Algebraic Multi-grid for Discrete Elliptic Second-Order Problems

  • Ferdinand Kickinger
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 3)


This paper is devoted to the construction of Algebraic Multi-Grid (AMG) methods, which are especially suited for the solution of large sparse systems of algebraic equations arising from the finite element discretization of second-order elliptic boundary value problems on unstructured, fine meshes in two or three dimensions. The only information needed is recovered from the stiffness matrix. We present two types of coarsening algorithms based on the graph of the stiffness matrix. In some special cases of nested mesh refinement, we observe, that some geometrical version of the multi-grid method turns out to be a special case of our AMG algorithms. Finally, we apply our algorithms on two and three dimensional heat conduction problems in domains with complicated geometry (e.g. micro-scales), as well as to plane strain elasticity problems with jumping coefficients.


Coarse Grid Multigrid Method Coarse Grid Correction Large Sparse System Coarse Grid Space 
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© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Ferdinand Kickinger
    • 1
  1. 1.Institute for MathematicsJohannes Kepler University LinzAustria

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