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Graph-Based Algebraic Multigrid for Lagrange-Type Finite Elements on Simplicial Meshes

Please always quote using this URN: urn:nbn:de:0297-zib-4100
  • We present an algebraic multigrid preconditioner which uses only the graphs of system matrices. Some elementary coarsening rules are stated, from which an advancing front algorithm for the selection of coarse grid nodes is derived. This technique can be applied to linear Lagrange-type finite element discretizations; for higher-order elements an extension of the multigrid algorithm is provided. Both two- and three-dimensional second order elliptic problems can be handled. Numerical experiments show that the resulting convergence acceleration is comparable to classical geometric multigrid.

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Metadaten
Author:Rudolf Beck
Document Type:ZIB-Report
Tag:Algebraic multigrid; mesh coarsening; preconditioning
MSC-Classification:65-XX NUMERICAL ANALYSIS
65-XX NUMERICAL ANALYSIS / 65Fxx Numerical linear algebra / 65F10 Iterative methods for linear systems [See also 65N22]
65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N55 Multigrid methods; domain decomposition
Date of first Publication:1999/07/21
Series (Serial Number):ZIB-Report (SC-99-22)
ZIB-Reportnumber:SC-99-22
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