Improvement of the rate of convergence estimates for multigrid algorithm

Tavakoli, Ali; Kerayechian, Asghar

doi:10.1016/j.amc.2006.09.128

Cited by 2 publications

(2 citation statements)

References 7 publications

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“…Nevertheless, the main defect of iterative methods is that these will work very well in a few iterations, but after that these methods will be converged slowly. Multi-grid algorithms will solve this problem (Bramble and Pasciak, 1987;Tavakoli and Kerayechian, 2007;Tavakoli, 2010). Multi-grid methods are the fastest known methods for the solution of the large systems of equations arising from the discretisation of partial differential equations (for more details see Bramble, 1993).…”

Section: Introductionmentioning

confidence: 99%

Multi-grid Beam and Warming scheme for the simulation of unsteady flow in an open channel

Rahimpour

Tavakoli

2011

WSA

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In this paper, a multi-grid algorithm is applied to a large-scale block matrix that is produced from a Beam and Warming scheme. The Beam and Warming scheme is used in the simulation of unsteady flow in an open channel. The Gauss-Seidel block-wise iteration method is used for a smoothing process with a few iterations. It is also shown that the governing equations determine the type of prolongation and restriction operators for the multi-grid algorithm.

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Section: Introductionmentioning

confidence: 99%

Multi-grid Beam and Warming scheme for the simulation of unsteady flow in an open channel

Rahimpour

Tavakoli

2011

WSA

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“…Various convergence proofs for multigrid algorithms has been widely presented so far ( [2,5]). Attempts has been accomplished for improvement of convergence rates ( [4,11]). However, less work has been done on the convergence of multigrid algorithms including an artificial damping.…”

Section: Introductionmentioning

confidence: 99%

Convergence of multigrid algorithms incorporating an artificial damping

Tavakoli¹,

Kerayechian²

2007

imf

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When the solution and coefficients in a problem are highly oscillatory, there exists sometimes a glaring difference between solution and physical results. This occurrence can be arisen by the fact that the coarse grid problem is still huge and poorly-conditioned. In this case, one way for solving such problems is to apply an artificial damping in multigrid algorithm. In [9], a multigrid algorithm incorporating an artificial damping has been used for solving a model problem, but the convergence proof has not been presented. In this paper, a multigrid algorithm is presented and the convergence of the algorithm is proved for a general problem.

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Improvement of the rate of convergence estimates for multigrid algorithm

Cited by 2 publications

References 7 publications

Multi-grid Beam and Warming scheme for the simulation of unsteady flow in an open channel

Multi-grid Beam and Warming scheme for the simulation of unsteady flow in an open channel

Convergence of multigrid algorithms incorporating an artificial damping

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