Preserving Causality in Time Domain Integral Equation-Based Methods

The critical relevance of ensuring the excitation's causality in electromagnetic (EM) simulations is exploited by the computation of strictly causal time domain interaction integrals as they occur in the partial element equivalent circuit (PEEC) method. Under the hypothesis of thin, almost zero thickness objects, the presented formulas represent analytical impulse responses and, as such, are used within convolutions in the framework of the time domain PEEC solver. The proposed approach is compared with other standard approaches and clearly behaves better than frequency-domain methods in accurately catching the propagation delay and, thus, preserving the causality. Further, improved stability is observed compared to marching-on-in-time methods.