Polynomial preconditioning and the Generalized Minimal Residual algorithm solver for the 2-D Boltzmann transport equation

Tizaoui, Abdelkader

doi:10.1016/j.crma.2007.06.011

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Cited by 3 publications

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“…This points is one steps to accelerate the speed of the convergence. A work is in progress to accelerate this algorithm by using the preconditioning method [15,16] and confirm theses by the numerical results.…”

Section: Discussionsupporting

confidence: 60%

Theoretical and numerical analysis of the Minimal Residual Method for solving the neutron transport equation in spherical geometry

Tizaoui¹

2023

Preprint

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This paper focuses on an infinite dimensional adaptation of the Minimal Residual method for solving the neutron transport equation in spherical geometry. This method is based on a splitting of the collision operator strategy taking into account the characteristics of the transport operator. The theoretical and numerical analysis of this algorithm are given and compared to the methods given in [1, 2, 3].

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Section: Discussionsupporting

confidence: 60%

Theoretical and numerical analysis of the Minimal Residual Method for solving the neutron transport equation in spherical geometry

Tizaoui¹

2023

Preprint

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Iterative Methods for Solving the Neutron Transport Equation in 1-D Spherical Geometry

Tizaoui

2009

J Fusion Energ

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A Preconditioned Minimal Residual Solver for a Class of Linear Operator Equations

Awono

Tagoudjeu

2010

Comput. Methods Appl. Math.

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We consider the class of linear operator equations with operators admitting self-adjoint positive definite and m-accretive splitting (SAS). This splitting leads to an ADI-like iterative method which is equivalent to a fixed point problem where the operator is a 2 by 2 matrix of operators. An infinite dimensional adaptation of a minimal residual algorithm with Symmetric Gauss-Seidel and polynomial preconditioning is then applied to solve the resulting matrix operator equation. Theoretical analysis shows the convergence of the methods, and upper bounds for the decrease rate of the residual are derived. The convergence of the methods is numerically illustrated with the example of the neutron transport problem in 2-D geometry.

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Polynomial preconditioning and the Generalized Minimal Residual algorithm solver for the 2-D Boltzmann transport equation

Cited by 3 publications

References 4 publications

Theoretical and numerical analysis of the Minimal Residual Method for solving the neutron transport equation in spherical geometry

Theoretical and numerical analysis of the Minimal Residual Method for solving the neutron transport equation in spherical geometry

Iterative Methods for Solving the Neutron Transport Equation in 1-D Spherical Geometry

A Preconditioned Minimal Residual Solver for a Class of Linear Operator Equations

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