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arXiv · 1803.08864

On local Fourier analysis of multigrid methods for PDEs with jumping and random coefficients

Prashant Kumar·Carmen Rodrigo·Francisco J. Gaspar·Cornelis W. Oosterlee
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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.

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Prashant Kumar, Carmen Rodrigo, Francisco J. Gaspar, Cornelis W. Oosterlee. 2018-03-14. On local Fourier analysis of multigrid methods for PDEs with jumping and random coefficients. https://arxiv.org/abs/1803.08864

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