Tuning Multigrid Methods with Robust Optimization and Local Fourier Analysis

2021 ◽  
Vol 43 (1) ◽  
pp. A109-A138
Author(s):  
Jed Brown ◽  
Yunhui He ◽  
Scott MacLachlan ◽  
Matt Menickelly ◽  
Stefan M. Wild
Keyword(s):  
Fourier Analysis ◽  
Robust Optimization ◽  
Multigrid Methods ◽  
Local Fourier Analysis

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

2019 ◽  
Vol 41 (3) ◽  
pp. A1385-A1413 ◽  
Author(s):  
Prashant Kumar ◽  
Carmen Rodrigo ◽  
Francisco J. Gaspar ◽  
Cornelis W. Oosterlee
Keyword(s):  
Fourier Analysis ◽  
Multigrid Methods ◽  
Random Coefficients ◽  
Local Fourier Analysis

scholarly journals Local Fourier Analysis of Multigrid Methods with Polynomial Smoothers and Aggressive Coarsening

2015 ◽  
Vol 8 (1) ◽  
pp. 1-21 ◽  
Author(s):  
James Brannick ◽  
Xiaozhe Hu ◽  
Carmen Rodrigo ◽  
Ludmil Zikatanov
Keyword(s):  
Finite Difference ◽  
Fourier Analysis ◽  
Multigrid Methods ◽  
Structured Grids ◽  
Numerical Tests ◽  
Local Fourier Analysis ◽  
Spatial Dimensions ◽  
Optimal Values ◽  
Element Discretizations ◽  
Theoretical Results

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 determineautomaticallythe 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.

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