## Algebraic Multigrid Preconditioners on Hierarchical Triangular Grids Based on Trisection

- Yu. R. Hakopian, A. Ranjbar
- 2011

2 Excerpts

- Published 1994

Multilevel preconditioning methods for finite element matrices for the approximation of second-order elliptic problems are considered. Using perturbations of the local finite element matrices by zero-order terms it is shown that one can control the smallest eigenvalues. In this way in a multilevel method one can reach a final coarse mesh, where the remaining problem to be solved has a condition number independent of the total degrees of freedom, much earlier than if no perturbations were used. Hence, there is no need in a method of optimal computational complexity to carry out the recursion in the multilevel method to a coarse mesh with a fixed number of degrees of freedom.

@inproceedings{Axelsson1994MultilevelPF,
title={Multilevel preconditioning for perturbed finite element matrices},
author={Owe Axelsson and Yu. R. HAKOPIAN},
year={1994}
}