Simulating Nonlinear Resistive Networks using a Behavioral Splitting

Abstract

An operator splitting method is developed for computing operating points of nonlinear resistive networks. Our behavioral formulation separates the device laws from Kirchhoff's laws and casts simulation as a zero-finding problem. Branch port resistances then provide a diagonal preconditioner for the relaxed Peaceman-Rachford iteration in scattering variables. Each iteration requires solving independent scalar equations and a linear system with a fixed weighted Laplacian matrix. Convergence is established for maximal monotone device laws when an operating point exists. Contractive branch reflections also yield a linear convergence bound independent of network topology. Numerical experiments on crossbar arrays illustrate the computational advantages.

arXiv commentSubmitted to European Control Conference 2027