Fundamental Locally One-Dimensional Method for 3-D Thermal Simulation
Summary :
This paper presents a fundamental locally one-dimensional (FLOD) method for 3-D thermal simulation. We first propose a locally one-dimensional (LOD) method for heat transfer equation within general inhomogeneous media. The proposed LOD method is then cast into compact form and formulated into the FLOD method with operator-free right-hand-side (RHS), which leads to computationally efficient update equations. Memory storage requirements and boundary conditions for both FLOD and LOD methods are detailed and compared. Stability analysis by means of analyzing the eigenvalues of amplification matrix substantiates the stability of the FLOD method. Additionally, the potential instability of the Douglas Gunn (DG) alternating-direction-implicit (ADI) method for inhomogeneous media is demonstrated. Numerical experiments justify the gain achieved in the overall efficiency for FLOD over LOD, DG-ADI and explicit methods. Furthermore, the relative maximum error of the FLOD method illustrates good trade-off between accuracy and efficiency.
- Publication
- IEICE TRANSACTIONS on Electronics Vol.E97-C No.7 pp.636-644
- Publication Date
- 2014/07/01
- Publicized
- Online ISSN
- 1745-1353
- DOI
- 10.1587/transele.E97.C.636
- Type of Manuscript
- Special Section PAPER (Special Section on Recent Advances in Simulation Techniques and Their Applications for Electronics)
- Category
Authors
Wei CHOON TAY
Nanyang Technological University
Eng LEONG TAN
Nanyang Technological University
Ding YU HEH
Nanyang Technological University
Keyword
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Wei CHOON TAY, Eng LEONG TAN, Ding YU HEH, "Fundamental Locally One-Dimensional Method for 3-D Thermal Simulation" in IEICE TRANSACTIONS on Electronics,
vol. E97-C, no. 7, pp. 636-644, July 2014, doi: 10.1587/transele.E97.C.636.
Abstract: This paper presents a fundamental locally one-dimensional (FLOD) method for 3-D thermal simulation. We first propose a locally one-dimensional (LOD) method for heat transfer equation within general inhomogeneous media. The proposed LOD method is then cast into compact form and formulated into the FLOD method with operator-free right-hand-side (RHS), which leads to computationally efficient update equations. Memory storage requirements and boundary conditions for both FLOD and LOD methods are detailed and compared. Stability analysis by means of analyzing the eigenvalues of amplification matrix substantiates the stability of the FLOD method. Additionally, the potential instability of the Douglas Gunn (DG) alternating-direction-implicit (ADI) method for inhomogeneous media is demonstrated. Numerical experiments justify the gain achieved in the overall efficiency for FLOD over LOD, DG-ADI and explicit methods. Furthermore, the relative maximum error of the FLOD method illustrates good trade-off between accuracy and efficiency.
URL: https://global.ieice.org/en_transactions/electronics/10.1587/transele.E97.C.636/_p
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@ARTICLE{e97-c_7_636,
author={Wei CHOON TAY, Eng LEONG TAN, Ding YU HEH, },
journal={IEICE TRANSACTIONS on Electronics},
title={Fundamental Locally One-Dimensional Method for 3-D Thermal Simulation},
year={2014},
volume={E97-C},
number={7},
pages={636-644},
abstract={This paper presents a fundamental locally one-dimensional (FLOD) method for 3-D thermal simulation. We first propose a locally one-dimensional (LOD) method for heat transfer equation within general inhomogeneous media. The proposed LOD method is then cast into compact form and formulated into the FLOD method with operator-free right-hand-side (RHS), which leads to computationally efficient update equations. Memory storage requirements and boundary conditions for both FLOD and LOD methods are detailed and compared. Stability analysis by means of analyzing the eigenvalues of amplification matrix substantiates the stability of the FLOD method. Additionally, the potential instability of the Douglas Gunn (DG) alternating-direction-implicit (ADI) method for inhomogeneous media is demonstrated. Numerical experiments justify the gain achieved in the overall efficiency for FLOD over LOD, DG-ADI and explicit methods. Furthermore, the relative maximum error of the FLOD method illustrates good trade-off between accuracy and efficiency.},
keywords={},
doi={10.1587/transele.E97.C.636},
ISSN={1745-1353},
month={July},}
Copy
TY - JOUR
TI - Fundamental Locally One-Dimensional Method for 3-D Thermal Simulation
T2 - IEICE TRANSACTIONS on Electronics
SP - 636
EP - 644
AU - Wei CHOON TAY
AU - Eng LEONG TAN
AU - Ding YU HEH
PY - 2014
DO - 10.1587/transele.E97.C.636
JO - IEICE TRANSACTIONS on Electronics
SN - 1745-1353
VL - E97-C
IS - 7
JA - IEICE TRANSACTIONS on Electronics
Y1 - July 2014
AB - This paper presents a fundamental locally one-dimensional (FLOD) method for 3-D thermal simulation. We first propose a locally one-dimensional (LOD) method for heat transfer equation within general inhomogeneous media. The proposed LOD method is then cast into compact form and formulated into the FLOD method with operator-free right-hand-side (RHS), which leads to computationally efficient update equations. Memory storage requirements and boundary conditions for both FLOD and LOD methods are detailed and compared. Stability analysis by means of analyzing the eigenvalues of amplification matrix substantiates the stability of the FLOD method. Additionally, the potential instability of the Douglas Gunn (DG) alternating-direction-implicit (ADI) method for inhomogeneous media is demonstrated. Numerical experiments justify the gain achieved in the overall efficiency for FLOD over LOD, DG-ADI and explicit methods. Furthermore, the relative maximum error of the FLOD method illustrates good trade-off between accuracy and efficiency.
ER -
English
