A waveform relaxation approach to determining periodic responses of linear differential-algebraic equations

Yao Lin Jiang; Richard M.M. Chen; Omar Wing

doi:10.1109/iscas.2001.922080

A waveform relaxation approach to determining periodic responses of linear differential-algebraic equations

Yao Lin Jiang
, Richard M.M. Chen
, Omar Wing

School of Mathematics and Statistics

City University of Hong Kong
Chinese University of Hong Kong

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

5 Scopus citations

Abstract

We propose an algorithm, which is based on the waveform relaxation (WR) approach, to find the periodic responses of differential-algebraic equations. We derive an analytic expression of the spectral radius for the WR operator under a periodic constraint. Convergent splittings are obtained from this expression. Discrete waveforms are computed by the finite difference method. Numerical examples further illustrate the theoretical work in this paper.

Original language	English
Title of host publication	ISCAS 2001 - 2001 IEEE International Symposium on Circuits and Systems, Conference Proceedings
Publisher	IEEE Computer Society
Pages	443-446
Number of pages	4
ISBN (Print)	0780366859, 9780780366855
DOIs	https://doi.org/10.1109/iscas.2001.922080
State	Published - 2001
Event	2001 IEEE International Symposium on Circuits and Systems, ISCAS 2001 - Sydney, NSW, Australia Duration: 6 May 2001 → 9 May 2001

Publication series

Name	ISCAS 2001 - 2001 IEEE International Symposium on Circuits and Systems, Conference Proceedings
Volume	5

Conference

Conference	2001 IEEE International Symposium on Circuits and Systems, ISCAS 2001
Country/Territory	Australia
City	Sydney, NSW
Period	6/05/01 → 9/05/01

Keywords

Differential-algebraic equations
circuit simulation
finite difference
periodic responses
spectra of linear operators
waveform relaxation

Access to Document

10.1109/iscas.2001.922080

Cite this

Jiang, Y. L., Chen, R. M. M., & Wing, O. (2001). A waveform relaxation approach to determining periodic responses of linear differential-algebraic equations. In ISCAS 2001 - 2001 IEEE International Symposium on Circuits and Systems, Conference Proceedings (pp. 443-446). Article 922080 (ISCAS 2001 - 2001 IEEE International Symposium on Circuits and Systems, Conference Proceedings; Vol. 5). IEEE Computer Society. https://doi.org/10.1109/iscas.2001.922080

Jiang, Yao Lin ; Chen, Richard M.M. ; Wing, Omar. / A waveform relaxation approach to determining periodic responses of linear differential-algebraic equations. ISCAS 2001 - 2001 IEEE International Symposium on Circuits and Systems, Conference Proceedings. IEEE Computer Society, 2001. pp. 443-446 (ISCAS 2001 - 2001 IEEE International Symposium on Circuits and Systems, Conference Proceedings).

@inproceedings{e049268fe2c04b7489b226e80f0b1d4b,

title = "A waveform relaxation approach to determining periodic responses of linear differential-algebraic equations",

abstract = "We propose an algorithm, which is based on the waveform relaxation (WR) approach, to find the periodic responses of differential-algebraic equations. We derive an analytic expression of the spectral radius for the WR operator under a periodic constraint. Convergent splittings are obtained from this expression. Discrete waveforms are computed by the finite difference method. Numerical examples further illustrate the theoretical work in this paper.",

keywords = "Differential-algebraic equations, circuit simulation, finite difference, periodic responses, spectra of linear operators, waveform relaxation",

author = "Jiang, \{Yao Lin\} and Chen, \{Richard M.M.\} and Omar Wing",

year = "2001",

doi = "10.1109/iscas.2001.922080",

language = "英语",

isbn = "0780366859",

series = "ISCAS 2001 - 2001 IEEE International Symposium on Circuits and Systems, Conference Proceedings",

publisher = "IEEE Computer Society",

pages = "443--446",

booktitle = "ISCAS 2001 - 2001 IEEE International Symposium on Circuits and Systems, Conference Proceedings",

note = "2001 IEEE International Symposium on Circuits and Systems, ISCAS 2001 ; Conference date: 06-05-2001 Through 09-05-2001",

}

Jiang, YL, Chen, RMM & Wing, O 2001, A waveform relaxation approach to determining periodic responses of linear differential-algebraic equations. in ISCAS 2001 - 2001 IEEE International Symposium on Circuits and Systems, Conference Proceedings., 922080, ISCAS 2001 - 2001 IEEE International Symposium on Circuits and Systems, Conference Proceedings, vol. 5, IEEE Computer Society, pp. 443-446, 2001 IEEE International Symposium on Circuits and Systems, ISCAS 2001, Sydney, NSW, Australia, 6/05/01. https://doi.org/10.1109/iscas.2001.922080

A waveform relaxation approach to determining periodic responses of linear differential-algebraic equations. / Jiang, Yao Lin; Chen, Richard M.M.; Wing, Omar.
ISCAS 2001 - 2001 IEEE International Symposium on Circuits and Systems, Conference Proceedings. IEEE Computer Society, 2001. p. 443-446 922080 (ISCAS 2001 - 2001 IEEE International Symposium on Circuits and Systems, Conference Proceedings; Vol. 5).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - A waveform relaxation approach to determining periodic responses of linear differential-algebraic equations

AU - Jiang, Yao Lin

AU - Chen, Richard M.M.

AU - Wing, Omar

PY - 2001

Y1 - 2001

N2 - We propose an algorithm, which is based on the waveform relaxation (WR) approach, to find the periodic responses of differential-algebraic equations. We derive an analytic expression of the spectral radius for the WR operator under a periodic constraint. Convergent splittings are obtained from this expression. Discrete waveforms are computed by the finite difference method. Numerical examples further illustrate the theoretical work in this paper.

AB - We propose an algorithm, which is based on the waveform relaxation (WR) approach, to find the periodic responses of differential-algebraic equations. We derive an analytic expression of the spectral radius for the WR operator under a periodic constraint. Convergent splittings are obtained from this expression. Discrete waveforms are computed by the finite difference method. Numerical examples further illustrate the theoretical work in this paper.

KW - Differential-algebraic equations

KW - circuit simulation

KW - finite difference

KW - periodic responses

KW - spectra of linear operators

KW - waveform relaxation

UR - https://www.scopus.com/pages/publications/0035008520

U2 - 10.1109/iscas.2001.922080

DO - 10.1109/iscas.2001.922080

M3 - 会议稿件

AN - SCOPUS:0035008520

SN - 0780366859

SN - 9780780366855

T3 - ISCAS 2001 - 2001 IEEE International Symposium on Circuits and Systems, Conference Proceedings

SP - 443

EP - 446

BT - ISCAS 2001 - 2001 IEEE International Symposium on Circuits and Systems, Conference Proceedings

PB - IEEE Computer Society

T2 - 2001 IEEE International Symposium on Circuits and Systems, ISCAS 2001

Y2 - 6 May 2001 through 9 May 2001

ER -

Jiang YL, Chen RMM, Wing O. A waveform relaxation approach to determining periodic responses of linear differential-algebraic equations. In ISCAS 2001 - 2001 IEEE International Symposium on Circuits and Systems, Conference Proceedings. IEEE Computer Society. 2001. p. 443-446. 922080. (ISCAS 2001 - 2001 IEEE International Symposium on Circuits and Systems, Conference Proceedings). doi: 10.1109/iscas.2001.922080

A waveform relaxation approach to determining periodic responses of linear differential-algebraic equations

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