Application of two preconditioned generalized conjugate gradient methods to three-dimensional neutron and photon transport equations

G. S. Chen; R. D. Sheu

doi:10.1016/j.pnucene.2004.08.003

Application of two preconditioned generalized conjugate gradient methods to three-dimensional neutron and photon transport equations

G. S. Chen, R. D. Sheu

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

2 Scopus citations

Abstract

The application of preconditioned generalized conjugate gradient methods to solve the linear system of equations that arise in three-dimensional neutron and photon transport equations is discussed. These generalized conjugate gradient methods are the conjugate gradient square (CGS) algorithm and the bi-conjugate gradient stabilized (Bi-CGSTAB) algorithm. These methods have good residual error control procedures during computation and have good convergence rates. The results of the analysis show that the preconditioned CGS and Bi-CGSTAB methods with the preconditioner ILU are more efficient than with the preconditioner MILU in the test problem.

Original language	English
Pages (from-to)	11-23
Number of pages	13
Journal	Progress in Nuclear Energy
Volume	45
Issue number	1
DOIs	https://doi.org/10.1016/j.pnucene.2004.08.003
State	Published - 2004
Externally published	Yes

Keywords

Bi-CGSTAB
CGS
Neutron transport
Preconditioner
TORT

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10.1016/j.pnucene.2004.08.003

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title = "Application of two preconditioned generalized conjugate gradient methods to three-dimensional neutron and photon transport equations",

abstract = "The application of preconditioned generalized conjugate gradient methods to solve the linear system of equations that arise in three-dimensional neutron and photon transport equations is discussed. These generalized conjugate gradient methods are the conjugate gradient square (CGS) algorithm and the bi-conjugate gradient stabilized (Bi-CGSTAB) algorithm. These methods have good residual error control procedures during computation and have good convergence rates. The results of the analysis show that the preconditioned CGS and Bi-CGSTAB methods with the preconditioner ILU are more efficient than with the preconditioner MILU in the test problem.",

keywords = "Bi-CGSTAB, CGS, Neutron transport, Preconditioner, TORT",

author = "Chen, \{G. S.\} and Sheu, \{R. D.\}",

note = "Funding Information: This research was partially supported by Grant NSC-89E-007-064 of the National Science Council, Taiwan, ROC.",

year = "2004",

doi = "10.1016/j.pnucene.2004.08.003",

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journal = "Progress in Nuclear Energy",

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T1 - Application of two preconditioned generalized conjugate gradient methods to three-dimensional neutron and photon transport equations

AU - Chen, G. S.

AU - Sheu, R. D.

N1 - Funding Information: This research was partially supported by Grant NSC-89E-007-064 of the National Science Council, Taiwan, ROC.

PY - 2004

Y1 - 2004

N2 - The application of preconditioned generalized conjugate gradient methods to solve the linear system of equations that arise in three-dimensional neutron and photon transport equations is discussed. These generalized conjugate gradient methods are the conjugate gradient square (CGS) algorithm and the bi-conjugate gradient stabilized (Bi-CGSTAB) algorithm. These methods have good residual error control procedures during computation and have good convergence rates. The results of the analysis show that the preconditioned CGS and Bi-CGSTAB methods with the preconditioner ILU are more efficient than with the preconditioner MILU in the test problem.

AB - The application of preconditioned generalized conjugate gradient methods to solve the linear system of equations that arise in three-dimensional neutron and photon transport equations is discussed. These generalized conjugate gradient methods are the conjugate gradient square (CGS) algorithm and the bi-conjugate gradient stabilized (Bi-CGSTAB) algorithm. These methods have good residual error control procedures during computation and have good convergence rates. The results of the analysis show that the preconditioned CGS and Bi-CGSTAB methods with the preconditioner ILU are more efficient than with the preconditioner MILU in the test problem.

KW - Bi-CGSTAB

KW - CGS

KW - Neutron transport

KW - Preconditioner

KW - TORT

UR - https://www.scopus.com/pages/publications/10644221061

U2 - 10.1016/j.pnucene.2004.08.003

DO - 10.1016/j.pnucene.2004.08.003

M3 - Article

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SN - 0149-1970

VL - 45

SP - 11

EP - 23

JO - Progress in Nuclear Energy

JF - Progress in Nuclear Energy

IS - 1

ER -

Application of two preconditioned generalized conjugate gradient methods to three-dimensional neutron and photon transport equations

Abstract

Keywords

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