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Abstract
This paper is concerned with the convergence behaviour of multigrid methods for two dimensional discrete convectiondiffusion equations. In Elman and Ramage (BIT 46:283299, 2006), we showed that for constant coefficient problems with gridaligned flow and semiperiodic boundary conditions, the twogrid iteration matrix can be reduced via a set of orthogonal transformations to a matrix containing individual 4 × 4 blocks, enabling a trivial computation of the norm of the iteration matrix. Here we use a similar Fourier analysis technique to investigate the individual contributions from the smoothing and approximation property matrices which form the basis of many standard multigrid analyses. As well as the theoretical results in the semiperiodic case, we present numerical results for a corresponding Dirichlet problem and examine the correlation between the two cases.
Original language  English 

Pages (fromto)  4356 
Number of pages  14 
Journal  Computing and Visualization in Science 
Volume  10 
Issue number  1 
DOIs  
Publication status  Published  1 Mar 2007 
Keywords
 diffusion equation
 Dirichlet problem
 coarse grid
 mutligrid method
 iteration matrix
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Dive into the research topics of 'Some observations on multigrid convergence for convectiondiffusion equations'. Together they form a unique fingerprint.Projects
 1 Finished

Research visit to University of Maryland
Ramage, A. & Elman, H.
10/07/23 → 11/07/23
Project: Research Conference / Short Visit  attendance