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

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

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)A1385-A1413
JournalSIAM Journal on Scientific Computing
Volume41
Issue number3
DOIs
Publication statusPublished - 2019
Externally publishedYes

Keywords

  • Local Fourier analysis
  • Multigrid
  • Multilevel Monte Carlo
  • PDEs
  • Random coefficients
  • Uncertainty quantification

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