Aspects of multigrid methods for problems in three dimensions

Kettler, R.; Wesseling, Pieter

doi:10.1016/0096-3003(86)90102-5

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Introduction1

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1998

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Cited by 13 publications

(3 citation statements)

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“…As the coarse grid operators defined by (11), (12), (14), (15) are equivalent to a. finite volume discretization the following result is immediate. THEOREM 1.…”

Section: A13mentioning

confidence: 97%

See 1 more Smart Citation

A simple cell-centered multigrid method for 3D interface problems

Molenaar

1996

Computers & Mathematics with Applications

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A multigrid algorithm is presented for cell-centered discretizations of interface problems. Instead of constructing the coarse grid operators by means of the Ga.lerkin approximation, the coarse grid operators are obtained by discretiza.tion on the coarse grids. The advantage of this approach is that we obtain M-matrices on all grids, and that the sparsity pattern of the fine grid matrix is retained on a.II grids. Moreover, the coarse grid operators are very easy to construct. Numerical results of several test problems are presented.

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“…As the coarse grid operators defined by (11), (12), (14), (15) are equivalent to a. finite volume discretization the following result is immediate. THEOREM 1.…”

Section: A13mentioning

confidence: 97%

“…In the 3D case, alternating plane relaxation appears to be the only robust smoothers for problems with strong anisotropies (cf. [15]); therefore we use alternating plane Gauss-Seidel (APGS) relaxation for three-dimensional problems. The 2D probk..ns in a plane are then solved approximately by the 2D multigrid method.…”

Section: A13mentioning

confidence: 99%