59
Views
17
CrossRef citations to date
0
Altmetric
Original Articles

Algebraic multigrid methods based on element preconditioning

, , &
Pages 575-598 | Received 20 Sep 2000, Published online: 10 Jun 2010
 

Abstract

This paper presents a new algebraic multigrid (AMG) solution strategy for large linear systems with a sparse matrix arising from a finite element discretization of some self-adjoint, second order, scalar, elliptic partial differential equation. The AMG solver is based on Ruge/Stübens method. Ruge/Stübens algorithm is robust for M-matrices, but unfortunately the “region of robustness“ between symmetric positive definite M-matrices and general symmetric positive definite matrices is very fuzzy.

For this reason the so-called element preconditioning technique is introduced in this paper. This technique aims at the construction of an M-matrix that is spectrally equivalent to the original stiffness matrix. This is done by solving small restricted optimization problems. AMG applied to the spectrally equivalent M-matrix instead of the original stiffness matrix is then used as a preconditioner in the conjugate gradient method for solving the original problem.

The numerical experiments show the efficiency and the robustness of the new preconditioning method for a wide class of problems including problems with anisotropic elements.

AMS Subject Classifications:

C.R. Categories:

*This work has been supported by the Austrian Science Fund under the grand Fonds zur Förderung der wissenschaftlichen Forschung (FWF) - under the project SFB FOI3 Numerical and Symbolic Scientific Computing

[email protected]

[email protected]

§ [email protected]

*This work has been supported by the Austrian Science Fund under the grand Fonds zur Förderung der wissenschaftlichen Forschung (FWF) - under the project SFB FOI3 Numerical and Symbolic Scientific Computing

[email protected]

[email protected]

§ [email protected]

Notes

*This work has been supported by the Austrian Science Fund under the grand Fonds zur Förderung der wissenschaftlichen Forschung (FWF) - under the project SFB FOI3 Numerical and Symbolic Scientific Computing

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.