Multigrid solver for 2D heat conduction problems

Y. Y. Koh, J. W.S. Lim, Y. L. Chua

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

As analytical solutions to heat transfer problems are difficult to obtain. Computational methods are presented as important analysis tools but conventional computational methods like Gauss-Seidel iteration are slow to converge. Therefore, a multigrid solver is introduced to address this issue. This report covers the two-dimensional rectangular heat conduction being solved using the finite-difference method and accelerated by the multigrid method. A brief explanation of multigrid will be presented. The result obtained from the analytical solutions were used as the baseline for comparison with the multigrid method. Once the results from the multigrid are validated, the single-grid method (Gauss-Seidel) is compared with the multigrid method in term of convergence rate and accuracy of results.

Original languageEnglish
Title of host publication5th International Conference on Green Design and Manufacture, IConGDM 2019
EditorsShayfull Zamree Bin Abd. Rahim, Mohd Mustafa Al-Bakri Bin Abdullah
PublisherAmerican Institute of Physics Inc.
ISBN (Electronic)9780735418714
DOIs
Publication statusPublished - 30 Jul 2019
Event5th International Conference on Green Design and Manufacture 2019, IConGDM 2019 - Kota Bandung, Jawa Barat, Indonesia
Duration: 29 Apr 201930 Apr 2019

Publication series

NameAIP Conference Proceedings
Volume2129
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Conference

Conference5th International Conference on Green Design and Manufacture 2019, IConGDM 2019
CountryIndonesia
CityKota Bandung, Jawa Barat
Period29/04/1930/04/19

Fingerprint

multigrid methods
conductive heat transfer
heat
iteration
heat transfer
methodology
grids
finite difference method
method

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

Cite this

Koh, Y. Y., Lim, J. W. S., & Chua, Y. L. (2019). Multigrid solver for 2D heat conduction problems. In S. Z. B. A. Rahim, & M. M. A-B. B. Abdullah (Eds.), 5th International Conference on Green Design and Manufacture, IConGDM 2019 [020033] (AIP Conference Proceedings; Vol. 2129). American Institute of Physics Inc.. https://doi.org/10.1063/1.5118041
Koh, Y. Y. ; Lim, J. W.S. ; Chua, Y. L. / Multigrid solver for 2D heat conduction problems. 5th International Conference on Green Design and Manufacture, IConGDM 2019. editor / Shayfull Zamree Bin Abd. Rahim ; Mohd Mustafa Al-Bakri Bin Abdullah. American Institute of Physics Inc., 2019. (AIP Conference Proceedings).
@inproceedings{e491ebd5b3ba41c6b7aa78438f57ee21,
title = "Multigrid solver for 2D heat conduction problems",
abstract = "As analytical solutions to heat transfer problems are difficult to obtain. Computational methods are presented as important analysis tools but conventional computational methods like Gauss-Seidel iteration are slow to converge. Therefore, a multigrid solver is introduced to address this issue. This report covers the two-dimensional rectangular heat conduction being solved using the finite-difference method and accelerated by the multigrid method. A brief explanation of multigrid will be presented. The result obtained from the analytical solutions were used as the baseline for comparison with the multigrid method. Once the results from the multigrid are validated, the single-grid method (Gauss-Seidel) is compared with the multigrid method in term of convergence rate and accuracy of results.",
author = "Koh, {Y. Y.} and Lim, {J. W.S.} and Chua, {Y. L.}",
year = "2019",
month = "7",
day = "30",
doi = "10.1063/1.5118041",
language = "English",
series = "AIP Conference Proceedings",
publisher = "American Institute of Physics Inc.",
editor = "Rahim, {Shayfull Zamree Bin Abd.} and Abdullah, {Mohd Mustafa Al-Bakri Bin}",
booktitle = "5th International Conference on Green Design and Manufacture, IConGDM 2019",

}

Koh, YY, Lim, JWS & Chua, YL 2019, Multigrid solver for 2D heat conduction problems. in SZBA Rahim & MMA-BB Abdullah (eds), 5th International Conference on Green Design and Manufacture, IConGDM 2019., 020033, AIP Conference Proceedings, vol. 2129, American Institute of Physics Inc., 5th International Conference on Green Design and Manufacture 2019, IConGDM 2019, Kota Bandung, Jawa Barat, Indonesia, 29/04/19. https://doi.org/10.1063/1.5118041

Multigrid solver for 2D heat conduction problems. / Koh, Y. Y.; Lim, J. W.S.; Chua, Y. L.

5th International Conference on Green Design and Manufacture, IConGDM 2019. ed. / Shayfull Zamree Bin Abd. Rahim; Mohd Mustafa Al-Bakri Bin Abdullah. American Institute of Physics Inc., 2019. 020033 (AIP Conference Proceedings; Vol. 2129).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

TY - GEN

T1 - Multigrid solver for 2D heat conduction problems

AU - Koh, Y. Y.

AU - Lim, J. W.S.

AU - Chua, Y. L.

PY - 2019/7/30

Y1 - 2019/7/30

N2 - As analytical solutions to heat transfer problems are difficult to obtain. Computational methods are presented as important analysis tools but conventional computational methods like Gauss-Seidel iteration are slow to converge. Therefore, a multigrid solver is introduced to address this issue. This report covers the two-dimensional rectangular heat conduction being solved using the finite-difference method and accelerated by the multigrid method. A brief explanation of multigrid will be presented. The result obtained from the analytical solutions were used as the baseline for comparison with the multigrid method. Once the results from the multigrid are validated, the single-grid method (Gauss-Seidel) is compared with the multigrid method in term of convergence rate and accuracy of results.

AB - As analytical solutions to heat transfer problems are difficult to obtain. Computational methods are presented as important analysis tools but conventional computational methods like Gauss-Seidel iteration are slow to converge. Therefore, a multigrid solver is introduced to address this issue. This report covers the two-dimensional rectangular heat conduction being solved using the finite-difference method and accelerated by the multigrid method. A brief explanation of multigrid will be presented. The result obtained from the analytical solutions were used as the baseline for comparison with the multigrid method. Once the results from the multigrid are validated, the single-grid method (Gauss-Seidel) is compared with the multigrid method in term of convergence rate and accuracy of results.

UR - http://www.scopus.com/inward/record.url?scp=85070547533&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85070547533&partnerID=8YFLogxK

U2 - 10.1063/1.5118041

DO - 10.1063/1.5118041

M3 - Conference contribution

AN - SCOPUS:85070547533

T3 - AIP Conference Proceedings

BT - 5th International Conference on Green Design and Manufacture, IConGDM 2019

A2 - Rahim, Shayfull Zamree Bin Abd.

A2 - Abdullah, Mohd Mustafa Al-Bakri Bin

PB - American Institute of Physics Inc.

ER -

Koh YY, Lim JWS, Chua YL. Multigrid solver for 2D heat conduction problems. In Rahim SZBA, Abdullah MMA-BB, editors, 5th International Conference on Green Design and Manufacture, IConGDM 2019. American Institute of Physics Inc. 2019. 020033. (AIP Conference Proceedings). https://doi.org/10.1063/1.5118041