The hierarchical basis multigrid method
type: Item
instance of: scholarly article
title: The hierarchical basis multigrid method
zbMATH Open document ID: 0645.65074
DOI: 10.1007/BF01462238
author: Randolph E. Bank
author: Todd F. Dupont
author: Harry Yserentant
published in: Numerische Mathematik
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/133245
review text: Based on earlier work of the third author and the PLTMG package of the first author, the authors describe, analyze and implement the mentioned method for the numerical solution of a standard self-adjoint twodimensional elliptic problem as a symmetric block Gauß-Seidel method with inner iterations (which can be rewritten in V-cycle manner). For the discretization, linear triangular elements are employed. The point is here that the triangulation may be generated (refined) adaptively: The described multigrid method does not assume that the numbers of unknowns on the different refinement levels grow geometrically to assure a work estimate per iteration of the overall unknown number since on any level only the new points are iterated. The analysis also does not require the usual strong ellipticity condition. The price for these advantages is that the number of iterations depends on the number of levels.
reviewed by: Gisbert Stoyan
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65F35
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 4052943
zbMATH Keywords: hierarchical basis multigrid method
zbMATH Keywords: finite elements
zbMATH Keywords: condition number
zbMATH Keywords: mesh refinement
zbMATH Keywords: symmetric block Gauß-Seidel method
zbMATH Keywords: inner iterations
zbMATH Keywords: V-cycle
zbMATH Keywords: linear triangular elements
MaRDI profile type: Publication
cites work: Q3323187
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cites work: Hierarchical bases give conjugate gradient type methods a multigrid speed of convergence
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description: scientific article; zbMATH DE number 4052943