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Computing

, Volume 74, Issue 4, pp 319–335 | Cite as

Computing Interpolation Weights in AMG Based on Multilevel Schur Complements

  • J. K. KrausEmail author
Article

Abstract

This paper presents a particular construction of neighborhood matrices to be used in the computation of the interpolation weights in AMG (algebraic multigrid). The method utilizes the existence of simple interpolation matrices (piecewise constant for example) on a hierarchy of coarse spaces (grids). Then one constructs by algebraic means graded away coarse spaces for any given fine-grid neighborhood. Next, the corresponding stiffness matrix is computed on this graded away mesh, and the actual neighborhood matrix is obtained by computing the multilevel Schur complement of this matrix where degrees of freedom outside the neighborhood have to be eliminated. The paper presents algorithmic details, provides model complexity analysis as well as some comparative tests of the quality of the resulting interpolation based on the multilevel Schur complements versus element interpolation based on the true element matrices.

AMS Subject Classifications:

65F10 65N20 65N30 

Keywords

Algebraic multigrid multilevel Schur complements element-free interpolation graded away coarsening 

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Copyright information

© Springer-Verlag Wien 2004

Authors and Affiliations

  1. 1.Johann-Radon-Institute for Computational and Applied MathematicsAustrian Academy of SciencesLinzAustria

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