Nilpotent Waveform Relaxation Methods for Chains of Passive Circuits

Abstract

New results on the nilpotency of the waveform relaxation (WR) algorithm are presented for chains of general linear time-invariant circuits. Strictly dissipative impedance coupling is used in the WR method to decouple the cascaded parts. Three relaxation schemes: Gauss-Jacobi, Gauss-Seidel and relaxation by forward and reverse sweeping implement the WR iterations. The analysis of the operator matrices in the Fourier domain leads to the characterization of the nilpotent WR operator for the three relaxation schemes.