Fast Convolution Schemes for Piecewise Approximation of Large-Scale Electromagnetic Systems in Emerging Applications

Time-domain macromodeling represents an effective technique for generating compact models of the linear time-invariant portion of complex electromagnetic systems. Among the various techniques, a well-known one involves the computation of the port impulse response at the system's ports, which is then used for calculating convolution integrals. Such computation is typically slow. Recently, a method has been proposed to accelerate such computation by exploiting a piecewise constant approximation of the impulse responses, leading to the so-called segment fast convolution approach. The contribution of the present work is twofold: i) to extend the aforementioned method to the case of piecewise linear approximation of the port impulse responses in the case of linear time-invariant circuits; ii) to define a highly efficient quasi-recursive convolution computation algorithm for both constant and linear piecewise approximations. Moreover, vectorization is exploited to further improve computational efficiency. The proposed convolution schemes are validated in the case of a simple two-port network and then applied to relevant case studies of large-scale electromagnetic systems. Specifically, Reconfigurable Intelligent Surfaces (RISs) and neuromorphic circuits are modeled and validated. The numerical evaluation shows that the proposed schemes are able to guarantee high accuracy together with significant computational speed-ups.