Low-Frequency Stable Discretization of the Electric Field Integral Equation based on Poincaré's Lemma

Integral equations become inaccurate in the low-frequency regime not only due to a low-frequency breakdown (i.e., growth of the condition number), but also due to catastrophic round-off errors in the discretization of the excitation. In this work, we propose a testing strategy for the excitation that results in a low-frequency stable discretization irrespective of the topology (i.e., simply- or multiply-connected) or orientability of the object. We obtain this by leveraging the lemma of Poincare to derive vector potentials for a general class of excitations. Numerical results demonstrate the effectiveness of our approach.