Local Fourier Analysis of Multigrid Methods with Polynomial Smoothers and Aggressive coarsening
Abstract
We focus on the study of multigrid methods with aggressive coarsening and polynomial smoothers for the solution of the linear systems corresponding to finite difference/element discretizations of the Laplace equation. Using local Fourier analysis we determine automatically the optimal values for the parameters involved in defining the polynomial smoothers and achieve fast convergence of cycles with aggressive coarsening. We also present numerical tests supporting the theoretical results and the heuristic ideas. The methods we introduce are highly parallelizable and efficient multigrid algorithms on structured and semi-structured grids in two and three spatial dimensions.
Keywords
Cite
@article{arxiv.1310.8385,
title = {Local Fourier Analysis of Multigrid Methods with Polynomial Smoothers and Aggressive coarsening},
author = {James Brannick and Xiaozhe Hu and Carmen Rodrigo and Ludmil Zikatanov},
journal= {arXiv preprint arXiv:1310.8385},
year = {2014}
}
Comments
Submitted to the special issue of "Numerical Mathematics Theory, Methods and Applications" for Weizmann Workshop of Numerical Mathematics: Theory, Methods and Applications