# Preconditioning and Two-Level Multigrid Methods of Arbitrary Degree of Approximation By

@inproceedings{Axelsson2010PreconditioningAT, title={Preconditioning and Two-Level Multigrid Methods of Arbitrary Degree of Approximation By}, author={Owe Axelsson and Ivar Gustafsson}, year={2010} }

- Published 2010

Let A be a mesh parameter corresponding to a finite element mesh for an elliptic problem. We describe preconditioning methods for two-level meshes which, for most problems solved in practice, behave as methods of optimal order in both storage and computational complexity. Namely, per mesh point, these numbers are bounded above by relatively small constants for all h > h0, where h0 is small enough to cover all but excessively fine meshes. We note that, in practice, multigrid methods are actually… CONTINUE READING

#### Citations

##### Publications citing this paper.

Showing 1-10 of 31 extracted citations

## Algebraic Multilevel Preconditioning in Isogeometric Analysis : Construction and Numerical Studies

View 10 Excerpts

Method Support

Highly Influenced

## Tomar Algebraic Multilevel Preconditioning in Isogeometric Analysis : Construction and Numerical Studies

View 10 Excerpts

Method Support

Highly Influenced

## Algebraic multilevel preconditioning in three-dimensional H ( div ) space S

View 6 Excerpts

Highly Influenced

## On parallel solution of linear elasticity problems. Part III: higher order finite elements

View 9 Excerpts

Method Support

Highly Influenced

## Robust algebraic multilevel preconditioning in H(curl) and H(div)

View 4 Excerpts

Highly Influenced

## An efficient hierarchical preconditioner for quadratic discretizations of finite element problems

View 5 Excerpts

Method Support

Highly Influenced

## Algebraic multilevel preconditioning in H(Ω, curl)

View 4 Excerpts

Highly Influenced

## ALGEBRAIC MULTILEVEL PRECONDITIONING IN HpΩ, curl q

View 4 Excerpts

Highly Influenced

## Isogeometric Analysis: Condition Number Estimates and Fast Solvers

View 3 Excerpts

Method Support

Highly Influenced

## HYBRID F-CYCLE ALGEBRAIC MULTILEVEL PRECONDITIONERS

View 5 Excerpts

Method Support

Highly Influenced

#### Citation Statistics

#### 102 Citations

Citations per Year

Semantic Scholar estimates that this publication has

**102**citations based on the available data.See our **FAQ** for additional information.

#### References

##### Publications referenced by this paper.

Showing 1-9 of 9 references

## Analysis of a Two-Level Scheme for Solving Finite Element Equations, Report CNA-159, Center for Numerical Analysis, The University of Texas

View 5 Excerpts

Highly Influenced

## Introduction to multigrid methods," Colloquium Numerical Solution of Partial Differential Equations

View 2 Excerpts

## Stability and Rate of Convergence of Modified Incomplete Cholesky Factorization Methods, Thesis, Report 79.02R

View 2 Excerpts

## The incomplete Cholesky conjugate gradient method for the iterative solution of systems of linear equations,

View 1 Excerpt