Fast and Stable Circuit Simulation via Interpolation- Supported Numerical Inversion of the Laplace Transform

The modified numerical inversion of the Laplace transform (dubbed NILT) has been recently proposed as a fast and provably stable numerical simulation for general circuits. Although it has enabled increasing the simulation time step, it highlighted the need for robust approach that can recover the full waveform in between the time points generated by NILT. This article presents a new approach that addresses this challenge. The proposed approach leverages the NILT framework from a high-order approximation paradigm that computes points on the circuit waveforms to a methodology that computes high-order derivatives of the waveforms at the same points. Using those derivatives, an interpolation approach based on Hermite interpolation is used to construct the circuit waveforms on dense points. Numerical experiments are presented to demonstrate the accuracy of both approaches.