Convergence properties of waveform relaxation circuit simulation methods

Author

Gristede, George Diedrich ; Ruehli, Albert E. ; Zukowski, Charles Albert

Author_Institution

IBM Thomas J. Watson Res. Center, Yorktown Heights, NY, USA

Volume

45

Issue

7

fYear

1998

fDate

7/1/1998 12:00:00 AM

Firstpage

726

Lastpage

738

Abstract

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

Keywords

circuit analysis computing; continuous time systems; convergence of numerical methods; iterative methods; linear systems; time-varying systems; continuous-time linear time-varying system; convergence; differential equation; numerical method; waveform relaxation circuit simulation; Capacitors; Circuit simulation; Convergence; Costs; Differential equations; Production; Relaxation methods; Runtime; Sufficient conditions; Time varying systems;

fLanguage

English

Journal_Title

Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on

Publisher

ieee

ISSN

1057-7122

Type

jour

DOI

10.1109/81.703839

Filename

703839