Transient analysis of high-speed channels via Newton-GMRES Waveform Relaxation

Abstract

This paper presents a technique for the numerical simulation of coupled high-speed channels terminated by arbitrary nonlinear drivers and receivers. The method builds on a number of existing techniques. A Delayed-Rational Macromodel is used to describe the channel in compact form, and a general Waveform Relaxation framework is used to cast the solution as an iterative process that refines initial estimates of transient scattering waves at the channel ports. Since a plain Waveform Relaxation approach is not able to guarantee convergence, we turn to a more general class of nonlinear algebraic solvers based on a combination of the Newton method with a Generalized Minimal Residual iteration, where the Waveform Relaxation equations act as a preconditioner. The convergence of this scheme can be proved in the general case. Numerical examples show that very few iterations are indeed required even for strongly nonlinear terminations.