and $\mathbf{V}_2$, preserving inter-block couplings in the reduced operator $\tilde{\mathbf{A}}$. Numerical results on a 1 m dipole show substantial reductions in required high-fidelity solves (e.g., 14 vs 41 for 1e-3 accuracy) and improved impedance accuracy and solenoidity preservation compared to a monolithic MOR. The approach yields smaller, more accurate ROMs across a wide frequency band, enabling efficient frequency-sweep simulations for PEEC-like integral-equation formulations.

Abstract

A Block Structure Preserving Model Order Reduction approach is proposed for Integral Equations methods based on the Augmented Electric Field Integral Equation. This approach allows for representing the unknown fields with dedicated subspaces. Numerical results show that this leads to smaller reduced-order models and higher accuracy.

Figures (3)

• Figure 1: Impedance $Z$ of the antenna over frequency.
• Figure 2: Relative error in the impedance over frequency.
• Figure 3: Relative deviation from solenoidality over frequency.