Transient Simulation of Complex High-Speed Channels via Waveform Relaxation

This paper presents a class of numerical schemes for fast transient simulation of electrically long and complex linear channels terminated by linear or nonlinear networks. The common denominator of all schemes is waveform relaxation. Domain decomposition approaches based on longitudinal and transverse partitioning are pursued, leading to various iterative methods characterized by different properties and numerical efficiency. For each scheme, we present a detailed convergence analysis and a set of numerical results obtained on industrial benchmarks. The main contribution of this paper is a novel theoretical framework based on a combination of longitudinal and transverse relaxation, leading to particularly efficient simulations when combined with compact channel representations based on delay-rational macromodels. Our prototypal implementation outperforms SPICE solvers, with speedup of up to two orders of magnitude.