Convergence properties of waveform relaxation circuit simulation methods

• Published in: IEEE transactions on circuits and systems. 1, Fundamental theory and applications Vol. 45; no. 7; pp. 726 - 738
• Main Authors: Gristede, G.D., Ruehli, A.E., Zukowski, C.A.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.07.1998; Institute of Electrical and Electronics Engineers
• Subjects: Applied sciences; Capacitors; Circuit simulation; Convergence; Costs; Design. Technologies. Operation analysis. Testing; Differential equations; Electronic equipment and fabrication. Passive components, printed wiring boards, connectics; Electronics; Exact sciences and technology; Integrated circuits; Production; Relaxation methods; Runtime; Semiconductor electronics. Microelectronics. Optoelectronics. Solid state devices; Sufficient conditions; Time varying systems; Waveform; Time varying system; Circuit design; Simulation; Theoretical study; Relaxation method; Linear time; Convergence
• DOI: 10.1109/81.703839
• ISSN: 1057-7122

A new method for the analysis and understanding of the convergence properties of the waveform relaxation (WR) circuit simulation method is derived. The method describes the convergence properties of WR through a continuous-time linear time-varying (LTV) system convergence equation. From the LTV convergence equation, new sufficient conditions for the convergence of WR are derived that are less restrictive than those of all known previous work. The new sufficient conditions are shown to be valid both for the case of an exact solution of the circuit differential equations and the real-life case of an approximate numerical solution of these equations. An example is given, illustrating the application of the LTV convergence equation and comparing the new sufficient conditions for convergence of the WR method against previous work.