Computing and Visualization in Science

, Volume 13, Issue 5, pp 207–220 | Cite as

A practical framework for the construction of prolongation operators for multigrid based on canonical basis functions



We discuss a general framework for the construction of prolongation operators for multigrid methods. It turns out that classical black-box prolongation or prolongation operators based on smoothed aggregation can be classified as special cases. The approach is suitable both for geometric and for purely algebraic multigrid settings. It allows for a simple and efficient implementation and parallelization by introducing canonical basis functions. We show numerical results for several diffusion problems with strongly varying or jumping coefficients. As one possible application for our method we choose three-dimensional medical image segmentation. In addition to that a nonsymmetric convection-diffusion problem is presented.


Multigrid Prolongation Matrix-dependent transfer operators Jumping coefficients Image segmentation Nonsymmetric convection-diffusion problem 


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© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Mathematical InstituteUniversity of CologneCologneGermany
  2. 2.Lehrstuhl Informatik 10 (Systemsimulation)Universität Erlangen-NurembergErlangenGermany

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