Improving the convergence rate to steady state of parabolic ADI methods

Saul S. Abarbanel; Douglas L. Dwoyer; David Gottlieb

doi:10.1016/0021-9991(86)90111-7

Improving the convergence rate to steady state of parabolic ADI methods

Saul S. Abarbanel
, Douglas L. Dwoyer
, David Gottlieb

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

The rate of convergence to steady state of parabolic ADI solvers is analyzed in terms of the L₂-norms of the residuals. The analysis allows one to predict the number of iterations necessary for convergence as function of the Courant number, λ. A simple modification of existing ADI codes is devised. It improves the convergence rate substantially and is insensitive to the Courant number in a large range of λ.

Original language	English
Pages (from-to)	1-18
Number of pages	18
Journal	Journal of Computational Physics
Volume	67
Issue number	1
DOIs	https://doi.org/10.1016/0021-9991(86)90111-7
State	Published - Nov 1986
Externally published	Yes

Bibliographical note

Funding Information:
* Research was supported in part by the U.S. Air Force Office of Scientific Research under Grant AFOSR-80-0249 and in part by the NASA Cooperative Agreement NCCl-45. + Research was supported in part by the U.S. Army Research and Standardization Group (Europe) under Contract DAJA 38-80-C-0032 and in part by NASA Contract NAS l-15810 while the author was in residence at ICASE, NASA Langley Research Center, Hampton, Virginia 23665.

Funding

* Research was supported in part by the U.S. Air Force Office of Scientific Research under Grant AFOSR-80-0249 and in part by the NASA Cooperative Agreement NCCl-45. + Research was supported in part by the U.S. Army Research and Standardization Group (Europe) under Contract DAJA 38-80-C-0032 and in part by NASA Contract NAS l-15810 while the author was in residence at ICASE, NASA Langley Research Center, Hampton, Virginia 23665.

Funders	Funder number
NASA Langley Research Center, Hampton, Virginia	23665
U.S. Army Research and Standardization Group	NAS l-15810, DAJA 38-80-C-0032
National Aeronautics and Space Administration	NCCl-45
Air Force Office of Scientific Research	AFOSR-80-0249

Access to Document

10.1016/0021-9991(86)90111-7

Cite this

@article{ebd75e031c8d4a7d8c3ac9a26a1c65ae,

title = "Improving the convergence rate to steady state of parabolic ADI methods",

abstract = "The rate of convergence to steady state of parabolic ADI solvers is analyzed in terms of the L2-norms of the residuals. The analysis allows one to predict the number of iterations necessary for convergence as function of the Courant number, λ. A simple modification of existing ADI codes is devised. It improves the convergence rate substantially and is insensitive to the Courant number in a large range of λ.",

author = "Abarbanel, \{Saul S.\} and Dwoyer, \{Douglas L.\} and David Gottlieb",

note = "Funding Information: * Research was supported in part by the U.S. Air Force Office of Scientific Research under Grant AFOSR-80-0249 and in part by the NASA Cooperative Agreement NCCl-45. + Research was supported in part by the U.S. Army Research and Standardization Group (Europe) under Contract DAJA 38-80-C-0032 and in part by NASA Contract NAS l-15810 while the author was in residence at ICASE, NASA Langley Research Center, Hampton, Virginia 23665.",

year = "1986",

month = nov,

doi = "10.1016/0021-9991(86)90111-7",

language = "אנגלית",

volume = "67",

pages = "1--18",

journal = "Journal of Computational Physics",

issn = "0021-9991",

publisher = "Academic Press Inc.",

number = "1",

}

TY - JOUR

T1 - Improving the convergence rate to steady state of parabolic ADI methods

AU - Abarbanel, Saul S.

AU - Dwoyer, Douglas L.

AU - Gottlieb, David

N1 - Funding Information: * Research was supported in part by the U.S. Air Force Office of Scientific Research under Grant AFOSR-80-0249 and in part by the NASA Cooperative Agreement NCCl-45. + Research was supported in part by the U.S. Army Research and Standardization Group (Europe) under Contract DAJA 38-80-C-0032 and in part by NASA Contract NAS l-15810 while the author was in residence at ICASE, NASA Langley Research Center, Hampton, Virginia 23665.

PY - 1986/11

Y1 - 1986/11

N2 - The rate of convergence to steady state of parabolic ADI solvers is analyzed in terms of the L2-norms of the residuals. The analysis allows one to predict the number of iterations necessary for convergence as function of the Courant number, λ. A simple modification of existing ADI codes is devised. It improves the convergence rate substantially and is insensitive to the Courant number in a large range of λ.

AB - The rate of convergence to steady state of parabolic ADI solvers is analyzed in terms of the L2-norms of the residuals. The analysis allows one to predict the number of iterations necessary for convergence as function of the Courant number, λ. A simple modification of existing ADI codes is devised. It improves the convergence rate substantially and is insensitive to the Courant number in a large range of λ.

UR - https://www.scopus.com/pages/publications/30244540563

U2 - 10.1016/0021-9991(86)90111-7

DO - 10.1016/0021-9991(86)90111-7

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:30244540563

SN - 0021-9991

VL - 67

SP - 1

EP - 18

JO - Journal of Computational Physics

JF - Journal of Computational Physics

IS - 1

ER -

Improving the convergence rate to steady state of parabolic ADI methods

Abstract

Bibliographical note

Funding

Access to Document

Other files and links

Fingerprint

Cite this