On local Fourier analysis of multigrid methods for PDEs with jumping and random coefficients
Abstract
In this paper, we propose a novel non-standard Local Fourier Analysis (LFA) variant for accurately predicting the multigrid convergence of problems with random and jumping coefficients. This LFA method is based on a specific basis of the Fourier space rather than the commonly used Fourier modes. To show the utility of this analysis, we consider, as an example, a simple cell-centered multigrid method for solving a steady-state single phase flow problem in a random porous medium. We successfully demonstrate the prediction capability of the proposed LFA using a number of challenging benchmark problems. The information provided by this analysis helps us to estimate a-priori the time needed for solving certain uncertainty quantification problems by means of a multigrid multilevel Monte Carlo method.
Keywords
Cite
@article{arxiv.1803.08864,
title = {On local Fourier analysis of multigrid methods for PDEs with jumping and random coefficients},
author = {Prashant Kumar and Carmen Rodrigo and Francisco J. Gaspar and Cornelis W. Oosterlee},
journal= {arXiv preprint arXiv:1803.08864},
year = {2019}
}