Computing and Visualization in Science

, Volume 7, Issue 3, pp 121–127

On an energy minimizing basis for algebraic multigrid methods

Regular article

DOI: 10.1007/s00791-004-0147-y

Cite this article as:
Xu, J. & Zikatanov, L. Comput. Visual Sci. (2004) 7: 121. doi:10.1007/s00791-004-0147-y


This paper is devoted to the study of an energy minimizing basis first introduced in Wan, Chan and Smith (2000) for algebraic multigrid methods. The basis will be first obtained in an explicit and compact form in terms of certain local and global operators. The basis functions are then proved to be locally harmonic functions on each coarse grid “element”. Using these new results, it is illustrated that this basis can be numerically obtained in an optimal fashion. In addition to the intended application for algebraic multigrid method, the energy minimizing basis may also be applied for numerical homogenization.

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Department of MathematicsThe Pennsylvania State UniversityUSA

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