Tecniche avanzate di riduzione dell'ordine del modello di modelli PEEC ritardati

The partial element equivalent circuit (PEEC) method is a widely recognized electromagnetic computational technique due to its ability to represent electromagnetic phenomena using equivalent circuits. It is a popular technique in electromagnetic compatibility (EC) analysis, antenna, and interconnect design. Quasi-static PEEC models are represented by a set of ordinary differential equations (ODEs). However, delayed PEEC models are better suited for accurately capturing the behavior of complex electrically long structures where propagation delays are significant. These delayed PEEC models are formulated using neutral delayed differential equations (NDDEs). Due to the large number of state variables, PEEC models can be computationally intensive. We present advanced model order reduction (MOR) techniques for PEEC models. This work focuses on the development and application of proper orthogonal decomposition (POD)-based MOR techniques used for delayed PEEC models. We present the traditional and incremental singular value decomposition (SVD) techniques in frequency domain to optimize the reduction. We also modify the snapshot collection by considering the derivatives snapshots in the frequency domain which not only improve the accuracy of the reduced order models (ROMs) but also reduce the computational complexity during the construction of ROMs. The effectiveness of these approaches is validated through extensive numerical examples in both the frequency and time domain, demonstrating significant improvements in computational efficiency without compromising model accuracy. This research contributes to advancing MOR techniques for EM analysis and extends the applicability of PEEC models to more complex EM-circuit problems.