Methods and Algorithms for Scientific Computing

On Local Fourier Analysis of Multigrid Methods for PDEs with Jumping and Random Coefficients


In this paper, we propose a novel nonstandard 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 predictive capability of the proposed LFA using a number of challenging benchmark problems. The information provided by this analysis could be used to estimate a priori the time needed for solving certain uncertainty quantification problems by means of a multigrid multilevel Monte Carlo method.


  1. PDEs
  2. random coefficients
  3. multigrid
  4. local Fourier analysis
  5. multilevel Monte Carlo
  6. uncertainty quantification

MSC codes

  1. 65F10
  2. 65M22
  3. 65M55

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Information & Authors


Published In

cover image SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Pages: A1385 - A1413
ISSN (online): 1095-7197


Submitted: 5 March 2018
Accepted: 19 March 2019
Published online: 2 May 2019


  1. PDEs
  2. random coefficients
  3. multigrid
  4. local Fourier analysis
  5. multilevel Monte Carlo
  6. uncertainty quantification

MSC codes

  1. 65F10
  2. 65M22
  3. 65M55



Funding Information

Diputacion General de Aragon : E24_17R
Horizon 2020 Framework Programme : 705402
Federación Española de Enfermedades Raras : MTM2016-75139-R

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