On the Utilization of Edge Matrices in Algebraic Multigrid

  • J. K. Kraus
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3743)


We are interested in the design of efficient algebraic multigrid (AMG) methods for the solution of large sparse systems of linear equations arising from finite element (FE) discretization of second-order elliptic partial differential equations (PDEs). In particular, we introduce the concept of so-called “edge matrices”, which–in the present context–are extracted from the individual element matrices. This allows for the construction of spectrally equivalent approximations of the original stiffness matrix that can be utilized in the framework of AMG.

The edge matrices give rise to modify the definition of “strong” and “weak” connections (edges), which provides a basis for selecting the coarse-grid nodes in algebraic multigrid methods. Moreover, a reproduction of edge matrices on coarse levels offers the opportunity to combine classical coarsening algorithms with effective (energy minimizing) interpolation principles involving small-sized “computational molecules” (small collections of edge matrices). This yields a flexible and robust new variant of AMG, which we refer to as AMGm.


Element Matrice Algebraic Multigrid Method Spectral Condition Number Large Sparse System Edge Matrix 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • J. K. Kraus
    • 1
  1. 1.Johann Radon Institute for Computational and Applied MathematicsLinzAustria

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