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Nearly optimal convergence result for multigrid with aggressive coarsening and polynomial smoothing

Petr Vaněk, Marian Brezina (2013)

Applications of Mathematics

We analyze a general multigrid method with aggressive coarsening and polynomial smoothing. We use a special polynomial smoother that originates in the context of the smoothed aggregation method. Assuming the degree of the smoothing polynomial is, on each level k , at least C h k + 1 / h k , we prove a convergence result independent of h k + 1 / h k . The suggested smoother is cheaper than the overlapping Schwarz method that allows to prove the same result. Moreover, unlike in the case of the overlapping Schwarz method, analysis...

Nonconforming Galerkin methods based on quadrilateral elements for second order elliptic problems

Jim Douglas Jr., Juan E. Santos, Dongwoo Sheen, Xiu Ye (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Low-order nonconforming Galerkin methods will be analyzed for second-order elliptic equations subjected to Robin, Dirichlet, or Neumann boundary conditions. Both simplicial and rectangular elements will be considered in two and three dimensions. The simplicial elements will be based on P1, as for conforming elements; however, it is necessary to introduce new elements in the rectangular case. Optimal order error estimates are demonstrated in all cases with respect to a broken norm in H1(Ω)...

Numerical study of two sparse AMG-methods

Janne Martikainen (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

A sparse algebraic multigrid method is studied as a cheap and accurate way to compute approximations of Schur complements of matrices arising from the discretization of some symmetric and positive definite partial differential operators. The construction of such a multigrid is discussed and numerical experiments are used to verify the properties of the method.

Numerical Study of Two Sparse AMG-methods

Janne Martikainen (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

A sparse algebraic multigrid method is studied as a cheap and accurate way to compute approximations of Schur complements of matrices arising from the discretization of some symmetric and positive definite partial differential operators. The construction of such a multigrid is discussed and numerical experiments are used to verify the properties of the method.

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