On the preconditioned sor method

Usui, Masataka; Kohno, Toshiyuki; Niki, Hiroshi

doi:10.1080/00207169508804459

Cited by 8 publications

(4 citation statements)

References 8 publications

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“…Further, Usui et al [5] reported that the preconditioned SOR iterative method using I ϩ F is effective in the number of iterations compared with the SOR iterative method.…”

Section: Preconditioned Iterative Methodsmentioning

confidence: 98%

A study on preconditioning iterative methods and relativity of pressure in the numerical calculation of fluid flow

Hirano¹,

Yoshida²,

Ozoe³

et al. 2004

Numerical Methods Partial

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This article presents the effect of preconditioning iterative methods on boundary conditions of the pressure-correction in the numerical computation of fluid flow with known velocity components on all boundaries using the SIMPLE algorithm. In such computation, a set of solutions of the pressure-correction is indefinite, because only the Neumann condition is imposed on all boundaries. However, solutions become unique if the value of pressure-correction is fixed at least on one boundary point, and the Dirichlet condition is additionally imposed. Though both conditions must give exactly the same velocity and temperature fields, this problem arises from the relativity of the pressure. The mathematical illustration for this problem is provided using the numerical computation of the natural convection in an enclosure. It is concluded that the preconditioner adopted and the condition that only the Neumann condition on all boundaries is given are effective to reduce the number of iterations in solving the linear system of equations of the pressure-correction at the computation of the natural convection.

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“…Further, Usui et al [5] reported that the preconditioned SOR iterative method using I ϩ F is effective in the number of iterations compared with the SOR iterative method.…”

Section: Preconditioned Iterative Methodsmentioning

confidence: 98%

A study on preconditioning iterative methods and relativity of pressure in the numerical calculation of fluid flow

Hirano¹,

Yoshida²,

Ozoe³

et al. 2004

Numerical Methods Partial

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“…It is investigated in [86,97] the preconditioned AOR method. For α = 1 it is proposed in [75] for the preconditioned Gauss-Seidel method and in [74,57] for the preconditioned SOR method. Denote…”

Section: 31)mentioning

confidence: 99%

On preconditioned AOR method for solving linear systems

Song¹

2020

Preprint

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In this paper, we investigate the preconditioned AOR method for solving linear systems. We study two general preconditioners and propose some lower triangular, upper triangular and combination preconditioners. For A being an L-matrix, a nonsingular M-matrix, an irreducible L-matrix and an irreducible nonsingular M-matrix, four types of comparison theorems are presented, respectively. They contain a general comparison result, a strict comparison result and two Stein-Rosenberg type comparison results. Our theorems include and are better than almost all known corresponding results.

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“…Usui, Kohno and Niki [4,5] proposed the adaptive GS method and its extension to the SOR method. In both papers some comparisons between upper bounds of the spectral radius of the iteration matrices have been obtained.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper we will present some theoretical results for the SOR method applied to the preconditioned linear system [4,5] where A = ( I + u ) A and & = (…”

Section: Introductionmentioning

confidence: 99%

Further results on the preconditioned sor method

Martins

Evans

Yousif

2001

International Journal of Computer Mathematics

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Several methods have been developed on the preconditioned iterative methods, i.e., iterative methods applied to preconditioned linear systems. Usui, Kohno and Niki [4] have proposed the adaptive Gauss-Seidel (GS) method, and the same authors [S] have presented the preconditioned SOR method. They have shown, with the aid of numerical examples, that the two methods have a better rate of convergence in comparison with the classical SOR method. In this paper we w i l l prove theoretically the improvement in the rate of convergence.

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On the preconditioned sor method

Cited by 8 publications

References 8 publications

A study on preconditioning iterative methods and relativity of pressure in the numerical calculation of fluid flow

A study on preconditioning iterative methods and relativity of pressure in the numerical calculation of fluid flow

On preconditioned AOR method for solving linear systems

Further results on the preconditioned sor method

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