In this talk we combine the element agglomeration AMGe (from [2]) and the adaptive AMG (from [1]). The former method is used to generate an initial V-cycle that coarsens only the nullspace of the respective H(div) or H(curl) form, whereas the second method is used to gradually augment the current coarse grids and interpolation matrices. The numerical tests indicate that 3 to 5 adaptive cycles are sufficient in order to achieve an efficient AMG solver. A main tool in the adaptation process is the hierarchical construction of the modified interpolation matrices, see [3], which is based on solving local constrained minimization problems, fitting one "algebraically smooth" vector at a time.

[1] M. Brezina, R. Falgout, S. MacLachlan, T. Manteuffel, S. McCormick, and J. Ruge, "Adaptive Algebraic Multigrid Methods," SIAM J. Sci. Comp., 2004, submitted.
[2] J. Jones and P. Vassilevski, "AMGe Based on Element Agglomerations," SIAM J. Sci. Comp., 23(2001), pp. 109-133.
[3] P. Vassilevski and L. Zikatanov "Multiple Vector Preserving Interpolation Mappings in Algebraic Multigrid," Lawrence Livermore National Laboratory Technical Report UCRL-JRNL-208036, November 2004.