Download:
|
by James H. Bramble, Xuejun Zhang
Math. Comp
http://www.math.tamu.edu/~bramble/psfiles/anis.ps
Add To MetaCart
Abstract:
In this paper, we consider the linear systems arising from the standard finite element discretizations of certain second order anisotropic problems. We study the performance of a V-cycle multigrid method applied to the finite element equations. Since the usual "regularity and approximation " assumption does not hold for the anisotropic finite element problems, the standard multigrid convergence theory cannot be applied directly. In this paper, a modification of the theory of Braess and Hackbusch will be presented. We show that the V-cycle multigrid iteration with a line smoother is a uniform contraction in the energy norm. In the verification of the hypotheses in our theory, we use a weighted L
Citations
|
266
|
Iterative methods by space decomposition and subspace correction
– Xu
- 1992
|
|
98
|
On the angle condition in the finite element method
– Babuska, Aziz
- 1976
|
|
90
|
Convergence estimates for multigrid algorithms without regularity assumptions
– Bramble, Pasciak, et al.
- 1991
|
|
62
|
Old and new convergence proofs for multigrid methods
– YSERENTANT
- 1993
|
|
43
|
A new convergence proof for the multigrid method including the V -cycle
– Braess, Hackbusch
- 1983
|
|
39
|
On the robustness of ILU smoothing
– Wittum
- 1989
|
|
36
|
New estimates for multilevel algorithms including the V-cycle
– Bramble, E
- 1993
|
|
29
|
New convergence estimates for multigrid algorithms
– Bramble, Pasciak
- 1987
|
|
14
|
Variational multigrid theory, Multigrid Methods
– Mandel, McCormick, et al.
- 1987
|
|
12
|
Robustness of the additive and multiplicative frequency decomposition multilevel method
– Stevenson
- 1995
|
|
8
|
Tensor-product-type subspace splittings and multilevel iterative methods for anisotropic problems
– Griebel, Oswald
- 1995
|
|
8
|
Robustness of multi-grid applied to anisotropic equations on convex domains with reentrant corners
– Stevenson
- 1993
|
|
7
|
V-Cycle Convergence with Unsymmetric Smoothers and Application to an Anisotropic Model Problem
– Neuss
- 1998
|
|
6
|
Multigrid methods for problems with a small parameter in the highest derivative
– Hemker
- 1984
|
|
6
|
Linear iterations as smoothers in multigrid methods: theory with applications to incomplete decompositions
– Wittum
- 1989
|
|
3
|
New Estimates of the Contraction Number of V-cycle Multi-Grid with Applications to Anisotropic Equations
– Stevenson
- 1993
|
|
3
|
Uniform convergence estimates for multigrid V-cycle algorithms with less than full elliptic regularity
– Bramble, Pasciak
- 1994
|
|
3
|
Robust Multi-grid with 7-point ILU Smoothing
– Stevenson
- 1994
|
|
2
|
estimates for multilevel algorithms including the V-cycle
– New
- 1993
|
|
2
|
convergence estimates for multigrid V-cycle algorithms with less than full elliptic regularity, Domain Decomposition Methods in Science and Engineering
– Uniform
- 1994
|
|
2
|
Multi-Grid Methods and Applications, Springer series in computational mathematics
– Hackbusch
- 1985
|
|
1
|
of multi-grid applied to anisotropic equations on convex domains and domains with re-entrant corners
– Robustness
|
|
1
|
ILU as a smoother, Numer
– Modified
- 1994
|
|
1
|
multi-grid with 7-point ILU smoothing, Multigrid Methods
– Robust
- 1994
|
|
1
|
of the additive and multiplicative frequency decomposition multi-level method, Computing 54
– Robustness
- 1995
|
|
1
|
Multi-Grid Methods and Applications, vol. 4 of Springer series in computational mathematics
– Hackbusch
- 1985
|
|
1
|
Modified ILU as a smoother
– Stevenson
- 1994
|
