Convergence estimates for multigrid algorithms

To estimate convergence of the multigrid algorithms, we need some assumptions on smoothers. The assumptions for typical smoothers are well analyzed in the multigrid literature [1,2]. However, numerical evidence shows that Kaczmarz smoother does not satisfy above assumptions. Thus, we introduce a wea...

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Vydané v:Computers & mathematics with applications (1987) Ročník 34; číslo 9; s. 15 - 22
Hlavní autori: Kang, K.S., Kwak, D.Y.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Elsevier Ltd 01.11.1997
Predmet:
Kaczmarz smoothing
Multigrid method
Smoothing assumptions
Multigrid method
Smoothing assumptions
Kaczmarz smoothing
ISSN:0898-1221, 1873-7668
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Shrnutí:To estimate convergence of the multigrid algorithms, we need some assumptions on smoothers. The assumptions for typical smoothers are well analyzed in the multigrid literature [1,2]. However, numerical evidence shows that Kaczmarz smoother does not satisfy above assumptions. Thus, we introduce a weaker condition which is satisfied by Kaczmarz smoother as well as Jacobi and Gauss-Seidel smoother. Under these weaker assumptions, we show that the convergence factor of V-cycle multigrid algorithm is δ = 1 − 1 (C(j − 1)) . assumptions for Kaczmarz smoother are verified by numerical experiment.
ISSN:0898-1221
1873-7668
DOI:10.1016/S0898-1221(97)00185-5