A survey of Fourier smoothing analysis results

Wesseling, Pieter

doi:10.1007/978-3-0348-5712-3_7

Cited by 15 publications

(2 citation statements)

References 38 publications

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“…To this end, we perform Fourier analysis to gain an idea of the behavior of several basic iterative methods with FOCS. Our methodology and notations are similar to those used by Kettler [17] and Wesseling [18]. A detailed treatment of Fourier analysis of iterative methods for elliptic problems can be found in Chan and Elman [19].…”

Section: A Fourier Analysismentioning

confidence: 99%

On convergence and performance of iterative methods with fourth-order compact schemes

Zhang

1998

Numer. Methods Partial Differential Eq.

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We study the convergence and performance of iterative methods with the fourth-order compact discretization schemes for the one-and two-dimensional convection-diffusion equations. For the one-dimensional problem, we investigate the symmetrizability of the coefficient matrix and derive an analytical formula for the spectral radius of the point Jacobi iteration matrix. For the two-dimensional problem, we conduct Fourier analysis to determine the error reduction factors of several basic iterative methods and comment on their potential use as the smoothers for the multilevel methods. Finally, we perform numerical experiments to verify our Fourier analysis results.

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Section: A Fourier Analysismentioning

confidence: 99%

On convergence and performance of iterative methods with fourth-order compact schemes

Zhang

1998

Numer. Methods Partial Differential Eq.

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“…In order to take badly scaled variable coefficients into account, we use diagonal scaling [10]. [27], [11], [26]. The MGMF preconditioner on uniform and quasi-uniform grids can be analyzed using the same finite element analysis framework used in [6], although we will not pursue that in this paper.…”

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confidence: 99%

Multilevel Filtering Preconditioners: Extensions to More General Elliptic Problems

Tong¹,

Chan²,

Kuo³

1992

SIAM J. Sci. and Stat. Comput.

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Abstract. The concept of multilevel filtering (MF) preconditioning applied to second-order selfadjoint elliptic problems is briefly reviewed. It is then shown how to effectively apply this concept to other elliptic problems such as the second-order anisotropic problem, biharmonic equation, equations on locally refined grids and interface operators arising from domain decomposition methods.Numerical results are given to show the effectiveness of the MF preconditioners on these problems.

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