Two-color fourier analysis of the multigrid method with red-black Gauss-Seidel Smoothing
Applied Mathematics and Computation
On the maximum angle condition for linear tetrahedral elements
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
Computing
On red-black SOR smoothing in multigrid
SIAM Journal on Scientific Computing - Special issue on iterative methods in numerical linear algebra; selected papers from the Colorado conference
The black box multigrid numerical homogenization algorithm
Journal of Computational Physics
A Fast Direct Solution of Poisson's Equation Using Fourier Analysis
Journal of the ACM (JACM)
Asynchronous Iterative Methods for Multiprocessors
Journal of the ACM (JACM)
A multigrid tutorial: second edition
A multigrid tutorial: second edition
A review of algebraic multigrid
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. VII: partial differential equations
Multigrid
Fourier Analysis of GMRES(m) Preconditioned by Multigrid
SIAM Journal on Scientific Computing
BoomerAMG: a parallel algebraic multigrid solver and preconditioner
Applied Numerical Mathematics - Developments and trends in iterative methods for large systems of equations—in memoriam Rüdiger Weiss
Two-Level Fourier Analysis of a Multigrid Approach for Discontinuous Galerkin Discretization
SIAM Journal on Scientific Computing
A Massively Parallel Multigrid Method for Finite Elements
Computing in Science and Engineering
Journal of Computational and Applied Mathematics
Local Fourier Analysis of Multigrid for the Curl-Curl Equation
SIAM Journal on Scientific Computing
Fourier Analysis of Multigrid Methods on Hexagonal Grids
SIAM Journal on Scientific Computing
Fourier Analysis for Multigrid Methods on Triangular Grids
SIAM Journal on Scientific Computing
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In this paper a local Fourier analysis for multigrid methods on tetrahedral grids is presented. Different smoothers for the discretization of the Laplace operator by linear finite elements on such grids are analyzed. A four-color smoother is presented as an efficient choice for regular tetrahedral grids, whereas line and plane relaxations are needed for poorly shaped tetrahedra. A novel partitioning of the Fourier space is proposed to analyze the four-color smoother. Numerical test calculations validate the theoretical predictions. A multigrid method is constructed in a block-wise form, by using different smoothers and different numbers of pre- and post-smoothing steps in each tetrahedron of the coarsest grid of the domain. Some numerical experiments are presented to illustrate the efficiency of this multigrid algorithm.