Analysis of a block gauss-seidel iterative method for a finite element discretization of the neutron transport equation

Leonard J. Lorence; William R. Martin; Mitchell Luskin

doi:10.1080/00411458508211669

Analysis of a block gauss-seidel iterative method for a finite element discretization of the neutron transport equation

Leonard J. Lorence, William R. Martin, Mitchell Luskin

School of Mathematics

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Abstract

We prove the convergence of a finite element discretization of the neutron transport equation. The iterative solution of the resulting linear system by a block Gauss-Seidel method is also analyzed. This procedure is shown to require less storage than the direct solution by Gaussian elimination, and an estimate for the rate of convergence is used to show that fewer arithmetic operations are required.

Original language	English (US)
Pages (from-to)	35-62
Number of pages	28
Journal	Transport Theory and Statistical Physics
Volume	14
Issue number	1
DOIs	https://doi.org/10.1080/00411458508211669
State	Published - Mar 1 1985

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This work was supported by the National Science

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10.1080/00411458508211669

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abstract = "We prove the convergence of a finite element discretization of the neutron transport equation. The iterative solution of the resulting linear system by a block Gauss-Seidel method is also analyzed. This procedure is shown to require less storage than the direct solution by Gaussian elimination, and an estimate for the rate of convergence is used to show that fewer arithmetic operations are required.",

author = "Lorence, {Leonard J.} and Martin, {William R.} and Mitchell Luskin",

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AU - Martin, William R.

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N2 - We prove the convergence of a finite element discretization of the neutron transport equation. The iterative solution of the resulting linear system by a block Gauss-Seidel method is also analyzed. This procedure is shown to require less storage than the direct solution by Gaussian elimination, and an estimate for the rate of convergence is used to show that fewer arithmetic operations are required.

AB - We prove the convergence of a finite element discretization of the neutron transport equation. The iterative solution of the resulting linear system by a block Gauss-Seidel method is also analyzed. This procedure is shown to require less storage than the direct solution by Gaussian elimination, and an estimate for the rate of convergence is used to show that fewer arithmetic operations are required.

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Analysis of a block gauss-seidel iterative method for a finite element discretization of the neutron transport equation

Abstract

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