A study of some multigrid ideas
type: Item
instance of: scholarly article
title: A study of some multigrid ideas
zbMATH Open document ID: 0608.65050
DOI: 10.1016/0096-3003(85)90025-6
author: David Kamowitz
author: Seymour V. Parter
published in: Applied Mathematics and Computation
publication date: 1985-01-01T00:00:00Z
full work available at URL: http://digital.library.wisc.edu/1793/58528
review text: This paper studies some questions related to the multigrid approach to the solution of elliptic partial differential equations. In order to standardize and simplify matters, a model problem \(-(pu')'+bu'+qu=0\), \(u(0)=u(1)=0\) is considered throughout. In terms of this two-point boundary value problem, estimates are made of the quality of the method for various choices that are available. In particular, if m Jacobi iterations with damping parameter a are used in the ''smoothing'' steps of the method, then a rate of convergence can be analysed for this choice. In the two-grid case this rate can be found exactly and in the general multigrid case, an upper bound can be found. The theoretical conclusions are complemented by numerical investigations for a number of special choices within the model problem.
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 65N22
Mathematics Subject Classification ID: 34B05
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 65L50
zbMATH DE Number: 3984488
zbMATH Keywords: multigrid
zbMATH Keywords: finite-difference
zbMATH Keywords: interpolation operator
zbMATH Keywords: projection operator
zbMATH Keywords: smoothing operator
zbMATH Keywords: Jacobi iterations
zbMATH Keywords: convergence rates
zbMATH Keywords: numerical examples
MaRDI profile type: Publication
OpenAlex ID: W2071458353
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description: scientific article; zbMATH DE number 3984488