SUFFICIENT CONDITIONS FOR A GENERALIZED WAVEFORM RELAXATION TO CONVERGE LOCALLY.

Kiichi Urahama

Research output: Contribution to journalArticle

Abstract

This paper investigates convergence properties of a circuit simulation technique called Waveform Relaxation (WR). A general formulation of a family of WR algorithms called a generalized WR is introduced. This formulation reduces to some introduced WR algorithms in particular cases. The following two sufficient conditions for the generalized WR method to converge locally are given: i) the capacitance matrix of the circuit is block strictly diagonally dominant and a time-steplength is sufficiently small; ii) the conductance matrix of the circuit has the same property and a time-steplength is sufficiently large.

Original languageEnglish
Pages (from-to)106-109
Number of pages4
JournalTransactions of the Institute of Electronics, Information and Communication Engineers, Section E (
VolumeE70
Issue number2
Publication statusPublished - Feb 1 1987

Fingerprint

Networks (circuits)
Circuit simulation
Capacitance

All Science Journal Classification (ASJC) codes

  • Engineering(all)

Cite this

@article{7647972726b74fdebd574dd135f4e829,
title = "SUFFICIENT CONDITIONS FOR A GENERALIZED WAVEFORM RELAXATION TO CONVERGE LOCALLY.",
abstract = "This paper investigates convergence properties of a circuit simulation technique called Waveform Relaxation (WR). A general formulation of a family of WR algorithms called a generalized WR is introduced. This formulation reduces to some introduced WR algorithms in particular cases. The following two sufficient conditions for the generalized WR method to converge locally are given: i) the capacitance matrix of the circuit is block strictly diagonally dominant and a time-steplength is sufficiently small; ii) the conductance matrix of the circuit has the same property and a time-steplength is sufficiently large.",
author = "Kiichi Urahama",
year = "1987",
month = "2",
day = "1",
language = "English",
volume = "E70",
pages = "106--109",
journal = "Transactions of the Institute of Electronics, Information and Communication Engineers, Section E (",
number = "2",

}

TY - JOUR

T1 - SUFFICIENT CONDITIONS FOR A GENERALIZED WAVEFORM RELAXATION TO CONVERGE LOCALLY.

AU - Urahama, Kiichi

PY - 1987/2/1

Y1 - 1987/2/1

N2 - This paper investigates convergence properties of a circuit simulation technique called Waveform Relaxation (WR). A general formulation of a family of WR algorithms called a generalized WR is introduced. This formulation reduces to some introduced WR algorithms in particular cases. The following two sufficient conditions for the generalized WR method to converge locally are given: i) the capacitance matrix of the circuit is block strictly diagonally dominant and a time-steplength is sufficiently small; ii) the conductance matrix of the circuit has the same property and a time-steplength is sufficiently large.

AB - This paper investigates convergence properties of a circuit simulation technique called Waveform Relaxation (WR). A general formulation of a family of WR algorithms called a generalized WR is introduced. This formulation reduces to some introduced WR algorithms in particular cases. The following two sufficient conditions for the generalized WR method to converge locally are given: i) the capacitance matrix of the circuit is block strictly diagonally dominant and a time-steplength is sufficiently small; ii) the conductance matrix of the circuit has the same property and a time-steplength is sufficiently large.

UR - http://www.scopus.com/inward/record.url?scp=0023296046&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0023296046&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0023296046

VL - E70

SP - 106

EP - 109

JO - Transactions of the Institute of Electronics, Information and Communication Engineers, Section E (

JF - Transactions of the Institute of Electronics, Information and Communication Engineers, Section E (

IS - 2

ER -