Improved spectral multigrid methods for periodic elliptic problems
type: Item
instance of: scholarly article
title: Improved spectral multigrid methods for periodic elliptic problems
zbMATH Open document ID: 0569.65084
DOI: 10.1016/0021-9991(85)90159-7
author: Achi Brandt
author: Scott R. Fulton
author: G. D. (Jerry) Taylor
published in: Journal of Computational Physics
publication date: 1985-01-01T00:00:00Z
review text: The authors introduce for the periodic case some refinements which can substantially improve the overall efficiency of the spectral multigrid method. It is shown that by evaluating the fluxes at the midpoints between the usual collocation points a ''midpoint'' pseudospectral discretization is obtained which eliminates the need for filtering the highest modes, resulting in improved accuracy and efficiency. For the isotropic case a weighted residual relaxation scheme with a greatly improved smoothing rate is introduced and it is shown that by property scaling the relaxation parameters, the smoothing rates obtained for constant coefficient problems also hold even when the coefficients are not constant. Some comparisons of choices for coarse grid operators and residual transfers are also made. The authors introduce another relaxation scheme, based on defect corrections, which is efficient even for highly anisotropic problems. Numerical results are given.
Mathematics Subject Classification ID: 65N35
Mathematics Subject Classification ID: 65N50
Mathematics Subject Classification ID: 35B10
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 3909688
zbMATH Keywords: midpoint pseudospectral discretization
zbMATH Keywords: refinements
zbMATH Keywords: spectral multigrid method
zbMATH Keywords: collocation
zbMATH Keywords: weighted residual relaxation scheme
zbMATH Keywords: smoothing rate
zbMATH Keywords: comparisons
zbMATH Keywords: coarse grid operators
zbMATH Keywords: defect corrections
zbMATH Keywords: Numerical results
reviewed by: Karel Najzar
MaRDI profile type: Publication
full work available at URL: 0021-9991(85)90159-7
OpenAlex ID: W2036428428
cites work: Spectral Calculations of One-Dimensional Inviscid Compressible Flows
cites work: Spectral methods for problems in complex geometries
cites work: Spectral multigrid methods for elliptic equations
cites work: Spectral multigrid methods for elliptic equations. II
cites work: Multi-Level Adaptive Solutions to Boundary-Value Problems
cites work: Uniform rational approximation of functions of several variables
cites work: Spectral methods for multi-dimensional diffusion problems
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description: scientific article; zbMATH DE number 3909688